Measurement of the
pair production of b-jets
? in proton-proton collisions
at s = 7 TeV with the ATLAS detector
Dissertation
zur Erlangung des Grades
DOKTOR DER NATURWISSENSCHAFTEN
am Fachbereich Physik
der Johannes Gutenberg-Universität
in Mainz
von
Andrea Neusiedl
geboren in Kaiserslautern
Mainz, den 21.Mai 2012
Tag der Prüfung: 19.11.2012
Kurzfassung
In hadronischen Kollisionen entstehen bei einem Großteil der Ereignisse mit einem hohen
Impulsübertrag Paare aus hochenergetischen Jets. Deren Produktion und Eigenschaften
können mit hoher Genauigkeit durch die Störungstheorie in der Quantenchromodynamik
(QCD) vorhergesagt werden. Die Produktion von bottom-Quarks in solchen Kollisionen
kann als Maßstab genutzt werden, um die Vorhersagen der QCD zu testen, da diese
Quarks die Dynamik des Produktionsprozesses bei Skalen wieder spiegelt, in der eine
Störungsrechnung ohne Einschränkungen möglich ist. Auf Grund der hohen Masse von
Teilchen, die ein bottom-Quark enthalten, erhält der gemessene, hadronische Zustand
den größten Teil der Information von dem Produktionsprozess der Quarks. Weil sie eine
große Produktionsrate besitzen, spielen sie und ihre Zerfallsprodukte eine wichtige Rolle
als Untergrund in vielen Analysen, insbesondere in Suchen nach neuer Physik. In ihrer
herausragenden Stellung in der dritten Quark-Generation könnten sich vermehrt Zeichen im
Vergleich zu den leichteren Quarks für neue Phänomene zeigen. Daher ist die Untersuchung
des Verhältnisses zwischen der Produktion von Jets, die solche bottom-Quarks enthalten,
auch bekannt als b-Jets, und aller nachgewiesener Jets ein wichtiger Indikator für neue
massive Objekte. In dieser Arbeit werden die Produktionsrate und die Korrelationen von
Paaren aus b-Jets bestimmt und nach ersten Hinweisen eines neuen massiven Teilchens,
das bisher nicht im Standard-Modell enthalten ist, in dem invarianten Massenspektrum der
b-Jets gesucht. Am Large Hadr?on Collider (LHC) kollidieren zwei Protonenstrahlen bei
einer Schwerpunktsenergie von s  7 TeV, und es werden viele solcher Paare aus b-Jets
produziert. Diese Analyse benutzt die aufgezeichneten Kollisionen des ATLAS-Detektors.
Die integrierte Luminosität der verwendbaren Daten beläuft sich auf 34 pb1. b-Jets werden
mit Hilfe ihrer langen Lebensdauer und den rekonstruierten, geladenen Zerfallsprodukten
identifiziert. Für diese Analyse müssen insbesondere die Unterschiede im Verhalten von
Jets, die aus leichten Objekten wie Gluonen und leichten Quarks hervorgehen, zu diesen
b-Jets beachtet werden. Die Energieskala dieser b-Jets wird untersucht und die zusätzlichen
Unsicherheit in der Energiemessung der Jets bestimmt. Effekte bei der Jet-Rekonstruktion
im Detektor, die einzigartig für b-Jets sind, werden studiert, um letztlich diese Messung
unabhängig vom Detektor und auf Niveau der Hadronen auswerten zu können. Hiernach
wird die Messung zu Vorhersagen auf nächst-zu-führender Ordnung verglichen. Dabei stellt
sich heraus, dass die Vorhersagen in Übereinstimmung zu den aufgenommenen Daten sind.
Daraus lässt sich schließen, dass der zugrunde liegende Produktionsmechanismus auch in
diesem neu erschlossenen Energiebereich am LHC gültig ist. Jedoch werden auch erste
Hinweise auf Mängel in der Beschreibung der Eigenschaften dieser Ereignisse gefunden.
Weiterhin können keine Anhaltspunkte für eine neue Resonanz, die in Paare aus b-Jets
zerfällt, in dem invarianten Massenspektrum bis etwa 1.7 TeV gefunden werden. Für
das Auftreten einer solchen Resonanz mit einer Gauß-förmigen Massenverteilung werden
modell-unabhängige Grenzen berechnet.
i

Abstract
In hadronic collisions, a large amount of processes with large momentum transfer produce
a pair of high-pT jets. Their production rate and event properties can be predicted with
good precision using perturbative Quantum Chromodynamics (QCD). The production of
bottom-quarks in such collisions is a benchmark process in perturbative QCD because they
probe the underlying strong dynamics at a well-defined scale. Because of their large mass,
bottom-flavoured particles hold the most direct correspondence between the parton-level
production and the observed hadron level. The large pair production rate of bottom-quarks
and their corresponding decay products makes them important as background source
for many analyses including searches for new physics. Besides this, quarks of the third
generation could take an exceptional position among the quarks concerning the sensitivity
to new massive objects. Studies on the fraction of jets containing bottom-flavoured
particles, known as b-jets, relative to all-flavour jets could reveal such new phenomena. In
this thesis the production rate of and the correlation between pairs of b-jets is measured.
The invariant dijet mass spectrum is searched for indications for a new resonance in context
of physics beyond the Standard Model?. At the Large Hadron Collider (LHC) two proton
beams at a centre-of-mass energy of s  7 TeV collide, producing a large number of
such pairs of b-jets. This measurement makes use of the data recorded with the ATLAS
detector. The total integrated luminosity available for the analysis is about 34 pb1. b-jets
are identified via their long lifetime and the reconstruction of their charged decay products.
For this analysis differences between jets originating from light objects, like gluons and
light quarks, compared to jets containing bottom-flavoured objects have to be taken into
account. The jet energy scale of b-jets is established and the additional uncertainty on
the jet energy measurement is determined. Detector effects in the jet reconstruction
special to b-jets are studied in order to make the measurement independent of the detector
and to correct them to hadron level. Then the cross section measured is compared to
next-to-leading order Monte-Carlo predictions. These next-to-leading order predictions are
in agreement with ATLAS data. Consequently, the underlying production mechanism is
confirmed to also be valid in this new energy regime of the LHC. However, first indications
for deviations in the description of next-to-leading processes are discovered. Up to an
invariant dijet mass of about 1.7 TeV no evidence for a new resonance decaying into a pair
of high-pT b-jets is found. Therefore, model-independent upper limits are calculated for
signals following a Gaussian distribution with different signal widths.
iii

Für Mama.
v

Contents
1 Introduction 1
2 Theoretical introduction 3
2.1 The Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.1 The elementary particles . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.2 Electroweak interactions . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.3 Strong interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.4 Hadron-hadron interactions . . . . . . . . . . . . . . . . . . . . . . 10
2.2 Extensions of and departures from the Standard Model . . . . . . . . . . . 16
2.3 Monte-Carlo models and generators . . . . . . . . . . . . . . . . . . . . . . 17
2.3.1 Event generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3.2 Parton showers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3.3 Hadronisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3.4 The underlying event and beam remnants . . . . . . . . . . . . . . 20
2.3.5 NLO matrix element generators with shower programs . . . . . . . 21
3 Heavy flavour production 23
3.1 Bottom flavour in hadronic collisions . . . . . . . . . . . . . . . . . . . . . 23
3.1.1 Theory of bottom-quark production . . . . . . . . . . . . . . . . . . 24
3.1.2 Bottom flavour in jets . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.1.3 Bottom-quark fragmentation function . . . . . . . . . . . . . . . . . 31
3.1.4 Bottom-hadron decays . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2 History of bottom measurements and motivating measurements of bb̄ pair
production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.2.1 Past measurements of bb̄ pair production properties . . . . . . . . . 35
4 The Large Hadron Collider and the ATLAS detector 39
4.1 The Large Hadron Collider . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4.2 The machine parameters in 2010 ATLAS data . . . . . . . . . . . . . . . . 40
4.3 The ATLAS experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.3.1 The inner detector . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.3.2 The calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.3.3 The muon system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.3.4 The trigger system . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
4.3.5 Triggers for physics analyses . . . . . . . . . . . . . . . . . . . . . . 48
4.3.6 Data management . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.3.7 Detector simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.4 Monte-Carlo simulation samples . . . . . . . . . . . . . . . . . . . . . . . . 49
5 Data reconstruction in ATLAS 51
5.1 Jet reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
vii
Contents
5.1.1 Jet algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.1.2 The reconstruction of jet constituents from calorimeter cells . . . . 54
5.1.3 Jet calibration in ATLAS . . . . . . . . . . . . . . . . . . . . . . . 55
5.2 Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
5.2.1 The tracking algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.2.2 Primary vertex finding . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.2.3 Measurements of tracking performance . . . . . . . . . . . . . . . . 59
5.3 Muon reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
6 Bottom-tagging in ATLAS 65
6.1 Bottom-tagging algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
6.2 Secondary vertex tagger . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
6.3 Impact parameter tagger . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
6.4 Soft muon tagger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
7 Data and event selection 75
7.1 Data samples and quality . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
7.2 Quality criteria for jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
7.3 Trigger efficiency and usage concept . . . . . . . . . . . . . . . . . . . . . . 78
7.3.1 Trigger efficiency measurement . . . . . . . . . . . . . . . . . . . . 79
7.3.2 Concept of trigger usage . . . . . . . . . . . . . . . . . . . . . . . . 83
7.4 Event selection for cross section measurement . . . . . . . . . . . . . . . . 83
8 Object understanding and calibration 87
8.1 Jet and track properties in data and simulation . . . . . . . . . . . . . . . 87
8.1.1 Properties of inclusive jets . . . . . . . . . . . . . . . . . . . . . . . 87
8.1.2 Properties of tracks associated to jets . . . . . . . . . . . . . . . . . 90
8.1.3 Properties of b-tagged jets . . . . . . . . . . . . . . . . . . . . . . . 92
8.2 Calibration of bottom-tagging algorithms . . . . . . . . . . . . . . . . . . . 94
8.2.1 Calibrating the lifetime tagging algorithms . . . . . . . . . . . . . . 95
8.2.2 Extension of the calibration and validation . . . . . . . . . . . . . . 100
8.3 Jet energy scales and resolution . . . . . . . . . . . . . . . . . . . . . . . . 104
8.3.1 Inclusive jet energy scale uncertainties . . . . . . . . . . . . . . . . 105
8.3.2 Jet energy resolution . . . . . . . . . . . . . . . . . . . . . . . . . . 109
8.3.3 Energy scale uncertainties of jets with heavy-flavour content . . . . 113
9 The cross section measurement 129
9.1 Cross section definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
9.2 Correction factors and systematic uncertainties . . . . . . . . . . . . . . . 131
9.2.1 Event and jet cleaning selection . . . . . . . . . . . . . . . . . . . . 131
9.2.2 Trigger selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
9.2.3 b-tagging efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
9.2.4 b-tagging purity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
9.2.5 Jet energy scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
9.2.6 Unfolding correction . . . . . . . . . . . . . . . . . . . . . . . . . . 146
9.2.7 Systematics from pile-up and b-tagging algorithm . . . . . . . . . . 154
9.2.8 The cross section ratio measurement . . . . . . . . . . . . . . . . . 157
9.3 Results of the cross section measurements . . . . . . . . . . . . . . . . . . 160
viii
Contents
10 Next-to-leading order calculations 169
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
10.2 The NLO generators and predictions . . . . . . . . . . . . . . . . . . . . . 170
10.2.1 The MCFM Generator . . . . . . . . . . . . . . . . . . . . . . . . . 172
10.2.2 The MC@NLOgenerator . . . . . . . . . . . . . . . . . . . . . . . 175
10.2.3 The Powheg method . . . . . . . . . . . . . . . . . . . . . . . . . 177
10.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
11 Results of the cross section measurements 185
11.1 Dijet cross sections of b-jets . . . . . . . . . . . . . . . . . . . . . . . . . . 186
11.1.1 Cross section as a function of dijet mass . . . . . . . . . . . . . . . 186
11.1.2 Cross section as a function of ∆φ . . . . . . . . . . . . . . . . . . . 187
11.1.3 Cross section as a function of angular variable χ . . . . . . . . . . . 189
11.1.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
11.2 Ratio measurement between bb̄ dijets and inclusive dijets . . . . . . . . . . 192
12 Search for resonances in the cross section 197
12.1 Statistical method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
12.1.1 The BumpHunter method . . . . . . . . . . . . . . . . . . . . . . 198
12.1.2 Application to bb̄ dijet mass spectrum . . . . . . . . . . . . . . . . . 199
12.2 Search for an excess in the dijet mass spectrum . . . . . . . . . . . . . . . 200
12.2.1 Event selection and trigger . . . . . . . . . . . . . . . . . . . . . . . 202
12.2.2 Results on the search for resonances . . . . . . . . . . . . . . . . . . 203
12.3 Model independent limit setting . . . . . . . . . . . . . . . . . . . . . . . . 206
12.3.1 Bayesian limit on generic Gaussian signals . . . . . . . . . . . . . . 206
12.3.2 Limit on new heavy gauge boson Z 1 . . . . . . . . . . . . . . . . . . 209
13 Conclusion and outlook 215
List of acronyms 219
A Appendix: Analysis binning 223
B Appendix: Monte-Carlo samples 223
C Appendix: Data quality requirements 224
D Appendix: Jet energy calibration 226
E Appendix: Monte-Carlo comparisons 226
F Appendix: Calibration of bottom-tagging algorithms 228
G Appendix: Extension of calibration 233
H Appendix: Jet energy scale 234
I Appendix: Correction factors and systematics 238
J Appendix: Cross section measurement 253
ix
Contents
K Appendix: NLO calculation 256
L Appendix: Resonance search 256
Bibliography 259
Danksagung 267
x
1 Introduction
The study of matter and its motion has founded the discipline of physics way back in the
6th century BC. The concept of elementary particles forming all matter is very old. It
took until the end of the 19th century to discover and understand sub-atomic particles like
the electron. Thereafter the knowledge of the structure of matter increased rapidly. So did
the scattering of electrons on nucleons confirm the existence of sub-nuclear particles, the
quarks. Today physicists describe the universe with the help of these elementary particles
and the forces which govern them.
The experiments to test and reveal these smallest particles from which matter is built
of have become huge and complex in terms of design. These experiments are in general
comprised of a particle accelerator and a particle detector. Particles are brought to almost
the speed of light and two particle beams travelling in opposite directions are brought into
collision. Around the collision point, a particle detector surveys the particles emerging
from the collision.
The Large Hadron Collider (LHC), which was built at the European Organisation for
Nuclear Research (CERN) in Geneva, is the world’s largest and most powerful particle
accelerator. It has been designed to collide two proton beams at a centre-of-mass energy
of 14 TeV with very high luminosity. LHC is intended to test the current understanding
of high-energy physics and the properties of interactions at extreme energy densities. It
started regular operation in 2009. First collisions at a centre-of-mass energy at 7 TeV have
been recorded in early 2010. The operation of this accelerator has successfully continued
in 2011 and 2012.
One of the experiments, which detects the collision products, is the ATLAS experiment (A
Toroidal LHC ApparatuS). This particle detector is comprised of three main components
to measure the trajectories, the energy and specific particle types of collision products.
Quarks are charged particles with half-integral spin and are thought of as point-like
particles. There are six different types of quarks currently known and they differ in
their masses. The heavy types of these quarks are the most precisely measured objects
because they take an exceptional position among the quarks due to their large masses.
Their behaviour and consequently the behaviour of composite particles containing such
heavy quarks is significantly different from lighter types. Thus, experiments are able to
distinguish between light- and heavy-quark objects.
The second heaviest quark is called bottom-quark (b-quark). Evidence of its existence was
found in 1977 at the Fermilab for the first time. The long lifetime of composite particles
containing this quark type lets them travel a macroscopic distance before decaying (on
average 3 mm in the transverse plane at pT  50 GeV). The development and introduction
of silicon technology in particle detectors improved the identification of such decays and
in turn of particles containing the bottom-quark. In consequence of the refinements and
achievements of the experimental results, there has been also progress on the theoretical
side in order to explain the experimental outcome.
In nature any type of quark cannot exist as a free particle. In particle collisions, where
constituents of the protons scatter on each other with a large momentum transfer, only
1
1 Introduction
bound quark-systems, called hadrons, and their decay products are registered by the
detector. These particles emerging from the collision are not uniformly distributed but
collimated in narrow cones. These bundles of particles are known as jets. They are
reconstructed with the help of the particle detector and used to probe the properties
of the original proton constituent, which took part in the scatter during the collision,
and the underlying dynamic of the interaction. One impact of the heavy mass of the
bottom-quark is that there is a more direct connection between the observed quantities
and the underlying dynamics.
In this analysis, the production of bottom-quark pairs in proton-proton collisions at the
LHC is studied by identifying jets with bottom-quark content. The data used for this
study has been recorded by the ATLAS experiment in 2010. In Chapter 2 the elementary
particles and their interactions as described by the Standard Model are presented as well as
the Monte-Carlo techniques used to generate a realistic event sample of such interactions.
Chapter 3 focuses on the bottom-flavour production in hadronic collisions and closes
with an overview on the history of the bottom-quark. Chapters 4 and 5 describe the
LHC machine and running configuration, the ATLAS experiment and the reconstruction
methods used. In Chapter 6 the techniques for identifying b-jets are discussed, Chapter 7
presents the selection criteria for the measurement of the production rate of bottom-quark
pairs. Chapter 8 evaluates the main components of this measurement: the jet energy scale
and the b-tagging calibration. Chapter 9, finally, presents the cross section measurement
in data, followed by the description of the next-to-leading order predictions (Chapter 10)
which are subsequently compared to data in Chapter 11. After quantifying the agreement
between data and the current QCD theory, it is searched for hints on new phenomena
in the dijet mass spectrum. Furthermore, model independent limits are calculated for
resonance signals with a Gaussian shape. With the conclusions from this analysis and the
outlook on the LHC era Chapter 13 closes the thesis.
2
2 Theoretical introduction
2.1 The Standard Model
The Standard Model of particle physics is our current understanding of elementary particles
and all forces except gravity [1]. This theory contains all known elementary particles
which are believed to be the fundamental particles without an internal structure and is
able to describe the electroweak and strong interactions between them. Its understanding
is mainly derived from three sources of experimental information: scattering experiments,
measurements of decays and of bound states. Since the 1960s this theory has been
evolving and withstanding every experimental test. The Standard Model has become an
extraordinarily well understood foundation to describe the universe.
Despite all its success there are short-comings. The Standard Model does not incorporate
the gravitational force nor an explanation for the physics of dark energy, which is the most
accepted theory to describe our expanding universe. The remarkable difference measured
in the rotation curves of galaxies provides evidence for matter which is not seen by regular
observation methods. There are no particles known to the Standard Model which could
make up for this effect. The theory also includes some unnatural hierarchies between
couplings and masses which cannot be accommodated for in the Standard Model. Without
a doubt, our profound knowledge has to be extended by new physics with the help of the
upcoming experiments.
In the following sections the elementary particles and fundamental forces which are
described by the Standard Model are introduced. The calculation and modelling of
scattering processes of hadrons is explained and finally new physics models are discussed
briefly.
2.1.1 The elementary particles
All matter is built from spin 1 particles: six leptons (l), six quarks (q) and their antiparticles
2
(l̄, q̄). Generally, particles with spin 2n 1pn  0, 1, 2, ...q are known as fermions. The stable
2
material surrounding us consists of the lightest quarks and leptons: up-, down-quarks,
electrons and their partner neutrino. These particles and their antiparticles are the so-
called first generation. The second and third generations are heavier copies of the first
one. The force carriers of the strong (gluons g) and electroweak (Z,W and γ) interaction
have spin 1. Generally, particles with integral spin are known as bosons. All mentioned
particles are shown in Fig. 2.1. Within this thesis natural units are used, i.e. c  ~  1.
The quarks (coloured red in Fig. 2.1) carry fractional electric charges. All up-type quarks
(up (u), charm (c) and top (t)) carry charge  2 |e| and all down-type quarks (down (d),
3
strange (s) and bottom(b)) 1 |e|. The masses of the quarks increase from left to right. The
3
quark types, or flavours, are coarsely separated into light-flavour (light) quarks consisting
of u-, d- and s-quark with masses in the region of MeV and into heavy-flavour quarks
with masses in the GeV regime covering the remaining flavours. The heaviest quark is the
top-quark with a mass of 173.2 0.9 GeV [2]. Besides the electric charge all quarks carry
3
2 Theoretical introduction
a colour charge: blue, red or green.
There are two types of leptons, leptons with electric charge 1 e and neutral leptons
known as neutrinos (ν). The neutral neutrino and charged lepton of the same flavour are
paired. The masses of the charged leptons increase from left to right, as well. The tau
lepton (τ) is the heaviest lepton with a mass of 1.78 GeV [3]. In the Standard Model
the neutrinos are massless but the observation of neutrino-oscillation indicate a non-zero
mass. The measurement of the β-spectrum near its endpoint has set an upper limit on the
neutrino masses of the order of O(1 eV) [4]. The photon γ, the W- and Z-boson are the
force carriers of the electroweak interaction. The photon is massless, the other electroweak
bosons carry masses of 80.3990.023 GeV for the W -bosons and 91.18760.0021 GeV for
the Z-boson [3]. The mediators of the strong interaction are the gluons which are massless
and carry a colour charge. The yet unmentioned particle is the Higgs boson H which is
until now only predicted to exist. The Higgs boson and the Higgs field are postulated to
explain the observed mass hierarchies.
Fermions Bosons
H
  
Figure 2.1: The Standard Model of elementary particles including the predicted Higgs boson
which is to be found. Original picture taken from Ref. [5].
2.1.2 Electroweak interactions
The formalism of the electroweak interactions unites the electromagnetic and the weak
force. Compared to the strong force which is discussed in the following chapter the
electromagnetic and especially the weak force exhibit a smaller strength. Table 2.1 shows
a rough estimate of the relative force strengths evaluated for q  1 GeV. The strong
interaction as well as the electromagnetic interaction form bound states of fermions, the
weak interaction does not. It is nevertheless relevant for many decay processes in nature.
The electromagnetic interactions can be reduced to the elementary process shown in
Fig. 2.2: a charged particle, e.g. an electron, emits or absorbs a photon.1
The electromagnetic force has unlimited range due to the massless mediator (photon).
1For all Feynman-graphs the time will flow from left to right.
4
2.1 The Standard Model
Force Strength Theory Mediator
Strong 1 Chromodynamics Gluon
Electromagnetic 102 Electrodynamics Photon
Weak 106 Flavordynamics W, Z
Table 2.1: Overview on the fundamental forces in the Standard Model. Taken from Ref. [6].
γ

e e
Figure 2.2: Photon emission (or absorption).
?
The photon couples to the electric charge e and the coupling constant of each vertex is α.
In the limit of non-relativistic electron-proton scattering the Rutherford formula provides
a good description of the kinematics (neglecting spin):
dσ  e
4 1
dΩ 4m2ev
4 sin4p { q , (2.1)θ 2
where me and v are the mass and the velocity of the electron respectively. The angle θ is
called the scattering angle and represents the deflection of the electron trajectory.
In the relativistic description of electron-electron scattering (Feynman-graphs Fig. 2.3) by
Quantum Electrodynamics (QED), the fermions are described by spinors u representing
solutions of the Dirac equation, and the photon is described by a field strength tensor
and the Klein-Gordon equation for massless particles. The momentum transfer q between
the incoming electrons is given by the momentum difference of p1  p3 for the un-crossed
Feynman-graph (Fig. 2.3 left) and p1  p4 for the crossed Feynman-graph (Fig. 2.3 right)
respectively. The amplitude M1 of the?un-crossed Feynman-graph can be evaluated as
follows with the coupling co»nstant ge  4πα:
M1  p2πq4 d4qδp4qpp p4q1  p3  qqδ pp2  p4   qq
(2.2)
r p qp µq p qs igµνū p3 igeγ u p1 rūpp ν2 4qpigeγ qupp2qs .q
The amplitude M2 for the crossed Feynman-graph can be derived from M1 by exchanging
the momenta p3 Ø p4. There are four important parts in the amplitude formula: the phase
space integration, the delta distributions establishing energy and momentum conservation,
the vertex factors between the spinors of the two leptons and the photon propagator
connecting both vertices. The overall squared amplitude |M|2  |M1  M |22 includes
contributions from both Feynman-graphs and an interference term between them.
The common aspect of the weak and electromagnetic interaction is that each electromag-
netic process contains a neutral weak contribution from a Z-boson exchange. As long as the
5
2 Theoretical introduction
e, p   2 e , p4 e , p2 e , p4
γ γ
e, p 1 e , p e3 , p 1 e , p3
Figure 2.3: Electron-electron scattering.
momentum transfer of a scattering process is far below the large mass of the Z-boson, the
electromagnetic part is overwhelming. For completeness, in the Feynman-graphs in Fig. 2.3
the Z-boson has to be added to the force mediating photon γ. The amplitude for the
Z-boson exchange is calculated similar to Eq. 2.2 but with a vertex factor igZ γµpcf fV cAγ5q2
and the propagator ipgµνqµqν{pmq
2
2p q2 . The vertex factor also exhibits an important aspectq m
of the weak interaction, it adds an axial vector (γνγ5) to a vector coupling (γν) and
therefore does not conserve parity. The consequence of parity violation is that the weak
interactions distinguish between left-handed and right-handed particles. The strength of
the Z-boson’s axial and vector couplings described by cf fV and cA is particle dependent. All
fermions are affected by the weak force. Lepton-neutrino scattering confirmed (Fig. 2.4)
the existence of the Z boson. The large masses of both the charged mediators and the
neutral mediator reduce the range of the weak forces to very small distances. These weak
currents are lepton-flavour conserving (lepton number) but can change the quark flavour
and also connect quarks of different generations. Examples of such processes are shown by
the Feynman-graphs in Fig. 2.5: the neutron decay into a proton changes the d-flavour
into a u-flavour (left) and the generation transition of s- to a u-flavour (right). These
graphs are based on a simplified picture where the other quarks act as spectators. The
pure underlying quark-process-coupling to a W -boson is given by G  igW ν? W ? γ p1 γ
5q
2 2
and analogously gw  4παw. The W boson only interacts with left-handed fermions
and right-handed antifermions, described by cfV  cfA  1. The basic idea to describe
the observed generation transitions is that the weak eigenstates (d1, s1 and b1) are not
identical to the quark mass states (d, s and b) but rather linear combinations of them.
The mechanism explaining these generation transitions is written down in the so-called
CKM-matrix (Cabibbo-Kobayashi-Maskawa), which connects the weak and the mass
eigenstates via this unitary matrix:
    
 1d  Vud Vus Vub ds1   Vcd Vcs Vcb s . (2.3)
b1 Vtd Vts Vtb b
The diagonal elements describe transitions within one generation and are all nearly one.
The non-diagonal conversions, especially between first and third generation, are highly
suppressed and the suppression factor Vij alters the effective coupling as indicated in
Fig. 2.5.
The electroweak unification explains the electromagnetic and weak interactions by one
6
2.1 The Standard Model
ν ν
Z
l l
Figure 2.4: Lepton-neutrino scattering.
νe e s
u
W
d
d u s W dd s u
u u s s
Coupling: GWVud ’ ’ Coupling: GWVus
Figure 2.5: Flavor changing charged currents: within the first generation (left) and between
first and second generation (right).
single theoretical system and one single coupling given by the electric charge e. At high
energies (or small distances), both interactions are symmetric (possess the same strength)
and at low energies the symmetry between these interactions is broken due to the massive
mediator bosons of the weak processes. This is called electroweak symmetry breaking.
The success of this theory lies in the connection the electromagnetic and weak coupling
constants and in fact correctly predicts the particle-dependent Z-boson couplings. This
formalism introduces a new quantum number: the weak isospin T and its third component
T3. The electroweak unification introduces four mediating bosons: an isospin-triplet W
1
µ ,
W 2, W 3µ µ with the coupling constant g and an isospin-singlet Bµ with a different coupling
strength g1. Right-handed fermions do not interact with the W -bosons and are described as
isospin-singlets. Table 2.2 lists the new quantum number T for the multiplets of fermions.
 Multiplets of fermions T T3 z Qf  e
νe νµ ν 1τ + 01 2
2
e µ τ -1 -1
L L L 2
eR µR τR 0 0 -1
u  c  t +1 +21 2 3
d1 s1 b1
2
-1 -1
L L L 2 3
uR cR tR +
2
0 0 3
dR s b
1
R R -3
Table 2.2: Overview on weak isospin for all fermions.
The two known neutral currents (Z and γ) are described by orthogonal linear combi-
7
Quarks Leptons
2 Theoretical introduction
nations of W 3µ and Bµ. Their mixing is described by the electroweak mixing angle θW
(known as the Weinberg-angle) and is not predicted by theory, but is an experimentally
determined input value to the theory:
|γy  cos θW |Bµy   sin θW |W 3µy, (2.4)
|Zy   sin θW |W 3µy   cos θW |Bµy. (2.5)
The charged W -bosons are represented by a combination of W 1µ and W
2
µ . The mixing
angle [3] in the MS-scheme [7] is:2
sin2 θW  0.23116 0.00013. (2.6)
The electric charge and the weak coupling constants are connected as follows:
g1  tan θW , ge  gw  sin θW . (2.7)
gw
The coupling strength of the Z-boson to a fermion is given by the following equation:
gZpfq  gw  pT 23  zf sin θW q. (2.8)
cos θW
A mixing of different states should only happen if the involved states have similar energies
and hence masses. This is a shortfall of the theory of the electroweak unification discussed
so far and is theoretically explained by a spontaneous symmetry breaking. Therefore,
a complex doublet of scalar fields is predicted, the so-called Higgs field. The choice of
the vacuum expectation value of the Higgs field breaks the SUp2q b SUp1q symmetry.
The isospin triplet Wµ absorbs three out of four Higgs field components and they become
massive. The W -B mixing (cf. Eq. 2.5) results in a massless photon and a massive Z.
This leaves one single neutral Higgs boson remaining which is searched for. The mass of
the Higgs is a free parameter of the model but different sources of electroweak precision
data and direct searches in the context of the Standard Model have excluded the Higgs
Boson in various mass ranges. Recent results from the ATLAS experiment exclude the
Higgs Boson in the context of the Standard Model in the mass ranges from 110.0 GeV to
117.5 GeV, 118.5 GeV to 122.5 GeV, and 129 GeV to 539 GeV [8]. The coupling strength
of the Higgs field to all particles is proportional to their masses, so it preferably decays
into the heaviest available quark or lepton pair or pair of bosons.
2.1.3 Strong interactions
The theory of the strong interactions is Quantum Chromodynamics (QCD) [9]. It describes
the interactions between quarks and gluons. The gluons are the force mediating, massless
bosons for the strong interaction acting on quarks, antiquarks and other gluons. The
quarks are the physical representations of the flavour SUp3q gauge theory. The gluons
couple to the so-called colour charge: quarks have three different possible colours (green
(g), blue(b) and red (r)) and gluons have 8 different possible combinations (colour and
anticolour) of the three fundamental colours. The gluons are represented by the Gell-Mann
2MS-scheme is the modified minimal subtraction renormalisation scheme. Renormalisation schemes
regulate UV divergences like closed loop momentum integrals to render such integrals finite. The
chosen scheme defines the counterterms and the set of renormalisation conditions which are introduced
to treat these divergences.
8
2.1 The Standard Model
Q̄, b̄ Q1, r
rb̄
Q, r Q̄1, b̄
Figure 2.6: Strong interaction between quarks Q with colour charge red (r) and Q̄ with colour
charge antiblue (b). The colour charge is conserved.
matrices (33 matrices) which are an analogy to the Pauli-matrices of SUp2q. Unlike the
photons in QED gluons also carry a colour charge and therefore the field strength tensor
FAαβ contains a self-coupling term gf
ABCABa A
C
β leading to triplet and quartic gluon vertices:
    FA δ AA δ AA g fABCABACαβ α β β α s α β , (2.9)
where AAβ represents the gluon fields, gs the strong coupling constant and f
ABC the
structure constants. The indices A,B,C run over the eight colour degrees of freedom
of the gluon field. A complete quark state specification requires a Dirac spinor and a
three-element vector giving its colour. A strong interaction as shown in Fig. 2.6 changes
the colour state of a quark, not its flavour. The matrix element is calculable in analogy to
Eq. 2.2 in QED. For this purpose the coupling constant has to be exchanged (ge Ø gspαs))
and an extra factor carrying the colour charge of the gluon at each vertex needs to be
accounted for. Important experimental results were that the constituents inside a hadron
behave like point-like free particles if they are probed at high momentum transfers and
that all observed particles are colourless bound states. These two concepts in QCD are
known as asymptotic freedom and confinement. The behaviour of quarks and gluons as
point-like free constituents inside hadrons founded the parton model. Partons are identified
with quarks and gluons. This parton model is based on the diminishing coupling constant
at high energy (asymptotic freedom). The confinement, on the other hand, implies that
only hadrons, not individual quarks, can be observed as free particles. At low energy
and large separation of quarks the coupling gets strong enough to create pairs of quarks
and antiquarks. The phenomenon of asymptotic freedom is described by the running of
the coupling constant of the strong interaction αs. Here the dependence of a physical
observable R on the momentum transfer Q2 and a mass scale µ (renormalisation scale)
to remove ultraviolet divergences is absorbed into the running of the coupling constant
αspQ2q. The running of the coupling constant itself is determined by the renormalisation
group equation:
Q2
Bαs
B  βpαsq, (2.10)Q2
where βpαsq is the β-function with the expansion in QCD [6]: βpαsq  bα2sp1 Opαsqq. If
both αspQ2q and αspµ2q are in the perturbative region the renormalisation group equation
can be solved by neglecting higher order terms. The solution is then given by:
2
αsp 2q  αspµ qQ   p q 2 . (2.11)1 α µ2s b ln Qµ2
For increasing Q2 the running coupling α 2spQ q decreases logarithmically. The perturbative
region is reached at scales Q  1  2 GeV. In contrast to QED where the coupling
9
2 Theoretical introduction
0.5
July 2009
αs( Q)
Deep Inelastic Scattering
0.4 e
+e– A nnihilation
Heavy Quarkonia
0.3
0.2
0.1
QCD α s (Μ Z ) = 0.1184 ± 0.0007
1 10 100
Q [GeV]
Figure 2.7: Summary of measurements of αs as a function of the respective energy scale Q.
Plot is taken from Ref. [10].
decreases with decreasing Q2, a positive sign of b as found for Eq. 2.11 lets the strong
coupling increase with decreasing Q2 as seen in Fig. 2.7. Only in regions, where αs is
sufficiently small, processes can be calculated with means of perturbative QCD (pQCD).
In the regime of large distances the theory is non-perturbative and pQCD is inapplicable.
However static properties of QCD, like hadron masses and lifetimes [3], are calculable with
methods of lattice QCD.
The process of building colourless bound states which are observed in nature from single
produced partons is called hadronisation. As αs increases the partons reorganise themselves
and multiply to colour-singlet states illustrated in Fig. 2.8. Hadronisation is a dynamic
Figure 2.8: Visualisation of the principle of confinement by creating extra partons.
process on a large timescale involving larger values of αs which can only be described by
phenomenological models and is discussed in Section 2.3.3.
2.1.4 Hadron-hadron interactions
Hadron-hadron collisions may intuitively be separated into two classes:
 Soft interactions with small momentum transfers: These have typically large cross
10
2.1 The Standard Model
sections of the order O(mb) at the LHC and they are sensitive to long-distance
effects. Due to their non-perturbative nature phenomenological models are used for
their description. They are divided into several sub-categories: elastic, diffractive
and soft inelastic interactions.
 Hard interactions with large momentum transfers probing the internal structure of
the hadrons: These processes have, compared to the first class, small cross sections.
They are the main focus in this analysis and described in the following section. The
large momentum transfer allows them to be described perturbatively.
The current predictions for physical observables in hadron-hadron interactions are based
on the fundamental attribute of QCD, namely factorisation. Therefore a hadron-hadron
interaction can be decomposed into different parts illustrated in Fig. 2.9. Factorisation
states that these different components can be treated independently from each other. The
component which can be calculated in perturbative QCD is called the hard scatter. The
other components are the parton showers (PS), the underlying event (UE), the beam
remnants and the hadronisation (HAD). In the parton shower approach possible histories of
the initial and final states are handled. The prediction from parton showers represents an
approximate perturbative treatment of QCD dynamics of soft and collinear configurations
to all orders. A parton shower converts a highly virtual parton into a low virtual parton
with either positive or negative virtuality. With positive virtuality the state describes a
parton after final-state radiation at energies of about 1 GeV ready to hadronise, a state
with negative virtuality describes a parton before initial-state radiation emerging from
the incoming hadron. Hadronisation happens subsequently after the final-state parton
shower at energies of the order 1 GeV and contains the transition from a partonic final
state to a hadronic observable. Therefore detectable event features are described by the
means of collimated sprays of hadrons known as jets, which ideally are associated with
the primary partons. The principles used to identify jets are presented in Section 5.1. The
beam remnants are part of the non-perturbative components and describe the remaining
constituents of the hadrons not taking part in the hard scatter. The underlying event,
which is not illustrated in Fig. 2.9 for readability, treats the additional activity in an event
which is not directly associated with the hard scatter. This component describes multiple
parton interactions (MPI) which would produce additional hard scatters. The underlying
event is an important element of the environment at high-energy experiments polluting
the hard scatter.
An inelastic hadron collision results in a short-distance scattering process described by the
cross section σab between the quarks and gluons producing new partons with momenta p3
and p4 as shown on the left side of Fig. 2.9. The parton density functions fipxiq (PDF)
describe the probability of finding a constituent i with momentum fraction xi defined as
pi  xi  Pi in the hadron. These parton density functions and the formalism of the hard
scatter of a hadron-hadron interaction including important observables in high-energy
physics are discussed in detail in the next Sections 2.1.4.1 and 2.1.4.2. The parton shower,
the underlying event, remaining beam remnants and the hadronisation are needed to fully
describe an event. The process of parton branching within a parton shower is calculated
with pQCD. The subsequent generation of such branchings creates a parton shower and is
taken care of by a Monte-Carlo generator. The description of the underlying event, the
beam remnants and hadronisation are based on different models. All these components of
a hadron-hadron interaction in context of Monte-Carlo techniques are discussed in detail
in Section 2.3.
11
2 Theoretical introduction
P
1
f
1
p
1 p
3
σ
ab
p
P 2 p
2 4
f
2
Beam
Parton Shower remnant
Hard scatter Parton Shower Hadronisation
Figure 2.9: Illustration of a hadron-hadron interaction with incoming hadrons with momenta
P1 and P2 and outgoing final-state hadrons.
2.1.4.1 Parton density functions
The parton density functions are part of the non-perturbative region of QCD and their
functional form must be extracted from fits on a variety of experimental data. Two
important groups doing such global fits are the CTEQ [11] and MSTW [12] collaborations.
At leading order PDFs describe the longitudinal momentum fractions x at momentum
transfer Q2 carried by the different partons in a given hadron. In a qualitative picture
the proton consists of three valence quarks (uud) which are responsible for the electric
charge. In addition, measurements proof the existence of a sea of quark-antiquark pairs
and gluon constituents. The probability of a specific process in a hadron-hadron collision
as seen in Fig. 2.9 is the combination of the partonic cross section and the PDFs. PDF
fits from MSTW for the proton at two different scales Q2 are shown in Fig. 2.10. Both of
these PDF fits show the distributions of the momentum fraction x of the valence quarks
(u, d), the sea quarks (ū, d̄, c, c̄, s, s̄, b, b̄) and of the gluon constituents (g).3 The PDFs are
a function of the momentum fraction x as well as of the momentum transfer Q2 at which
the hadron is probed. The gluon density, probed at different momentum transfer scales
Q2, is dominating at low values of x. In a hadron-hadron interaction processes involving
incoming low x gluons are favoured. As the probing scale increases the number of gluons
which are resolved into quark-antiquark pairs with small momentum fraction increases.
This enhances the perturbatively produced quark-antiquark pairs contributing to the sea
distribution. On the contrary, the fraction of partons carrying a large momentum fraction
(valence quarks) decreases because q Ñ q   g processes are resolved. Both effects cause
the densities to fall more steeply and to populate lower regions in x. The evolution of
the PDFs is determined by the set of DGLAP equations [13] which are solved in pQCD.
3Strictly speaking also u and d quarks are of course part of the seq-quarks.
12
2.1 The Standard Model
The PDFs should be extracted at the same fixed-order as the partonic cross section is
calculated for factorisation.
MSTW 2008 LO PDFs (68% C.L.)
1.2 1.2
Q2 = 10 GeV2 Q2 = 104 GeV2
1 1
g/10 g/10
0.8 0.8
0.6 0.6 b,b u
u
0.4 d 0.4 c,c d
c,c s,s
0.2 s,s 0.2
u d du
0 0
-4 -3 -2 -1 -4 -3 -2 -1
10 10 10 10 1 10 10 10 10 1
x x
Figure 2.10: Extracted PDFs at leading order for the proton from the MSTW collaboration
taken from Ref. [12].
2.1.4.2 The hard scatter
The factorisation theorem of QCD allows the treatment of the hard scatter as a pure
perturbative strong interaction by cleanly separating long- and short-distance processes
by a factorisation scale µf . Processes with smaller scales than the factorisation scale
are factored into the parton distribution functions fipxi, µ2f q as being part of the hadron
structure. Therefore the cross section for a hard scatter initiated by two hadrons with
four-momenta P1 and P2 can be written as:
¸»  2 2
σpP 2 21, P2q  dx1dx2f1px1, µf qf2px2, µf qσij p1, p2, αsp
Q Q
µ2rq, , . (2.12)µ2 µ2
ij r f
The hard scale is given by Q. The renormalisation scale µr was introduced in Section 2.1.3.
σij is the partonic cross section of the scattering of partons of types i and j. For a
specific final state with partons k and l the cross section includes the matrix element
MijÑkl and the phase space terms. The incoming hadrons have a spectrum of longitudinal
momenta determined by the PDFs. As a consequence, the centre-of-mass frame of the
hard scatter is boosted with respect to the incoming hadrons. Therefore, it is convenient
to use variables with additive boost transformation along the z direction like the rapidity
y or pseudorapidity η:
 1 E   pzy ln , η   θln tan , (2.13)
2 E  pz 2
where θ is the polar angle. The polar angle θ and the azimuthal angle φ are defined with
respect to the beam direction along the z-axis and x-axis, respectively. The outgoing
partons can be fully described by the rapidity y, the transverse momentum pT and the
azimuthal angle φ:
b
pµ  pE, px, py, pzq  pmT cosh y, pT sinφ, p 2 2T cosφ,mT sinh yq, mT  pT  m . (2.14)
13
xxff((xx,,QQ22))
xxff((xx,,QQ22))
2 Theoretical introduction
g g g q q̄ q1
  
g g g q̄ q q̄1
Figure 2.11: A subset of possible 2 Ñ 2 scattering processes: (left) gluon fusion, (middle) gluon
annihilation, (right) quark-antiquark annihilation.
Because of momentum conservation, the two final-state particles k and l for a 2 Ñ 2
scattering are produced with equal momenta of opposite direction in the centre-of-mass
frame. If the transverse momenta of the incoming partons is negligible, those two partons
are back-to-back in azimuth (∆φ  π) and balanced in transverse momentum in the
laboratory frame. The Feynman-graphs in Fig. 2.11 show a subset of possible 2 Ñ 2
processes.
The partonic cross section for all possible 2 Ñ 2 scatterings with quarks and gluons in
the initial and final state is:
d3σ 1 ¸ fipx1, µ2f q fjpx2, µ2f q ¸ |Mpij Ñ klq|2 1 (2.15)
dy3dy 2 24dpT 16πŝ x x 1  δ
° i,j,k,lq,q̄,g
1 2 kl
with including the average and sum over initial- and final-state spins and colours respec-
tively and ŝ  pp 21   p2q being one of the Mandelstam variables. The energy-momentum
conservation fixes the values of x1 and x2 when the transverse momenta and the rapidities
of the outgoing partons are measured. The following relation holds:
x1  m?T p mey3   Tey4q, x y3 y42  ? pe   e q. (2.16)
s s
The scattering angle θ in the centre-of-mass frame is directly correlated to the rapidity
difference y3  y4 of the two outgoing partons in the laboratory frame. Thus, the angular
distribution is sensitive to the underlying 2 Ñ 2 matrix element. For convenience, the
angular distribution is expressed in the variable χ  exp |y3  y4| to study deviations from
the underlying QCD kinematics [14]. The relation to the centre-of-mass scattering angle
is:
1  cos θ
χ   . (2.17)1 cos θ
In addition to the large gluon densities in the proton, the dominant parton-parton
interaction, comparing the matrix elements, is the scattering process gg Ñ gg as shown in
Fig. 2.12. Therefore, proton-proton interactions at high energies are dominated for a large
energy range by gluon-gluon scatterings. The full matrix element for this process is the
squared sum of all four Feynman-graphs shown in Fig. 2.12. The singularities in the cross
section arising from t- and u-channel lead to the dominance of those scattering channels.
The χ-dependence of the subprocess gg Ñ gg which was calculated and is presented in
Fig. 2.13, is approximately constant over a large range. Therefore, dσggÑgg{dχ  constant
is a flat distribution. This linearity is only disturbed at χ À 3 where s-channel contributions
become more important. This behaviour is in agreement with the underlying kinematics
of pure Rutherford scattering (peaking at small θ) which is a t-channel exchange of a
spin-1 particle just like the t-channel shown in Fig. 2.12.
14
2.1 The Standard Model
   
Figure 2.12: Diagrams for 2 Ñ 2 processes involving two gluons in the initial and final state.
From left to right: s-channel, t-channel, u-channel and quartic vertex.
15
14
13
12
11
10
9
8
7
6
5
5 10 15 20 25 30
χ
2
Figure 2.13: The χ-dependence of the invariant matrix element squared dσ ŝdχ 4 for the subprocessgs
gg Ñ gg.
Furthermore, the contributions from the other important 2 Ñ 2 subprocesses can be
estimated qualitatively with respect to the dominant gg Ñ gg process. This is due to
2
the similar behaviour of dσ ŝ4 . Before the inclusion of the PDFs, with the help of colourdχ gs
factors, the contributions from the other 2 Ñ 2 subprocessesbe
have effectively like:2
Ñ Ñ Ñ  9 9qq qq : gq gq : gg gg 1 : : . (2.18)
4 4
Therefore, the angular distribution of χ is insensitive to the relative weighting of each
process and thus uncertainties arising from the PDFs are minimised.
The subprocess qq̄ Ñ q1q̄1 (quark-antiquark annihilation) is only realised by the s-channel
exchange of a gluon. Therefore this subprocess exhibits the specific angular distribution
shape of the s-channel whereas the subprocesses in Eq. 2.18 are a mixture of different
channels. This becomes important when searching for new particles or resonances. Fig. 2.14
shows the χ dependence of the matrix elements squared  dσ ŝ24 for the process qq̄ Ñ q1q̄1.dχ gs
Shown is also the shape comparison to the subprocess gg Ñ gg (dashed line) which is
scaled to converge with the matrix element from qq̄ Ñ q1q̄1 for large χ. Unlike the dominant
t-channel subprocesses shown before, in pure s-channel processes the outgoing quarks are
correlated in rapidity and dσ{dχ peaks at low χ.
The currently available precision of calculations in pQCD of hadron-hadron interactions
is of the order Opα3sq, called next-to-leading order (NLO). Fig. 2.11 shows the so-called
Born-level Feynman-graphs, these are leading order (LO) contributions. To obtain the
NLO predictions, corrections need to be added: σBorn   α pµ2s rq  σ1. Fig. 2.15 shows the
necessary processes and matrix elements at NLO. The first correction contributing to σ1 is
coming from one additional gluon radiation off any of the outgoing partons, the so-called
15
dσgg→gg/dχ s
2/g4 (arbitary units)
s
2 Theoretical introduction
0.2
0.18
Scaled dσ /dχ s2/g40.16 gg→gg s
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
5 10 15 20 25 30
χ
2
Figure 2.14: The χ-dependence of the invariant matrix element squared dσ ŝdχ 4 for the subprocessg
qq̄ Ñ q1q̄1
s
. The invariant matrix element squared for the subprocess gg Ñ gg is shown as dashed
line. It is scaled to converge at large χ.
real emission. These real emission contributions correspond to the lowest order matrix
element of 2 Ñ 2   g or generally 2 Ñ 3. The last contribution is referred to as virtual
emission and involves the emission of a gluon which is re-absorbed by the other parton
(as shown in Fig. 2.15) or by its emitter itself. Both additional terms include infrared
divergences (soft and collinear singularities) which cancel each other. The importance
of considering higher orders in pQCD calculations is established by the fact that NLO
corrections can lead to contributions as big as the leading order prediction.
1-loop
+ +
Born-level: Real emission: Virtual emission:
σ LO = |M (0)|2 σ LO = |M (0)|2 |M (1)M (0)|2
 X 2->2 X+1  2->3 2->2 2->2
Figure 2.15: Cross section up to NLO (for simplicity real emission from other leg and loops on
the same leg are not drawn).
2.2 Extensions of and departures from the Standard
Model
The observed deficiencies of the Standard Model lead to new theoretical developments.
There are mainly two categories of developments: pure extensions of the Standard Model
and new models in which the Standard Model is only an effective theory. All of these
theories have one thing in common: they urge to be in agreement with all known phenomena.
In the energy regime of past experiments, the Standard Model predictions were in consent
with the experimental data. Currently, new kinematic regions are explored by the Large
16
dσ → /dχ s
2/g4 (arbitary units)
qq  q'q' s
2.3 Monte-Carlo models and generators
Hadron Collider. There is a large variety of new physics models which can explain known
experimental phenomena by new underlying theories. Grand Unified Theories (GUT)
predict that at high-energy, the three gauge interactions of the Standard Model, namely
the electromagnetic, weak, and strong interactions, are merged into one single interaction
invoking higher dimensional gauge groups or left-right symmetric models [15, 16, 17].
These models could explain the quantisation of charges and the mass hierarchies. Another
popular model predicts supersymmetric partners for each particle. For every type of boson
(fermion) a corresponding fermion (boson) exists carrying the same internal quantum
numbers. Besides solving the hierarchy problem, this model could help solving cosmological
questions [18].
Until now quarks are believed to be point-like [19]. The best limits on the internal
structures from the Tevatron end at around 900 GeV probing scales of approximately 1017
cm. The Large Hadron Collider enables probing for a substructure in the TeV regime.
The observed mass hierarchy and generational structure of the quarks motivate models of
compositeness. If a quark is a composite particle, excited states [20] are expected. The
Randall-Sundrum model containing extra dimensions can connect the gravitational force
with the Standard Model and explain the observed mass hierarchies [21].
The common aspect of these models is the prediction of new heavy particles or resonances
produced via s-channel processes. They would decay into stable particles which would
be observed by deviations in measured cross sections with respect to Standard Model
predictions. A promising channel to search for such effects is observing the production of
two energetic partons which are reconstructed as jets. The measurement of the invariant
mass of the decay products is sensitive to new phenomena. In particular new resonances
and new unstable particles are expected to produce configurations which are more isotropic
in rapidity than QCD events which result mostly from spin-1-gluon exchanges in the
t-channel. Therefore, the angular distribution as a function of χ is highly sensitive to
such signatures and has the advantages of being independent from the underlying decay
width and calorimeter energy resolution. Both discussed variables are sensitive to such
new phenomena and would show an excess of events (cf. Fig. 2.14) at low χ and high
invariant mass.
2.3 Monte-Carlo models and generators
Generally, Monte-Carlo (MC) techniques are based on a random number generator to
sample random variables following a probability function. These techniques have become
indispensable in high-energy physics firstly because the calculation of a cross section
includes a vast number of integrations on phase space, helicities, spins and colours.
Secondly realistic QCD predictions of hadronic final states are required to be comparable
to experimental data.
There are two sorts of MC event generators: fixed-order and parton shower generators.
Their structures are directly linked to the factorisation in pQCD. The fixed-order generators
which are used for this analysis are next-to-leading order and they produce parton-level
and not hadron-level predictions as observed in experiments. They are discussed separately
in Section 10.
Parton shower event generators [22] simulate events to the point of having a fully specified
set of final-state hadrons. These are the main tools for experimentalists because their output
can be linked to any detector simulation. With their help detector designs and experimental
17
2 Theoretical introduction
strategies are developed and optimised. The generation of the hard subprocess is according
to the leading order matrix elements providing a good description of wide-angle and high
energy particles. The technical implementation is basically the same as for the fixed-order
generators. However, to provide a complete picture of a subprocess any fixed order is not
sufficient. Consequently, the leading order matrix element has to be complemented by
small-angle and/or low energy emissions described by the parton shower to evolve to a
final parton state. The hadronisation then forms colourless hadronic states. The following
Sections 2.3.1 and 2.3.4 give an overview of the event generators commonly used and their
implementation of the parton shower, hadronisation and underlying event. The problems
arising from connecting the parton shower and the hard scatter at next-to-leading order is
be briefly presented in Section 2.3.5.
2.3.1 Event generators
Two of the main parton shower event generators are Pythia (version 6.423) [23] and
Herwig++ (version 2.5.0) [24] and its FORTRAN-sibling Herwig (version 6.510) [25].4
Both show great success in reproducing experimental data. But not only the generator
and its version is important, also the tune. A tune is an accumulation of settings for event
generation, hadronisation and underlying event which are adjusted to a certain sample
of experimental data. The default Pythia tune is the so-called ATLAS Minimum Bias
Tune 1 (AMBT1) [26], which is the first tune of Pythia to LHC data recorded with the
ATLAS detector. Similar for Herwig, the first tune is called ATLAS Underlying Event
Tune 1 (AUET1) [27]. The default Herwig++ tune is the so-called LHC Underlying
Event Tune 1 (LHC-UE7-1). All mentioned tunes are made with the MRSTLO* [28]
PDF set.5 As long as not ?stated differently these tunes are called MC10 tunes using
a centre-of-mass energy of s  7 TeV and used throughout the analysis for Pythia,
Herwig and Herwig++.
2.3.2 Parton showers
The parton shower evolution converts a parton with a high virtuality t coming from the
hard scatter to a final-state parton of low virtuality t0 ready for the hadronisation phase.
This evolution can either be ordered in terms of the opening angle of the parton branching
as it is done in Herwig and Herwig++ or the transverse momentum of the process as in
Pythia. Each parton coming from the hard scatter at scale t undergoes successive steps
of branchings by a random generator until it reaches a cut-off scale t0 below which pQCD
no longer is valid and the evolution is terminated. The probability that a parton evolves
from scale t1 to t2 without a branching is the Sudakov factor. The branching processes are
q Ñ gq, g Ñ gg and g Ñ qq̄. They are described by a set of so-called splitting functions
P calculated in pQCD obeying the DGLAP evolution equations. They determine the
probability that a parton b which evolves from a scale t to t  δt converts into partons a
4Those version numbers are the default choice. If a different version is used it will be stated explicitly.
5These are modified LO PDFs. Cross sections and acceptances calculated with LO PDFs differ in both
shape and normalisation from calculations using NLO PDFs. LO* PDFs try to incorporate properties
to reduce these deficiencies. In general LO* PDFs should behave as LO as xÑ 0 and as close to NLO
as possible as xÑ 1
18
2.3 Monte-Carlo models and generators
and a1 carrying momentum fractions z and p1 zq respectively [6]:
P pbÑ apzq   δt αspt, zqa1p1 zq when tÑ t  δtq  Pabpzq. (2.19)
t 2π
The concept of parton showers has the advantage that leading order is sufficient for the
matrix element describing the hard scatter. Its success is to describe jet sub-structure and
event shapes. But there are shortcomings due to its approximate nature. Interference
between initial-state and final-state radiation is not handled. Additionally, the emission of
hard partons at large angles and high energy is not well accounted for and this leads to
deviations in the rate of observed hard partons.
2.3.3 Hadronisation
The hadronisation step of a hadron-hadron interaction is not in the perturbative regime
but is needed for full simulation of final states. The hadronisation of a parton is presumed
to be universal e.g. not depending on the environment of the production. The formation of
hadrons is described by means of phenomenological models which are tuned to experimental
data. The function describing hadronisation is called the fragmentation function fpzq
parametrised as a function of the momentum fraction carried by the hadron with respect
to the parton. Parametrisations for these functions differ depending on the kinematic
arguments used to derive them. Also here the DGLAP equations can be used for scale
evolution. Similar to PDF fitting these functions are extracted from and tuned by
experimental data. Hadronisation models are based on the observation that global features
of hadronic systems (multiplicities, angular distributions and inclusive energy spectra etc.)
calculated at the parton level, agree very well with the measured ones. This concept is
called parton-hadron duality, in which hadron-level flow of energy, momentum and flavour
should follow parton-level. In the following paragraphs the two main models used by
Pythia and both Herwig implementations are discussed [22].
2.3.3.1 The cluster model
The pre-confinement property of pQCD [29] is the motivation for using cluster objects
formed at the end of the parton shower. The key idea is to enforce that remaining gluons at
the shower cut-off scale are split non-perturbatively into quark-antiquark pairs beforehand.
The colour flow in the parton shower causes colour-singlet pairs of a quark and antiquark
to end up close in phase space. The mass spectrum of these colour-singlet clusters is
asymptotically independent of the hard subprocess type, scale and the beam energy. The
hadronisation step combines adjacent colour lines which form physical clusters. This
approach is illustrated in Fig. 2.16(a) and is the core of the hadronisation in both Herwig
implementations. If a cluster is too heavy it splits into two clusters, otherwise these excited
mesonic states decay directly into two hadrons according to the two-hadron density of
states. Clusters too light for such a decay form into one hadron directly. This principle
presents a well-founded and very simple attempt to describe hadronisation without using
a fragmentation function. Nevertheless, there are special cases, like suppression of the
production of baryons and heavy flavors, that need an intervention within this model.
19
2 Theoretical introduction
    
(a) Via the cluster model (b) Via the string model
Figure 2.16: A hard process followed by parton shower and hadronisation.
2.3.3.2 The string model
The linear confinement at large distances is the starting point for the string model.
Calculations [30] have shown that the energy stored in the colour dipole field between a
charge and an anticharge increases linearly with the distance of the charges. So two partons
moving apart from each other are the extremes of colour flux tubes. With increasing
distance a tube is stretched and the rising potential may break the string and create
new qq̄ pairs. The probability of breaking the string is given by the quantum mechanical
probability of tunnelling through a potential barrier. Hence, the fragmentation to heavy
quark pairs is suppressed due to their higher masses. Charm and heavier quarks are not
expected to be produced in those soft fragmentations. The fragmentation continues until
all strings end with quarks and antiquarks and all systems reach a cut-off scale. Then
the string transforms, according to its mass and flavour content, into a hadron or excited
hadronic state. A schematic picture of a multi-hadronic state formed by the string model
is shown in Fig. 2.16(b). One important property of this model is collinear and infrared
safety. The Pythia generator uses this hadronisation model. Although this complex
model has proven its ability to reproduce data very well, whether it is its underlying
physical concept or its flexibility based on the large number of unrestricted parameters is
unknown.
2.3.4 The underlying event and beam remnants
In hadron collisions a description of the beam remnants and multiple parton interactions
(MPI) is needed. The beam remnant (non-perturbative) is colour-connected to the hard
interaction, and forms part of the same fragmenting system. The activity in a hadron-
hadron collision is heavily dependent on the centre-of-mass energy and MC tunes are
adjusted consequently. The underlying event physics are built from perturbative models
based on the 2 Ñ kl with k, l  q, g scattering processes. In a hadron-hadron collision a
20
2.3 Monte-Carlo models and generators
beam particle contains a multitude of partons. Consequently more than one separate scatter
can be observed. An effective pKmin scale is introduced, below which the perturbative cross
section is assumed to completely vanish or to be strongly damped. The average number
of interactions per collision is then given by the ratio between the total hadronic cross
section σkl and the total partonic cross section σtot:
xnyp q  σklppKminqpKmin p q (2.20)σtot pKmin
with xnyppKminq giving the average of the distribution of the number of parton-parton
interactions above pKmin per hadron-hadron collision. In Pythia, multiple interactions
are ordered in pK and the sum of x fractions of each successive interaction can never be
greater than unity. In the Herwig++ and Herwig model, the generation step is stopped
once the energy-momentum conservation is broken.
2.3.5 NLO matrix element generators with shower programs
The approximative nature of parton showers can be improved by NLO calculations of
the hard kinematics and cross sections. But these NLO calculations have problems when
trying to describe collinear and soft partons whereas the parton showers are doing well
in describing those. As a consequence the results from parton shower event generators
are only reliable for the shape of distributions, not the absolute normalisation. Clearly
a combination of both techniques would improve the description of any partonic state.
However, adding a NLO matrix element generator to a parton shower is not trivial. But
it is the only way to overcome the deficiencies of NLO calculations. More sophisticated
prescriptions are needed due to the problems of double counting jets which are either
generated by real emission or along with the parton shower and correctly covering phase
space. There are two groups of approaches. The first approach introduces a merging scale
where any parton produced above that scale is generated by the NLO matrix element and,
conversely, any parton produced below is generated by the shower. In the second approach
which is adapted for some of the NLO generators used in this analysis (see Section 10)
higher-order corrections to an inclusive process are integrated into the parton shower.
21

3 Heavy flavour production
Heavy flavour production is a benchmark process in perturbative QCD because it probes
the underlying strong dynamics at a well-defined scale. The mass scale of the heavy quarks
mQ Á 1 GeV is above the application limit for pQCD. Because of this heavy-flavour jets
are of intrinsic interest because they hold the most direct correspondence between the
parton-level production and the observed hadron level. At the LHC QCD jet and dijet
production is the dominant process. The bb̄ jet pairs are produced abundantly with a cross
section of about 300 µb as shown in Fig. 3.1. Studying the agreement of bb̄ dynamics and
production is not only interesting in the context of tests of our knowledge of pQCD, but
also in the context of searches for new heavy objects and deviations from the Standard
Model. Heavy-flavour quarks could arise from new heavy objects and studies of the fraction
of heavy-quark jets relative to all-flavour (inclusive) jets could reveal this. Besides they and
their decay products, especially leptons, are background to many searches for new physics.
Besides their abundant production b-quarks are also very important for top-quarks studies
because the top-quark directly decays into a b-quark without interacting with other quarks.
This chapter will discuss the production and fragmentation of b-quarks and emphasise the
differences to light flavour quarks. Finally, past measurements on bb̄ dijet production will
be presented.
3.1 Bottom flavour in hadronic collisions
With an approximate bottom quark mass of mb  4.75 GeV the corresponding value of
αspmbq is around 0.24 (see Fig. 2.7) and therefore perturbation theory is expected to
hold.1 Restricting the final state to bb̄ leaves two sets of 2 Ñ 2 processes of Fig. 2.11
to be considered at leading order: gluon fusion and light-quark annihilation. Within
pQCD calculations, the light-flavour quarks are considered massless which introduces a
singularity in the propagators and the need for an appropriate cut-off scale. In contrast,
the propagators for bottom production cannot develop such poles. Furthermore, the
fragmentation functions can therefore be analysed to a greater extent with perturbative
means. The main difference to light quark fragmentation is that a heavy quark is not
slowed down as much when picking a light quark to form a hadronic state. Therefore the
b-hadron retains about 70% of the original b-quark momentum.
In the following the dijet cross section of b-jets with contributing subprocesses is presented
at NLO. Then aspects of the measurement of heavy-flavours in jets are discussed followed
by the presentation of parametrisations for the heavy quark fragmentation functions.
Finally, techniques for identifying bottom-flavour in jets are explained. For these purposes
jets are formed by the clustering algorithm anti-kt [32, 33] with radius parameter R = 0.4
in simulated events with the MC10 tune at the level of stable particles. Details on the jet
reconstruction can be found in Section 5.1. The definition of a b-jet in MC simulation is as
1This mass definition uses the pole mass as reference: 4.5-5 GeV. The pole mass of the heavy quark is
defined as the position of the pole in the quark propagator in perturbation theory.
23
3 Heavy flavour production
proton - (anti)prot on cross sections
9 9
10 10
8 8
10 10
σ
tot
7 7
10 Tevatron LHC 10
6 6
10 10
5 5
10 10
σ
4 b 4
10 10
3 3
10 10
jet
2 σ (E  > √s/20)
10 jet T
2
10
1 1
10 σW 10
0 σZ 010 10
jet
σ (E  > 100 GeV)
jet T
-1 -1
10 10
-2 -2
10 10
-3 -3
10 σ 10
t
jet
-4 σ (E  > √s/4)
10 jet T
-4
10
-5 σ (M =120 GeV) -5
10 Higgs H 10
200 GeV
-6 -6
10 10
500 GeV
WJS2009
-7 -7
10 10
0.1 1 10
√s (TeV)
?
Figure 3.1: Standard Model cross sections as a function of centre-of-mass energy s. Indicated
are the Tevatron centre-of-mass energy of 1.96 TeV and the possible centre-of-mass energies
of 7, 10 and 14 TeV of the LHC. The Tevatron is a synchrotron that accelerates protons and
antiprotons. The LHC accelerates two beams of protons. Taken from Ref. [31].
follows: a jet containing any bottom-flavoured hadron with at least pbhadronT ¡ 5 GeV and
at a maximum distance ∆R   0.3 to the jet axis will be labelled a b-jet. Subsequently,
if a jet does not contain a b-hadron it is searched for a c-hadron and under the same
conditions the jet is labelled a c-jet. If both matches fail the jet is automatically labelled
a light-jet representing the cases of light-quark and gluon-initiated jets.2 From now on
quantities not specific further represent implicitly jet quantities.
3.1.1 Theory of bottom-quark production
In the partonic cross section two mass effects need to be considered affecting the matrix
element and the phase-space integ?ration. The latter is restricted by energy conservation
and the cross section vanishes for ŝ ¤ 2mb. The subprocesses contributing to the matrix
element at LO, i.e. Opα2sq are:
gg Ñ bb̄,
qq̄ Ñ bb̄
as shown in Fig. 3.2.
2The cases in which electrons or taus fake jets are neglected.
24
σ (nb)
33 -2 -1
 events / sec for L = 10  cm s
3.1 Bottom flavour in hadronic collisions
So the cross section is sensitive to the gluon content down to low x-values of the incoming
hadrons. The matrix elements [9] calculated with the
se Feynman-graphs are
1 ¸ 2|Mpqq̄ Ñ bb̄q|2 4 4m τ
2   τ 2   b , (3.1)
g4 9 1 2 
2ŝ 

1 ¸ 2 2|Mpgg Ñ bb̄q|2  1  3 2 2 4mb 4mτ b1   τ2    (3.2)g4 6τ1τ2 8 b 2ŝ ŝτ1τ2
with τ1,2  1	β cos θ 2, the heavy-quark velocity β  1 4m and the scattering angle θ2 ŝ
(cf. Eq. 2.1). Using the variables in Eq. 2.16 and Eq. 2.17 these matrix elements and
the cross section can be expressed in terms of ∆y or χ in analogy to Paragraph 2.1.4.2.
Additional mass-terms need to be added to the cross section formula but the overall
conclusions from Fig. 2.13 and Fig. 2.14 are still valid. The cross section reveals the
following rapidity dependence [9, 34]:
1 ¸
dσ̂9 2p   p qq |Mpij Ñ bb̄q| , (3.3)1 cosh ∆y 2
with
¸  
 
1 | 4 1 m2Mpqq̄ Ñ bb̄q|2     
cosh ∆y  
b ,
g4¸ 9 1 cosh ∆y  m
2
T 
 (3.4)
1 | p Ñ 1 8 cosh ∆y 1 m
2 m4
M gg bb̄q|2  cosh ∆y   2 b  2 b . (3.5)
g4 24 1  cosh ∆y m2 4T mT
Both cross sections only depend on ∆y and not on the rapidities themselves. Eq. 3.3 shows
that the cross section is damped at large ∆y. Furthermore, the light-quark annihilation
via the s-channel is peaked at small rapidity differences and decreases very rapidly with
q̄ b̄

q b
(a) s-channel
b̄ b̄ b̄
  
b b b
(b) left to right: t-channel, u-channel and s-channel
Figure 3.2: Lowest-order Feynman-graphs for bb̄ production: (top) light-quark annihilation,
(bottom) gluon fusion
25
3 Heavy flavour production
increasing ∆y. In the gluon-fusion process the t- and u-channel poles in the matrix
elements at vanishing scattering angle θ favour a large ∆y but this behaviour is damped
by the 1{ŝ29 1p   q2 term. Therefore the dependence on the rapidity difference for the1 cosh ∆y
gluon-fusion process leads to a much broader distribution peaked at around ∆y  1. The
resulting rapidity distributions showing this behaviour are presented in Fig. 3.3(a) and
Fig. 3.4(a) with the corresponding projections along the x-axis. The projection is made
from the range -2 ¤ y2   -1.6. The projection is therefore peaked at around y1  1 to
0.6.
At LO and small dijet invariant mass gluon fusion is the dominating process making
10-1 0.5
2
1.5 0.4
1 -2 ≤ y  < -1.62
0.5 10
-2
0.3
0
-0.5 0.2
-3
-1 10
-1.5 0.1
-2
0
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2
rapidity y rapidity y
1 1
(a) (b)
Figure 3.3: (a) Rapi?dity distribution of gluon fusion bb̄ events generated with Pythia using a
centre-of-mass energy s  7 TeV with b-hadrons selected with pbhadronT ¡ 5 GeV. (b) Projection
along x-axis illustrating the cross section dependence on rapidity.
2 0.7
10-1
1.5 0.6
1 0.5 -2 ≤ y  < -1.610-2 2
0.5
0.4
0
10-3
-0.5 0.3
-1 0.2
10-4
-1.5
0.1
-2
-5 0
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 10 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2
rapidity y rapidity y
1 1
(a) (b)
Figure 3.4: (a) Rapidity distri?bution of light-quark annihilation bb̄ events generated with Pythia
using a centre-of-mass energy s  7 TeV with b-hadrons selected with pbhadronT ¡ 5 GeV. (b)
Projection along x-axis illustrating the cross section dependence on rapidity.
up about 90% of all events and producing mostly central configurations. This large
contribution from gluons in the initial state leads to a significant uncertainty in the
production cross section arising from the gluon PDF uncertainty at low x. With increasing
26
rraappiiddiittyy  yy rraappiiddiittyy  yy
22 22
1 dN 1 dN
N dy dy N dy dy
1 2 1 2
1/N dN/dy 1/N dN/dy
1 1
3.1 Bottom flavour in hadronic collisions
invariant mass of the outgoing two-parton system the light-quark annihilation becomes
more important.
The two-parton system is reconstructed with the help of the jets (cf. Section 5.1). The two
highest-pT jets, referred to as leading and sub-leading jets, are selected as the dijet system
and identified as the two outgoing partons. At an invariant dijet mass of about 1.8 TeV
more than 50% of the events are produced by light-quark annihilation as can be seen in
Fig. 3.5.3 The dijet mass range up to 5 TeV in Fig. 3.5 spans over 12 orders of magnitude
in the cross section. The point, at which the major fraction of events is produced by
light-quark annihilation, is determined by the slope of the gluon PDF. Dedicated studies
on the underlying production mechanism using such characteristics could improve our
knowledge on the PDFs.
The NLO contributions to the cross section contain the real and virtual emissions to
1 103
0.9 MC. stat. uncertainty
gg 10
0.8
-1
0.7 10
0.6 10-3
0.5
10-5
0.4
0.3 10-7qq
0.2 10-9
0.1
10-11
0 1000 2000 3000 4000 5000
bb dijet mass [GeV]
Figure 3.5: The bb̄ dijet mass cross section event fr?actions as a function of dijet mass calculated
at LO with Pythia using a centre-of-mass energy s  7 TeV (pT ¡ 40 GeV, |y|   2.1) show
the contributions from gluon fusion (gg) and light-quark-annihilation (qq̄). Superimposed is the
dijet mass cross section as a function of dijet mass.
the LO graphs, examples are shown in Fig. 3.6. Additional processes calculated with
leading-order precision appear at NLO. In summary the processes contributing at NLO
are:
gg Ñ bb̄g,
qq̄ Ñ bb̄g,
qg Ñ bb̄q,
q̄g Ñ bb̄q̄.
The subprocess with the initial partons g and q (or q̄) appears first at NLO level. In
addition there are new NLO process which lead to configurations identical to those from
LO with real emission. These are illustrated with the help of the Feynman-graphs in
Fig. 3.7. These diagrams can also be realised with the initial state gg. Traditionally, the
production processes at NLO are grouped into three categories: flavour creation (FCR),
flavour excitation (FEX) and gluon splitting (GSP). This grouping is intuitive and a useful
concept which in terms of pQCD however disregards interference terms. FCR contains the
3The selected phase space of pT ¡ 40 GeV, |y|   2.1 is motivated in the following measurement of
ATLAS data and will be explained later.
27
ffrraaccttiioonn  ooff  eevveennttss
dσ/dM [pb GeV -1]
3 Heavy flavour production
Born-level processes and in addition all diagrams with a gluon radiation to those 2 Ñ 2
terms. FEX illustrated on the left side in Fig. 3.7 describes diagrams in which an initial
state gluon splits into a bb̄ pair before the interaction with the parton from the other
colliding hadron. GSP on the other hand (right side of Fig. 3.7) consists of the diagrams
where a gluon splits into a bb̄ pair after the interaction. FEX and GSP both first appear
at NLO level. All-order event generators include GSP processes not from first principle in
the matrix element but they are realised by initial- and final-state radiation in the parton
shower step. Most all-order event generators include FEX processes already in the matrix
element. The kinematic properties of these processes are mirrored in the simulation but
the normalisation is inaccurate. The importance of these NLO processes in bottom-flavour
studies can be numerically estimated by the fragmentation process g Ñ bb̄ with occurs
in a fraction αspm2bq{2π of events. Its frequency increases with the centre-of-mass energy
and the large number of gluon-gluon processes at the LHC makes FEX and GSP the
dominating process.
The Born-level processes produce back-to-back configurations and the ∆φ distribution
is only a sharp peak at π. Gluon radiation populates the region below π and FEX and
GSP processes contribute to all regions. The angular distributions are very sensitive to
the different production mechanisms. This is presented with the help of simulated events
from Pythia with the MC10 tune in Fig. 3.8, where the b-hadrons are selected after
final-state radiation with at least pb-hadronT ¡ 5 GeV. To be able to distinguish between
different production processes to study their kinematic properties the following restriction is
imposed: in each event only the hardest bb̄ production process is selected. This requirement
is implied in the naming scheme of the histogram axis labels: σhardest (cf. Fig. 3.8). This
restriction is illustrated with the following example: if a GSP process generated in the
parton shower phase coincides with a FCR hard scatter process, the GSP process will be
discarded.
The next-to-leading order perturbative series of the partonic cross section at an energy
b̄ b
 
b b̄
Figure 3.6: A subset of Feynman-graphs representing NLO corrections to bb̄ production: (left)
one-loop correction to gluon fusion and (right) real emission correction to light-quark annihilation.
b b
 b̄  b̄
Figure 3.7: New contributions at NLO level from gluon splitting (right) and flavour excitation
(left). Both graphs also can be realised with the initial state gg.
28
3.1 Bottom flavour in hadronic collisions
×106
140 FCR+FEX+GSP
pb-hadron > 5 GeV
120 T FEX+GSP
GSP
100
80
60
40
20
0 0.5 1 1.5 2 2.5 3
∆φ [rad]
Figure 3.8: Azimuthal distance between simulated bb̄ hadrons with pbhadron? T ¡ 5 GeV after the
parton shower predicted by Pythia using a centre-of-mass energy s  7 TeV . Only the hardest
bb̄ production process is selected per event (σhardest).
scale Q (= factorisation scale µf ) is given by: 

2
σ̂ 2ij  α2pµ qA  α2 µspµ2q B   Aβ0 ln  Opα4sq. (3.6)Q2
The renormalisation is performed at arbitrary scale µ to compensate mass singularities.
The dependence on µ of the partonic cross section is shown in Eq. 3.6 and enters through
logarithms of the ratio between µ and the energy scale Q in the NLO term. Deviations due
to the variation of the scales are of the order Opα4sq but can nevertheless cause a sizable
effect on the cross section. Variations of the scales are one way to probe the sensitivity of
predictions to these uncalculated terms. In principle the choice of µ and Q is arbitrary
but has to be sensible or large logarithms can develop. Therefore choosing µ of the order
of Q, the logarithms are kept small. For differential cross sections it is reasonable to
chos°e µ2 proportional to m2  Q2, where Q is an invariant of the two-parton system (e.g.
pT, pTppartoniq etc. which are invariant under longitudinal boosts). In case of the
bottom-quark the inclusion of higher orders like GSP almost doubles the cross section and
therefore does not stabilise the calculation against scale changes. GSP and FEX are only
calculated with leading order accuracy and therefore it is expected that the predictions for
bb̄ pairs will be subject to large theoretical uncertainties arising from scale choices.
3.1.2 Bottom flavour in jets
The measurement of a jet containing one or more bottom hadrons focuses on the properties
of these jets, regardless of the momentum fraction of the jet carried by the bottom
hadron(b-hadron). From first principles a bottom-flavoured jet should be described by a
finite-order QCD calculation more precisely than a light-flavoured jet. The mass of the
bottom quark acts as a cut-off against final state collinear divergences. At leading order
the b-jet coincides with the bottom-hadron itself. At the next-to-leading order the b-jet
can be the heavy hadron, or it can contain a heavy hadron and a light companion, or even
both the b- and the b̄-hadron.
The detecting methods require certain acceptance regions due to the detector geometry
and resolution and reconstruction limits on objects like tracks, vertices and jets. A typical
29
ddσσhhaarrddeesstt//dd∆∆φφ  [[rraadd
--11]]
3 Heavy flavour production
lower limit on the transverse momentum in the reconstruction of jets is pT   20 GeV
due to jet identification and calorimeter properties. Consequently, also the b-hadrons are
required to have a certain amount of transverse momentum. In a leading-order picture, the
transverse momentum has to be at least 20 GeV. This causes two effects: the number of
measured b-hadrons is obviously reduced and the angular distribution is changed compared
to Fig. 3.8. This is due to the more heavily suppressed contributions from GSP and
FEX than from FCR and the enhancement of the collinear regions ∆φÑ 0 and ∆RÑ 0
as seen in figures Fig. 3.9(a) and Fig. 3.9(b). In the jet reconstruction with distance
parameter R, this leads to the inability to resolve two b-hadrons which are closer than 2R.
In general every cross section measurement is sensitive to the distance parameter R of the
jet reconstruction due to such resolution effects. In case of the b-hadrons, because of the
large fraction of bb̄ pairs produced via FEX and GSP, this effect is even more important.
The inclusive b-jet cross section as a function of pT is dominated by b-jets arising from
GSP. This can be concluded from Fig. 3.10. Below 200 GeV the main source of b-jets are
jets which contain one b-hadron produced by GSP, above 200 GeV both b-hadrons are
merged into one jet. These configurations are consequently lost in a dijet measurement
where the separate reconstruction of both bottom-flavours is required. Therefore the
dijet measurement is enhancing the FCR contributions and the resulting effect on the
measurement of the invariant dijet mass is shown in Fig. 3.11(a) by the differential cross
section and in Fig. 3.11(b) by the fraction of events from different processes. In total, the
subprocesses appearing at NLO contribute at most 10% to the dijet cross section due to
the requirement of a dijet topology.
The dominating fraction of FCR in the dijet cross section can also be seen in the cross
section as a function of angular variable χ (cf. Eq. 2.17). The shape of this cross section is
given by the FCR processes. With increasing angular separation in χ the cross section
decreases. The contribution from GSP falls more rapidly over almost 2 orders of magnitude
than the other two. In GSP processes the b-hadrons are strongly correlated in rapidity.
×1031000 108
900 FCR+FEX+GSP FCR+FEX+GSP
pb-hadron > 20 GeV pb-hadronFEX+GSP  > 20 GeV800 T FEX+GSP107 T
GSP GSP
700
600 106
500
400 105
300
200 104
100 <2R
0 0.5 1 1.5 2 2.5 3 0 1 2 3 4 5 6
∆φ [rad] ∆R
(a) (b)
Figure 3.9: (a) Azimuthal distance between siamulated bb̄ hadrons with p
bhadron
T ¡ 20 GeV
and (b) η  φ correlation expressed as ∆R  η2   φ2 between simulated bb̄ hadrons with
pbhadron?T ¡ 20 GeV after the parton shower predicted by Pythia using a centre-of-mass energy
s  7 TeV. Only the hardest bb̄ production process is selected per event (σhardest).
30
ddσσhhaarrddeesstt//dd∆∆φφ  [[rraadd
--11]]
ddσσhhaarrddeesstt//dd∆∆RR  [[ppbb]]
3.1 Bottom flavour in hadronic collisions
0.7
FCR
0.6 FEX
single GSP
0.5 merged GSP
0.4
0.3
0.2
0.1
0
0 50 100 150 200 250 300 350 400 450 500
p  [GeV]
T
Figure 3.10: Fractional inclusive b-jet pT distribution of differen?t production processes with
pT¡ 20 GeV predicted by Pythia using a centre-of-mass energy s  7 TeV: Distinguished
are GSP, FEX and FCR processes. Only the hardest bb̄ production process is selected per event
(σhardest).
3.1.3 Bottom-quark fragmentation function
Fragmentation is the process describing the transition between partons (cf. Section 2.3.3) to
sprays of hadrons reconstructed in an experiment. In an MC generator this is handled in the
hadronisation step where the production of partons is calculated down to a cut-off scale and
finally the hadronic final states are modelled by different schemes. Measurements [35, 36]
have confirmed early that hadrons formed by heavy quarks carry a larger part of the
energy of the initial heavy quark than in case of a light quark. The momentum spectrum
of hadrons, often referred to as the fragmentation function, is parametrised by a scaling
function fpzq which describes the development of the longitudinal fragmentation process
where z is the longitudinal momentum fraction carried by the hadron. There are a
variety of parametrisations available derived by different kinematic arguments describing
fragmentation function measurements. In Pythia the choice of the fragmentation function
can be steered by configuration parameters. The most commonly used functions are
implemented in Pythia. Light quarks are treated with the symmetric Lund function [37].
In Herwig no separate fragmentation parametrisation is needed because the fragmentation
is handled by the phase-space scheme of the two-body decays.
Phenomenological arguments for this non-perturbative part are used to derive the so-called
Peterson et al. [38] fragmentation function for heavy quarks:
1
fpzq9   2 , (3.7)
z 1 1  
z 1z
where the free parameter  is related to the effective quark masses mq of the meson
  pmq{m q2b and is derived from data. This function estimates the transition matrix
element with the help of the energy difference between the incoming partons and outgoing
hadrons. But high-energy physics data of past decades disfavours this fragmentation
function. This was observed for example in the measurement obtained by the SLD
collaboration [36]. This measurement is performed on hadronic Z decays where the
b-hadrons are weakly decaying. Reconstructed is the variable xB  EB{Ebeam where EB is
the energy of the weakly decaying b-hadron and Ebeam the energy of the electron-positron
beam. This variable is sensitive to the fragmentation and hadronisation model. The results
31
fraction of events (arbitrary units)
3 Heavy flavour production
2 FCR+FEX+GSP10 0.9
FEX+GSP 0.8
10 GSP 0.7
FCR
1 0.6 FEX
0.5 GSP
10-1
0.4
10-2 0.3
p  > 40 GeV, |y| < 2.1 0.2 p  > 40 GeV, |y| < 2.1
10-3 T T
0.1
10-4 00 100 200 300 400 500 600 700 800 0 100 200 300 400 500 600 700 800
bb dijet mass [GeV] bb dijet mass [GeV]
(a) (b)
Figure 3.11: (a) Simulated bb̄ dijet cross section as a function of dijet mass and (b) corresponding
fractions of production processe?s in the bb̄ dijet cross section as a function of dijet mass in Pythia
using a centre-of-mass energy s  7 TeV and pT ¡ 40 GeV and |y|   2.1. Only the hardest bb̄
production process is selected per event (σhardest).
102
FCR+FEX+GSP
FEX+GSP
10 GSP
110 GeV < M < 370 GeV
1
10-1
10-2
5 10 15 20 25 30
χ
Figure 3.12: Dijet cross section as a ?function angular variable χ (cf. Eq. 2.17) predicted by
Pythia using a centre-of-mass energy s  7 TeV and pT ¡ 40 GeV and |y|   2.1. Only the
hardest bb̄ production process is selected per event (σhardest).
presented in Fig. 3.13 show that the Petersen et al. function (bottom) is not favoured
by data. A much better description is given by the symmetric Bowler function [39] (cf.
Fig. 3.13 (top)). Recent simulated data from Pythia with the MC10 tune is using the
symmetric Bowler function to describe the fragmentation of heavy quarks:
1 bm2T
fpzq9     2 p1 zqae z , (3.8)z1 rQ b mQ
where a,b and rQ are free parameters of the model. The symmetric Bowler model contains
the transverse mass mT of the hadron created in the hadronisation process and the
transverse mass mQ of the heavy quark at the end of the string in the string fragmentation
process. The default ATLASMC10 fragmentation parameters are a  0.3, b  0.58 GeV2
and rQ  0.75.
32
ddσσ --11hhaarrddeesstt//ddMM  [[ppbb  GGeeVV ]]
ddσσ22 --11hhaarrddeesstt//ddMMddχχ  [[ppbb  GGeeVV ]]
fraction of events
3.1 Bottom flavour in hadronic collisions
Figure 3.13: Distribution of the reconstructed ratio xB between the energy of the weakly decaying
b-hadron and the beam energy (points) in hadronic Z-decays measured by the SLD?collaboration.
The data was collected between 1996 and 1997 at a centre-of-mass energy of s  92 GeV.
The predictions of three models are shown: (top) Bowler, (middle) Kartvelishvili et al. [40] and
(bottom) Peterson et al.. Subset of histograms taken from Ref. [36].
3.1.4 Bottom-hadron decays
The ability to identify jets with bottom-flavours is based on the following properties of the
b-hadron and its decay. Firstly, because of the long lifetime of b-hadrons, of the order of
1.5 ps, they will travel a significant distance in the transverse plane ( 3 mm in a jet with
pT  50 GeV) before decaying. Therefore they will produce secondary vertices displaced
from the primary interaction point. Furthermore, b-hadrons are massive objects producing
decay products with large transverse momentum with respect to the jet axis and large
opening angle allowing a separate reconstruction. Therefore the kinematics of the decay
products originating from b-hadrons allow a distinction between decay products from
lighter c-, light-quark and gluon jets. In addition, the decay mode into leptons (so-called
semi-leptonic decay) has a branching ratio of about 10% [3] and has the advantage of
very efficient and accurate lepton (= muon and electron) reconstruction at high-energy
experiments. In summary, b-jets can be identified with the help of the measurement of
displaced tracks and reconstruction of secondary vertices (SV) and by identifying leptons
from hadron decays in a jet.
33
3 Heavy flavour production
3.2 History of bottom measurements and motivating
measurements of bb̄ pair production
The discovery of the bottom quark at Fermilab near Chicago in 1977, where it manifested
itself in a colourless bb̄ bound state with a mass of roughly 10 GeV, initiated more than
30 successful years of b-physics measurements. This bound state was detected in the
dimuon spectra at the E288 experiment [41]. In the following years the first measurement
of the bottom production cross section was performed by the UA1 collaboration [42] at
the proton-antiproton collider Spp̄S. This measurement (shown in Fig. 3.14) of the semi-
?leptonic bottom decays into muons calculated the integrated bottom-quark cross section at
s  630 GeV. Although this result shows a slight excess to the NLO QCD prediction, it
?
Figure 3.14: UA1 measurement ( s  630 GeV) of the inclusive b-quark integrated cross
section for |y|   1.5 as a function of the transverse momentum threshold. The data correspond to
a integrated total luminosity of 4.7 pb1. The curve is the NLO QCD prediction and the dashed
lines represent the theory uncertainty. Taken from Ref. [42].
is in agreement with theory within systematic uncertainties. The measurements performed
by the next generation of high-energy experiments at the Tevatron namely the Collider
Detector at Fermilab (CDF) [43] and the D0 experiment [44] are not in agreement with
QCD predictions. Their first measurements [45, 46] showed a factor 2-4 excess in the
measured data with respect to theory [47]. This has led to many developments both in
theoretical calculations and in experimental research. Changes in inputs to theoretical and
experimental analyses have caused the largest impact. The more precise measurement of
PDFs especially of the gluon have improved the pQCD predictions as well as new techniques
for matching NLO calculations with parton showers. The other part with enormous progress
is the understanding and proper transfer of the fragmentation function of heavy quarks
from e e data to hadronic collisions. As a consequence of these improvements not only
does the differential cross section of b-hadron production show a remarkable agreement
with pQCD prediction in Fig. 3.15 but also the inclusive b-jet cross section as a function of
pT shown in Fig. 3.16 is in agreement with the NLO prediction. But this latter agreement
34
3.2 History of bottom measurements and motivating measurements of bb̄ pair production
is mostly due to the large theoretical uncertainties and systematic uncertainties in the
measurement. Especially in the high pT region, the shape between data and pQCD NLO
prediction does not agree well indicating enhancements of higher order contributions or
non-perturbative fragmentation effects of gluons. As demonstrated in Fig. 3.16, the usage
of jets enables probing a larger transverse momentum range due to the independence
from an exclusive decay measurement. In addition a jet measurement is less subject to
fragmentation and hadronisation effects due to the clustering of associated particles. In
the b-jet measurement shown in Fig. 3.16 the theoretical uncertainties already play a
major role at a centre-of-mass energy less than one third of the LHC centre-of-mass energy.
The measurement of bottom-flavour pair production and their angular correlations as
presented in Section 3.1.1 may help to understand the production mechanisms, test QCD
and provide means to search for new physics. In the following section a brief summary of
past measurements is presented.
4
10
Data with total uncertainties
FONLL theoretical prediction
Theoretical uncertainty
3
10
2
10
1
10
|y|<0.6
1
0 5 10 15 20 25
pT(Hb) GeV/c
Figure 3.15: Differential cross-section distribution of b-hadron p?roduction as a function of
transverse momentum pT(Hb) measured with the CDF detector at s = 1.96 TeV with a total
luminosity of 39.7 pb1. The solid line is the central theoretical values using the fixed order
plus next-to-leading logarithms (FONLL) calculations [48], the dashed line is the theoretical
uncertainty. FONLL calculations contain the NLO calculation and next-to-leading logarithm
resummation. Taken from Ref. [49].
3.2.1 Past measurements of bb̄ pair production properties
The advantage of measuring the bb̄ dijet systems lies in the inclusion of correlation
information on the underlying QCD production. Similarly to the measurements presented
on the inclusive bottom-flavour production the dijet measurements beginning with the
UA1 experiment revealed deviations from QCD predictions. The first measurement on
bb̄ correlations performed by the UA1 collaboration [51] with the help of a data sample
containing two muons shown in Fig. 3.17 exhibits an excess of 30-40% compared to NLO
QCD predictions. In Fig. 3.17 the QCD predictions are scaled by 30% and 40% for
the left and right plot, respectively. However, this disagreement is still covered by the
theoretical uncertainty. Also here more recent experiments at the Tevatron [52, 53, 54]
have exposed the inability of QCD predictions to describe data. As an example in Fig. 3.18
35
dσ/dpT(Hb) nb/(GeV/c)
3 Heavy flavour production
10
CDF RunII Preliminary Data
1
Systematic errors
-1
10 NLO prediction CTEQ6M
-2 corrected at hadron level
10
µ 2R=µ = P +m
2
F T  / 2b
-3
10 NLO uncertainties 
-4 (scale included µ  / 4 < µ < µ )0 0
10
MidPoint jets, R
-5 cone
=0.7, fmerge=0.75 
10
-1
s = 1.96 TeV,∫  L ~ 300 pb
-6
10
|Y|<0.7
-7
10
50 100 150 200 250 300 350 400
P  jet [GeV/c]
T
?
Figure 3.16: Inclusive b-jet differential cross section as a function of jet pT at s = 1.96 TeV
measured with the CDF detector and data corresponding to a total luminosity of 300 pb1. Taken
from Ref. [50].
the differential cross section as a function of ∆φ is measured with the CDF detector in a
data sample where one b-quark was identified by its decay into a muon and the other one
via displaced tracks. Neither is the cross section shape nor the normalisation correctly
described by the QCD prediction. The data is showing again an excess of the factor of
2. With the new developments the QCD predictions were considerably improved and
therefore also the consistency between data and theory. The CDF measurement [55] of bb̄
dijets, presented in Fig. 3.19 shows remarkable agreement between data and theory for the
dijet cross sections as a function of leading jet ET and invariant dijet mass. Furthermore,
the agreement in the angular correlation which is sensitive to the production processes,
is improved almost all the way down to the region ∆φ   1 when comparing data to the
NLO generator MC@NLO [56]. This is a fixed-order generator with the capability to be
connected to a parton shower generator (Herwig). This measurement has again proven
the importance of including the NLO processes GSP and FEX. Besides these measurements
the angular correlation as a function of rapidity difference and the ratio between the
production of all jets and bottom-flavoured jets is a powerful tool for searching for new
physics coupling to the third generation and probing key properties of the underlying
QCD formalism.
36
d2σ/dYdP  (nb/[GeV/c])
T
3.2 History of bottom measurements and motivating measurements of bb̄ pair production
Figure 3.17: Measurement of the bb̄ angular correlation using a data sample containing two
muons with the UA1 detector with a pT of the higher-pT quark ¡ 6 GeV (left) and ¡ 11 GeV
(right). Data is compared to Opα3sq QCD predictions (MNR) and to the effective QCD Monte-
Carlo (eff. QCD). The predictions are scaled by 30% and 40% respectively for the left and right
plot. The theoretical uncertainty on the NLO prediction is about 40%. Taken from Ref. [51].
10 2
10
0 0.5 1 1.5 2 2.5 3
Figure 3.18: The differential cross section measured with the CDF detector as a function of
δφ between an identified muon from a b-hadron decay and a b-jet selected by displaced tracks for
pµT ¡ 9 GeV, |ηµ|   0.6, EbT ¡ 10 GeV and |ηb|   1.5. The Data corr?esponds to a integrated
luminosity of 15.08 pb1 and was taken at a centre-of-mass energy of s  1.8 TeV. Data is
compared to theoretical Opα3sq QCD predictions. Taken from Ref. [52].
37
3 Heavy flavour production
CDF Run II Preliminary CDF Run II Preliminary
102
Data - Syst. uncertainty
Data - Syst. uncertainty
Pythia (CTEQ5L) Tune A
Pythia (CTEQ5L) Tune A
10 Herwig (CTEQ5L) + Jimmy
Herwig (CTEQ5L) + Jimmy
3
10 MC@NLO (CTEQ6M) + Jimmy
MC@NLO (CTEQ6M) + Jimmy
1
10-1 102 JetClu Rcone=0.4, |η|<1.2JetClu Rcone=0.4, |η|<1.2
ET,1>35 GeV, E >32 GeV
ET,1>35 GeV, E >32 GeV
T,2 T,2
-1
-2 s = 1.96 TeV, L~260 pb
-1 s = 1.96 TeV, L~260 pb
10
50 100 150 200 250 300 350 400 450 0 0.5 1 1.5 2 2.5 3
Di-jet invariant mass (GeV/c2) ∆ φ (rad)
(a) bb̄ differential cross section as a function of dijet (b) bb̄ differential cross section as a function of dijet
∆φ correlation invariant mass
Figure 3.19: The double differential dijet cross section of b-jets performed with the CDF
detector (|η|   1.2). The b-jets are identified via a reconstructed displaced, secondary vertex with
ET?¡ 20 GeV. The data corresponds to a total luminosity of 260 pb
1 at a centre-of-mass energy
of s  1.96 TeV. The shaded area represents the total systematic uncertainty. Taken from
Ref. [55].
38
d2σ/dη dM [pb/(GeV/c2)]
d2σ/dη d(∆ φ) [pb/rad]
4 The Large Hadron Collider and the
ATLAS detector
The Large Hadron Collider (LHC) is a hadron-hadron collider located underground at the
European Organisation for Nuclear Research (CERN) facility in Geneva, Switzerland [57].
The LHC accelerates two hadron beams -either protons or lead ions- in opposite directions
in the accelerator ring about 100 m underground. There are in total six experiments
making use of the hadron beam accelerated by LHC. Each experiment is unique and
specialised to a specific topic in particles or high-energy physics. There are two large
experiments, ATLAS (A Toroidal LHC ApparatuS) and CMS (Compact Muon Solenoid),
which are general-purpose detectors and used to analyse the properties of proton-proton
collisions at high luminosity. Building two experiments with similar abilities ensures
independent cross-confirmation of new discoveries. Besides these experiments, there are
two medium-size experiments, ALICE (A Large Ion Collider Experiment) and LHCb
(LHC-beauty), which are specialised detectors exploring specific phenomena in particle
physics. These four experiments are complemented by the experiments TOTEM (TOTal
Elastic and diffractive cross section Measurement) and LHCf (LHC-forward). They focus
on particles very close to the beam pipe of LHC. All experiments are located underground
around the ring of the LHC.
In this chapter the LHC is briefly discussed, a focus is set on the machine configuration
used in the data taking in 2010 with proton beams. This is followed by a description
of the ATLAS detector collecting data from collision, its trigger and data management
system. Finally, the simulation of the detector response is explained which is used to
generate large-scale MC simulation samples. With these a wide range of physics processes
and scenarios can be studied before events are recorded. In these samples the connection
between the particle’s properties as measured by the detector and the particle which
entered the detector is recoverable. They store the so-called MC truth information of the
particles entering the detector.
4.1 The Large Hadron Collider
The accelerator is hosted by the underground tunnels of the former Large Electron-Positron
collider (LEP). The accelerator ring has a circumference of 26.7 km. The LHC has been
designed to run at a beam energy of 7 TeV corresponding to a centre-of-mass energy of
14 TeV and an instantaneous luminosity of 1034 s1cm2. In vacuum beam pipes bunches
of protons are accelerated. Before a proton bunch is injected into the LHC, it has been
accelerated to 450 GeV by two successive acceleration steps. The number of protons in one
single bunch in the LHC is about 1  1011. Bunches in the LHC travel in radio frequency
buckets which have a minimum distance of 25 ns. The beam energies reached by LHC are
based on superconductive magnets to guide and focus the proton beams in the ring.
The proton bunches can collide at four experiments. A collision is evoked by dipole
39
4 The Large Hadron Collider and the ATLAS detector
magnets bending the beams to cross each other. Quadrupole magnets are used to squeeze
the proton bunches to collide with a transverse size of about 16 µm and a bunch length
of a few centimetres at the centres of the ATLAS and CMS detector. Once stable beam
with colliding bunches is established the experiments start collecting data. At best such
conditions are preserved over several hours.
4.2 The machine parameters in 2010 ATLAS data
Proton-proton collisions at a centre-of-mass energy of 7 TeV which have been recorded
between March and October 2010 are analysed. In Fig. 4.1(a) the time line of the total
integrated luminosity delivered by the LHC is presented. The luminosity is registered
after successful acceleration to the desired beam energy (delivered all) and after the beam
conditions are stabilised (delivered stable). After this last step the experiments start to
record data. In the end a total integrated luminosity of about 45 pb1 has been recorded
by ATLAS. The minimum distance of succeeding proton bunches was at minimum 150 ns
in 2010 data.
60
ATLAS
50 LHC Delivered
ATLAS Recorded
40 Total Delivered: 48.1 pb-1
Total Recorded: 45.0 pb-1
30
20
A B C D E F G H I
10
0
24/03 19/05 14/07 08/09 03/11
Day in 2010
(a) (b)
Figure 4.1: (a) Measurement of the total integrated luminosity of the LHC run period in 2010
taken from Ref. [58]. (b) The peak number of interactions per bunch crossing as measured online
by the ATLAS luminosity detectors [59] taken from Ref. [60].
Due to changes in the machine configurations and detector operation the data taking
period of ATLAS is grouped into different sub-periods labelled with capital letters. In
total data from 2010 is sub-divided into data periods A to I. One effect of the progression
in the commission of machine parameters is the evolution of the maximum number of
simultaneous, inelastic interactions (peak) derived from the online luminosity measurement.
This is presented in Fig. 4.1(b). Until the end of the run period of LHC in November,
the number of simultaneous interactions increased to about 3. The major part of the
luminosity therefore has been recorded with more than one interaction per bunch-crossing.
This increase is caused by the reduction of the transverse size of the beam and the growth
in the number of protons per bunch. Consequently the instantaneous luminosity increased
from 9.31026 to 2.1 1032 s1cm2.
40
TToottaall  IInntteeggrraatteedd  LLuummiinnoossiittyy  [[ppbb--11]]
4.3 The ATLAS experiment
The determination of the luminosity is a combined effort of the accelerator and the experi-
ment [59, 61]. Machine parameters need to be determined and the observed interaction
rate per crossing needs to be measured. The essential machine parameters are the beam
currents and the transverse profiles of the colliding beams. ATLAS measures the observed
interaction rate per crossing with a variety of detectors and several counting techniques.
The beam currents are measured with the help of electric instrumentation. The transverse
profiles are determined using so-called van der Meer scans [62]. For the 2010 data set a
systematic uncertainty of 3.4% has been determined.
4.3 The ATLAS experiment
ATLAS [63] is a general-purpose detector designed to cope with the conditions at the
high-luminosity accelerator LHC and to measure the properties of particles produced in the
proton-proton and heavy-ion collisions at unprecedented energies and luminosities. The
ATLAS experiment follows two goals. Firstly, to perform precision tests of the Standard
Model and secondly, to study physics beyond the Standard Model.
The design of the detector has been driven by the aim at the discovery of new phenomena.
As their appearance may occur in any process and at any energy, this imposes a set of gen-
eral requirements on the performance of the detector. Besides radiation hardness and fast
processing requirements for the LHC detectors in general, these physics goals demand for a
large acceptance in pseudorapidity as well as for a almost full azimuthal angle coverage. A
good charged-particle momentum resolution and a robust track reconstruction are essential
as well as an accurate energy measurement for objects such electrons, photons, jets and
for the global measurement of missing transverse energy. A good muon identification and
momentum resolution are in addition fundamental abilities for such goals. Further details
on the physics program can be found in Ref. [64].
The detector layout of ATLAS is presented in Fig. 4.2. The detector is symmetric in
forward-backward direction with respect to the nominal interaction point. The detector
consists of three sub-systems which are arranged concentric around the interaction point.
The main components are: the tracking system which reconstructs the trajectories of
charged particles, the sampling calorimeters which measure the energy of particles and
the muon system consisting of the muon detectors and a magnet system detecting muons
which originate from the interaction point. Beside these main components, ATLAS has a
number of detectors to perform luminosity measurements. These are placed in the forward
region: LUCID, a LUminosity Cherenkov Integrating Detector, and ALFA (Absolute
Luminosity for ATLAS).
The coordinate system used in this analysis has the origin in the interaction point. The
z-axis is parallel to the beam axis and the x-y plane transverse to it. The positive y-axis
is defined as pointing upwards, the positive x-axis is pointing towards the centre of the
acceleration ring of the LHC. The polar angle θ is measured with respect to the beam pipe
and the azimuthal angle φ is measured with respect to the x-axis. Frequently used are the
quantities rapidity y and pseudorapidity η which are identical in the high-energy limit.
The pseudorapidity is related to the polar angle as follows: η   ln tan θ . The rapidity
2
is defined as y  1 ln E pz , where E denotes the energy and pz is the component of the2 E pz
momentum along the z-axis. Transverse quantities are defined in the x-y plane which is
perpendicular to the beam axis. The detector is sub-divided into three regions: barrel
region, end-cap region and forward region.
41
4 The Large Hadron Collider and the ATLAS detector
The subsystems of the ATLAS detector are discussed briefly in the following, subsequently
the trigger system is presented which selects event for recording upon predefined require-
ments. At last the data management and monitoring system and the tools used to simulate
the detector response are discussed.
Figure 4.2: Cut-away view of the ATLAS detector. The dimensions of the detector are 25 m
in height and 44 m in length. The overall weight of the detector is approximately 7000 tonnes.
Taken from Ref. [63].
4.3.1 The inner detector
The inner detector provides the identification of charged particles and measurements of
the vertex at which the hard interaction took place, so-called primary vertex (PV), and
vertices originating from the decay of long-lived particles, so-called secondary vertices
(SV). The inner detector extends up to a pseudorapidity of |η|   2.5 and is immersed into
a 2 T solenoidal magnetic field which extends over a length of 5.3 m. The overall envelop
of the detector is R   115 cm and |z|   351 cm as can be seen in Fig. 4.3.
The ID consists of three independent sub-detectors. At inner radii, the silicon pixel
detector (Pixel) and the silicon microstrip tracker (SCT) deliver high-resolution tracking
capabilities. At larger radii, the transition tracker comprises many layers of gaseous straw
tubes interleaved with transition radiation material (TRT).
The Pixel detector and the SCT are arranged on concentric cylinders around the beam
axis in the barrel region and in the end-cap region on disks perpendicular to the beam axis.
The innermost layer of the Pixel detector at a radius of about 5 cm carries the name b-layer.
It holds the highest precision of the reconstruction of secondary vertices which can occur
in decays of bottom-flavoured hadrons. The highest precision in the position measurement
are achieved in the barrel are 10 µm in the R-φ plane and 115 µm in z-direction. The Pixel
detector can measure discrete three-dimensional space-points, whereas the SCT detector
measures stereo pairs of microstrip layers. The inherent accuracies from the SCT in the
barrel are 17 µm in the R-φ plane and 158 µm in z-direction.
The TRT which is constructed from straw tubes of 4 mm diameter, only provides R-φ
42
4.3 The ATLAS experiment
Figure 4.3: Cut-away view of the ATLAS Inner Detector. Taken from Ref. [63].
information, for which it has an intrinsic accuracy of 130 µm per straw. The TRT being
at large radii provides continuous tracking to enhance the patter recognition ability as
well as the momentum resolution. The inclusion of transition radiation material allows
an electron identification complementary to the calorimeters. The general goal on the
performance of the track momentum measurement is σp {pT  0.05%pT{ GeV ` 1%.T
The approximate operational fraction of readout channels in the inner detector is larger
than 95.9% for all three sub-systems.
4.3.2 The calorimeters
A schematic view of the ATLAS electromagnetic and hadronic calorimeters is presented in
Fig. 4.4. The calorimetry consists of the electromagnetic (EM) calorimeter which is closest
to the interaction point covering the region |η|   3.2, a hadronic calorimeter covering
|η|   3.2 and forward calorimeters extending to 3.1   |η|   4.9.
The EM calorimeter is divided into a barrel (EMB, |η|   1.475 ) part with two half-barrels
and two end-cap components (EMEC, |η|   3.2) realised as wheels. This calorimeter is
a lead-liquid argon (LAr) detector with accordion-shaped electrodes and lead absorber
plates over its full coverage. The architecture provides full azimuthal symmetry. Each part
has at most three layers in depth. The barrel part of the EM calorimeter has typically a
0.0250.025 granularity in η  φ space whereas the end-cap wheels have coarser lateral
granularities.
In the region of |η|   1.8, a presampler is placed in front of the EM calorimeter to
estimate the energy lost of particles in the material between the interaction point and the
calorimeters.
The hadronic calorimeter surrounds the EM calorimeters. The hadronic calorimeters use
two different technologies. The region |η|   1.7 of the hadronic calorimetry, which consists
of the Tile barrel and Tile extended barrel, is a sampling calorimeter using steel as absorber
and scintillating tiles as the active material. Both divisions are divided azimuthally into
43
4 The Large Hadron Collider and the ATLAS detector
64 modules. The scintillating tiles are oriented perpendicularly to the beam direction in
three layers and staggered in radial depth. The η  φ segmentation is typically 0.10.1.
Between the barrel and the extended barrel there is a gap of about 60 cm for supporting
structures. Scintillators cover this gap in the region 1.0   |η|   1.2. The crack scintillators
are located in the front of the LAr end-caps to cover the transition between barrel and
end-cap calorimeter. In the end-caps the hadronic calorimeters (HEC,1.5   |η|   3.2) use
the LAr technology with absorbers made of copper housed in two independent wheels. It
overlaps partially with the extended barrel tile calorimeters as well as with the calorimetry
in the forward region (|η| ¡ 3.1). Each wheel is divided into two segments in depth
and build of four layers per end-cap. The forward calorimeters (FCal) also use the LAr
technology. They consist of three modules each. The first module uses copper as absorber
and is optimised for electromagnetic measurements, while the other two modules are made
of tungsten absorbers which measure predominantly hadronic interactions. The FCal
calorimeters are cylindrical in shape with a hole in the middle for the beam pipe. The
chosen LAr technology also provides the radiation hardness needed in the proximity of the
beam. The architecture of the calorimeters achieves a seamless coverage and provides the
shielding for the muon system. On average the total amount of active material at the end
of the active calorimetry over the full acceptance region is at least 10 interactions lengths.1
The fraction of operational calorimetry for 2010 is at least 99.5%. The general performance
Figure 4.4: Cut-away view of the ATLAS calorimeter system. Taken from Ref. [63].
goals of the ATaLAS calorimeters using the presented architecture is to achieve a resolution of
σE{E  10%{ E{ GaeV`0.7% in the electromagnetic calorimeter for electrons and photons
and of σE{E  50%{ E{ GeV ` 3% in the hadronic barrel and end-cap calorimeters for
the jet energy measurement.
1The interaction length is the mean path length of a particle before undergoing an interaction which is
not elastic nor quasi-elastic.
44
4.3 The ATLAS experiment
4.3.3 The muon system
The calorimeter system is surrounded by the muon spectrometer presented in Fig. 4.5.
The muon measurement is based on the magnetic deflection of muon tracks in the large
superconducting air-core toroid magnets. The spectrometer is instrumented with separate
trigger and high-precision tracking chambers. Over the range of |η|   1.4, the magnetic
field is provided by a large barrel toroid and for 1.4   |η|   2.7 by³two smaller end-cap
magnets. The bending power is characterised by the field integral Bdl, where B is the
magnetic field component transverse to the muon direction and along the trajectory of
the muon. The barrel toroid provides a bending power of 1.5 to 5.5 Tm and the end-cap
toroids approximately 1 to 7.5 Tm. The performance goal of the muon system for the
momentum resolution is σp {pT  10% at pT  1 TeV.T
The track measurement of muons is performed over the full coverage in three layers. In
Figure 4.5: Cut-away view of the ATLAS muon system. Taken from Ref. [63].
the barrel these layers are arranged cylindrically, in the end-caps vertically. The track
coordinates in the principal bending direction of muons are over most of the pseudorapidity
coverage measured by Monitored Drift Tubes (MDT). At large pseudorapidity the mea-
surement is realised by multiwire proportional chambers, called Cathode Strip Chambers
(CSC). Beside the instrumentation for the precision measurements, the muon trigger system
uses Resistive Plate Chambers (RPC) in the barrel and Thin Gap Chambers (TGC) in
the end-cap regions to provide fast track information. The trigger chambers measure both
coordinates of the track, one in the bending plane and one in the non-bending plane.
45
4 The Large Hadron Collider and the ATLAS detector
4.3.4 The trigger system
At design luminosity and a bunch spacing of 25 ns, the mean number of interactions per
crossing is 23. Consequently, the interaction rate would be approximately 1 GHz and the
data rate 60 TB/s. However, the data recording rate is limited to 200 Hz or equivalent
300 MB/s. The trigger system is therefore designed to reduce the event rate down but
ensuring a maximum event selection efficiency. However, for short time periods in 2010 it
was possible to maintain output rates up to 600 Hz.
The ATLAS trigger system consists of three levels of event selection: Level-1 (L1), Level-2
(L2) and Event Filter (EF). The L2 and event filter together form the High-Level Trigger
(HLT). The L1 trigger is implemented using custom-made hardware components, whereas
HLT is mainly based on software running on commercial computers. The most important
tasks and data rates of the trigger system is illustrated in the schematic overview in
Fig. 4.6. The first trigger stage is L1. The event information processed by L1 comes from
the muon trigger system and from the calorimeters and has a reduced granularity. The
L1 decision must reach the buffers in which events are temporarily stored within 2.5 µs.
The maximum L1 rate which can be handled by the readout system is 75 kHz. Events not
selected by the L1 trigger are automatically removed from the system. The L2 trigger is
seeded from the information from L1, denoted as RoI (Region-of-Interest) and reconstructs
the RoIs with the help of the full granularity of the detector. L2 reduces the event rate
below 3.5 kHz and the L2 decision has to be made in 40 ms. The EF fully reconstructs
and analyses the events accepted by L2 in about 2 s. On these events, it selects events
down to a rate of 200 Hz.
Interaction rate Calo-
rimeter Muon Tracking~1 GHz
Data rate Timeconsumption
60 TB/s
~2.5 μs Level-1 L1<75 kHz Buffers
Readout
~40 ms Level-2 L2~3.5 kHz
Event building
Buffers
Event and
~2 s filter EF EF EF processing
300 MB/s ~200 Hz
  
Data
recording Data recording
Figure 4.6: Block diagram of the ATLAS trigger system.
4.3.4.1 Level-1 trigger
The L1 trigger performs an initial event selection based on the information from the
calorimeters and muon system. The calorimeter trigger at L1 (L1Calo) aims at the identifi-
cation of high-pT objects such as electrons, photons, decay products of τ ’s and jets, as well
46
4.3 The ATLAS experiment
°
as events with large total transverse energy ( ET) and missing transverse energy (E
miss
T ).
The muon trigger at L1 uses signals from the muon trigger chambers (TGC and RPC).
The trigger searches for high-pT muons and applies to identified candidates six different pT
thresholds. The information from both sub-systems are collected in the Central Trigger
Processor (CTP) which stores programmable trigger menus with up to 256 distinct trigger
items. The trigger items can be any combination of requirements on the input data. The
L1 trigger mainly counts multiplicities of trigger objects. In addition the CTP also has
inputs from specialised detectors which mostly cover the forward regions for calibration
and monitoring issues.
The L1 jet trigger: The L1Calo triggers are the main subject for measuring inclusive
jets as done in this analysis. The L1Calo system digitises the calorimeter signals with
a reduced granularity of η  φ = 0.10.1. The smallest objects used to find jets are
η  φ = 0.20.2. The electromagnetic and hadronic calorimeter signals are added and
based on this information a feature search is performed in overlapping, sliding windows.
The jet algorithm identifies ET sums within overlapping windows of sizes of η  φ =
0.40.4, 0.60.6, 0.80.8. ET sums with |η|   3.2 are compared to 8 pre-defined jet
energy thresholds, this comparison avoids by construction double-counting. Such local
maxima fulfilling any defined threshold give rise to a RoI object. Every defined jet
energy threshold in the rapidity region |η|   3.2 is identified with a single jet trigger
item, named L1 JX, where X stands for the trigger threshold in GeV at L1. The L1 JX
item is flagged as passed, if the L1Calo trigger identified at least one jet object with the
corresponding jet transverse energy. In 2010, except for the single jet trigger with the
lowest threshold the sliding window algorithm used a dimension of η  φ=0.80.8. The
jet trigger with lowest jet energy threshold was running with a window size of ηφ=0.40.4.
4.3.4.2 High-level trigger
L2 and EF are comprised of computer farms. As soon as L1 accepted an event, pipeline
memories which hold the data are activated to write out the corresponding event into the
data acquisition system (DAQ). The DAQ system receives and stores this data. L2 then
requests the detailed detector data on identified RoI’s. L2 processes each single RoI. Those
events not fulfilling the L2 criteria are expunged from the system. Each event accepted
is transferred to the event building stage. The reconstructed events are analysed by the
event filter and either are written to mass storage or dropped.
The HLT jet trigger: The detailed calorimeter information available at the HLT allows
for higher precision in the identification of jet objects. The EF jet trigger was not activated
during the data taking period in 2010. The L2 jet trigger was activated starting from
September 2010. The L2 jet reconstruction uses a cone algorithm with R  0.4 iterating
over cells from the RoI region (η  φ = 1.01.0). In 2010 data, the L2 jet trigger did not
apply any corrections to the energy measured in the non-compensating calorimeters. In
correspondence to L1 eight L2 thresholds are defined, in general placed 15 GeV above the
L1 trigger. The L2 jet trigger items are denoted as L2 jX in the following, where X stands
for the jet energy threshold in GeV at L2.
47
4 The Large Hadron Collider and the ATLAS detector
4.3.5 Triggers for physics analyses
All triggers used or mentioned in this analysis are required to be in coincidence with a
beam crossing in which both proton bunches are filled. This is ensured by the signals
from electrostatic beam pick-up devices [58]. To control the trigger rates on each trigger
item prescale factors (PS) can be applied, such that only 1 in N events passing the trigger
requirements is accepted at the corresponding trigger level. A defined trigger menu is
accompanied with a set of prescales to deal with a range of luminosities. Prescales are
auto-generated based on a set of rules taking into account the priorities for each trigger.
The most important triggers are the triggers to select a physics signal. If possible, they
should not be prescaled. However, especially the high rate of QCD events make it
impossible to retain unprescaled single jet triggers with increasing luminosity. The signal
triggers used in this analysis are the single jet triggers at L1 with the thresholds at 5, 10,
15, 30, 55, 75 and 95 GeV and in later data period the single jet triggers at L2 with the
following thresholds at 15, 25, 30, 45, 70, 90 GeV.
Furthermore, two other triggers sensitive to a minimum of detector activity are used. The
first one is based on two scintillator wheels of 32 counters mounted between the ID and
LAr end-cap calorimeter on each side of the interaction point. This sub-system is called
Minimum Bias Trigger Scintillators (MBTS) and their information is analysed at L1. The
trigger item uses the acronym L1 MBTS and requires one single scintillator counter over
threshold on either side. The second trigger uses the measurement of the Zero Degree
Calorimeter (ZDC) covering |η| ¥ 8.2 which is located 140 m away from the interaction
point in the ATLAS detector. It is a tungsten-quartz fiber calorimeter to detect neutral
particles. The trigger item is referred to as L1 ZDC and requires one hit over threshold on
either side.
Besides these physics triggers, there are also supporting triggers. One of them is a random
trigger which is used to collect data for calibration, background and pile-up studies. It is
a hardware based trigger from the random clock in the CTP which generates an accept
signal independent from the event topology.
4.3.6 Data management
The main components of the data acquisition system are: readout, L2 trigger, event
builder, event filter as well as configuration and control. The readout system receives
the data at L1 trigger rate from the on-detector frond-end systems. It stores the data
until a final trigger decision off-detector in readout buffers and sends data fragments
on request to the high-level trigger levels. Events passing all three stages of the trigger
system are moved to permanent storage at the CERN computing centre. In addition to
the storing and movement of data, the DAQ system provides the configuration, control
and monitoring of the hardware and software components which together provide the
data-taking functionality.
The Detector Control System (DCS) is the basis for coherent and safe operation of the
ATLAS detector. This system is interfaced to all sub-detectors and technical infrastructure
of the experiment. It controls, monitors and archives the operational parameters from
systems such as cooling, voltage supply and cryogenics. It also handles the communication
with vital systems outside the ATLAS detector for example to the LHC accelerator.
Besides the control over the hardware, networking and other facilities, it is vital to be able
to diagnose the quality of the data recorded rapidly. Therefore the ATLAS data quality
48
4.4 Monte-Carlo simulation samples
monitoring framework is setup, which incorporates online (during data taking) and offline
(after data taking) data quality operations. For the online monitoring a small fraction of
recorded events are reconstructed promptly and fed into data quality operations in an
express stream. These operations generate data distributions which represent the quality
of the data. On these distributions automated tests are performed and their results are
continuously stored and transferred to the ATLAS operation team.
4.3.7 Detector simulation
The simulation of ATLAS data is performed within the ATLAS simulation framework [65]
using the Geant4 software toolkit [66]. The simulation chain consists of different steps:
generation of the event and immediate decays using the event generators presented in
Section 2.3, simulation of the detector and physics interactions, digitisation of the energy
deposited in the active material of the detector into voltages and currents. The last two
steps are performed by Geant4. The output of the simulation chain into detector signals
is identical to the ATLAS data acquisition system and in turn reconstructed with the same
reconstruction software as data. Simulation samples, which have gone through this full
chain, are referred to as full-simulation samples. The ATLAS detector geometry used for the
simulation, digitisation and reconstruction is built from databases including the information
on the geometry of the system, materials involved, external electromagnetic fields and the
response of sensitive detector components. Geant4 models hadronic interactions with
the detector material using the Quark Gluon String model (QGSP) [67, 68, 69, 70, 71]
for the fragmentation of the nucleus and the Bertini cascade model [72, 73, 74, 75] for
the description of the interactions of hadrons in the nuclear medium [76]. This hadronic
interaction model has been validated with test-beam measurements using a slice of ATLAS
calorimeters [77]. An agreement within a few percent has been found.
The implementation of the ATLAS geometry and the amount of material is to the best
knowledge but causes, due to the imperfect description, systematic uncertainties. The
description of the geometry and amount of inactive materials will be improved with data.
Besides the default description, full-simulation samples are generated with geometries and
material descriptions which knowingly include distortions and changes in the material
budget to investigate the impact of these systematics.
4.4 Monte-Carlo simulation samples
The baseline Monte-Carlo full-simulation sample is generated with Pythia using the
MC10 tune and contains high-pT jets produced via the strong interaction. The default
ATLAS geometry used reflects the current best knowledge. Studies of the material of the
inner detector (in front of the calorimeters) are performed and if necessary systematic
studies are done using full-simulation samples with extra material added. The baseline
MC samples do not contain pile-up because all physical objects measured in data are
corrected for any effect from pile-up.
In order to optimise the production of events according to the steeply falling inclusive
cross section, the phase space is sliced in orthogonal divisions according to the transverse
momentum p̂T allowed in the hard scatter between two partons. The divisions are named
J with a serial number starting at zero. Each division can efficiently be generated with a
small amount of statistics in contrast to the full phase space. Physical distributions are
49
4 The Large Hadron Collider and the ATLAS detector
finally produced by adding all divisions according to weights. These weights are given by
a pre-defined luminosity LJ, the cross section σJ and the available statistics N : w  LJσJJ J .NJ
The pre-defined luminosity is default taken as 100 pb1. The statistical uncertainties on
the MC events are given by the root of the sum of weights squared.
The available statistics and cross sections of the nominal MC samples generated with
Pythia and Herwig++ are summarised in Table 4.1. The luminosity of the MC samples
with Pythia is about 10000 fb1. In Appendix B detailed information on the simulation
samples can be found.
MC dataset p̂T [GeV] Cross section [nb] Number of events
Pythia
J0 8-17 9860100 1398438
J1 17-35 678140 1397889
J2 35-70 40981 1397991
J3 70-140 2193.1 1396590
J4 140-280 87.707 1395487
J5 280-560 2.3502 1391492
J6 560-1120 3.3618102 1394670
J7 1120-2240 1.3744104 1386025
Herwig++
J0 8-17 9613900 397799
J1 17-35 743660 396897
J2 35-70 44307.0 398498
J3 70-140 2357.60 399598
J4 140-280 94.236 396443
J5 280-560 2.58130 397094
J6 560-1120 3.9439102 397597
Table 4.1: Summary of baseline Pythia samples and Herwig++ samples used.
Because the transverse size and position of the beam crossings change per run and period,
the MC samples are reweighted to match the z-distribution of primary vertices in data. In
data, the z-distribution of primary vertices which describes a Gaussian distribution, has a
width of σz  60 mm. The corresponding raw z-distributions measured in data and MC
are plotted as well as the reweighting factor applied to MC can be found in Appendix B
Fig. B.1.
For further systematic checks, pile-up samples which reflect the LHC bunch configuration
and pile-up situation in periods G to I are studied. Details on these samples are included
in Appendix B. The nominal Pythia samples are adapted to data from periods A to F
and is referred to as non-pile-up sample.
50
5 Data reconstruction in ATLAS
The previous chapter has given an overview of the ATLAS detector with an emphasis on
the most relevant subsystems for this measurement. The reconstruction of the physical
objects from data used in this analysis is presented here. The digitised, raw data from
the subsystems are processed in different steps by the reconstruction software. The
reconstruction of jets is discussed including the presentation of the jet calibration scheme
used in ATLAS. The reconstruction of vertices and tracks is explained as well as first
results from measurements on properties critical to the performance of the tracking system
are shown which are of use to this analysis. In the final section details on the reconstruction
of muons are given as they will be relevant for the calibration of b-tagging-algorithms.
5.1 Jet reconstruction
Jet clustering algorithms are the main tools to analyse high-energy partons which fragment
and emerge as collimated sprays of hadrons. There are two types of algorithms: cone and
recombination. They are used to provide from different levels a common view on event
properties. These different levels can be the parton level from fixed-order generators, the
particle level from simulations including parton shower and hadronisation processes or the
calorimeter (detector) level from reconstructed calorimeter information from the ATLAS
detector. Between the parton level and the particle level the reconstructed jets are changed
by hadronisation and underlying-event effects. The hadronisation may cause particles
originating from the parton from the hard scatter not to be clustered into the same jet.
The underlying event adds particles to the event not emerging from the hard scatter and
possibly increases the energy of each jet. In high-luminosity colliders like the LHC, one
single bunch crossing may produce several separate events (several protons interacting
with each other), called pile-up events. The reconstructed jets on calorimeter level are
also effected by pile-up which is dependent on accelerator parameters. Pile-up produces
independent overlapping energy depositions in the calorimeter.
The running of jet algorithms on particle level with stable particles in the MC simulation
determines the set of truth jets, e.g. variables are referred to as ptruthT . The default
definition of stable particles in this analysis includes all particles with a lifetime longer
than 10 ps excluding muons and neutrinos. Besides this definition particle jets can also
be constructed from stable particles and non-interacting (NI) muons and neutrinos. The
additional usage of the non-interacting particles will be stated explicitly and this collection
of jets denoted as NI jets.
In an experiment the measurement of jets starts with the energy depositions in the cells of
the electromagnetic and hadronic calorimeters. From these energy depositions calorimeter
clusters which are considered as input to jet finding are reconstructed. These jets formed
by the calorimeter energy depositions are reconstructed at the electromagnetic scale (EM)
which correctly reconstructs energy in an electromagnetic shower. The energy measurement
of jets is affected by the following detector effects:
51
5 Data reconstruction in ATLAS
 The non-compensating calorimeters of ATLAS only partially measure the energy
deposited by hadrons by nuclear interactions.
 Supporting structures of the sub-detectors and material in front of the calorimeters
cause energy losses.
 The finite calorimeter coverage causes incomplete enclosure of the hadron shower.
 Energy depositions are lost because charged particles are captured by the magnetic
field not reaching the calorimeters and are bent out of the reconstructed jet.
 Signal losses occur due to noise thresholds and inefficiencies in the calorimeter
clustering.
A jet energy calibration corrects for those effects and relates the simulated true energy
Etruth of the stable particles and the reconstructed energy Ereco in the calorimeters. A
truth jet and a reconstructed calorimeter jet are associated with each other if their jet axes
are separated in angular space ∆R by less than 0.3. The jet reconstruction performance is
typically expressed in terms of jet energy resolution and jet energy response. The energy
resolution is given by the width of the distribution of the relative difference between
reconstructed jet energy Ereco and simulated true energy Etruth of the matched truth jet:
fgC 
 G2 B F2
σ fe Ereco  Etruth  Ereco  Etruth . (5.1)
E Etruth Etruth
Analogously the resolutions for dijet mass, rapidity and azimuthal angle can be determined.
The jet energy response R is determined by the ratio of the reconstructed jet energy E
and the matched truth jet energy Etruth:
R  x Ereco y. (5.2)
Etruth
The jet pT response is defined analogous to the jet energy response, related are not the
reconstructed energies but the transverse momenta. In the following section jet algorithms
and the reconstruction of the calorimeter clusters which are input to the jet finding at
detector level are discussed and the jet energy calibration scheme is presented.
5.1.1 Jet algorithms
A jet algorithm takes hundreds of constituents measured in an event and maps them into a
few jets. Jet constituents can be the partons, the particles or the reconstructed calorimeter
clusters. A jet definition contains the algorithm itself, its parameters and a choice of a
recombination scheme. An important property for properly relating experimental results
with theoretical calculations is the infrared and collinear safety of a jet algorithm. The
final set of reconstructed jets should not be sensitive to the addition of an infinitely soft
parton or to the branching of a parton into a collinear pair of partons. This ensures the
cancellation of infrared divergences between real and virtual emission of soft gluons.
52
5.1 Jet reconstruction
5.1.1.1 The cone algorithms
Modern jet cone algorithms [78] are fully defined by the cone radius R, the overlap
parameter f , the number of iterations Npass and a minimum transverse momentum pT,min
in the recombination step. A jet is identified by a cone,defined in angular space (η, φ),
around the direction of the dominant energy flow. To find the direction of the dominated
energy flow some cone algorithms start to search for a seed (different sets of seeds can be
used) defining the starting point, and some ones start without a seed (= seedless). In the
starting point the centre of a cone with radius R is placed. All constituents in an event are
written into a list. The algorithm continues by adding all constituents that lie within the
cone with radius R around the starting point (or the former iterated centre of the cone)
and re-calculates the centre of the ET-weighted cone. This procedure is repeated until
the centres of the cone of iteration k and iteration k  1 are identical and consequently
the cone considered stable. Each stable cone is called a protojet. The constituents in
the stable cone are removed from the event list and the next stable cone is iterated until
no constituents are left or the number of repetitions is bigger than Npass. Then the
recombination step is performed with overlap parameter f and a minimum transverse
momentum. This step is called split-merge procedure and describes the method handling
overlapping jets. Iterative°ly all protojets ordered by the scalar sum of the constituents
transverse momenta p̃T  iPprotojet |pT,i| above a minimum transverse momentum pT,min
which overlap with another protojet are either split or merged. Two protojets are merged
if the fraction of shared transverse momentum of the jet with smaller p̃T is bigger than f .
Otherwise the jets are split and the constituents are assigned according to their distance
to the protojet axis. After this step the protojets defined by stable cones become the final
set of reconstructed jets.
With few exceptions, jet cone algorithms are not infrared and collinear safe.
5.1.1.2 The clustering algorithms
The clustering algorithms use sequential recombination of the constituents parametrised
by a given power of the energy scale in the distance measure. Realisations of such jet
algorithms are the kt [79, 80] and anti-kt [32, 33] algorithms. The anti-kt algorithm used
in this analysis is a kt algorithm with negative power in the distance measurement. Both
jet algorithms are defined by:
2
dij  minpk2p
∆ij
ti , k
2p
tj q , (5.3)R2
diB  k2pti , (5.4)
where ∆2 2ij  pyi  yjq   pφi  φ q2j , kti is the transverse momentum of constituent i and
dij is the distance between constituents i and j and diB the distance between constituent
i and the beam. The algorithm identifies and starts from the smallest of all possible
distances dij between all constituents in the event. As long dij is smaller than diB the
constituents i and j are combined and their four-momenta are added. The clustering stops
if diB   dij and a final jet is created from these constituents. The constituents which
formed a jet are removed from the constituent list and with the remaining constituents
and their distances dij the algorithm is repeated until the constituent list is empty. For
p = 1 Eq. 5.4 describes the kt and for p = -1 the anti-kt algorithm.
The negative sign in the anti-kt algorithm causes the hardest constituents (= constituents
53
5 Data reconstruction in ATLAS
with the highest transverse momenta) to be merged in the first iteration. Subsequently
softer constituents are clustered with the hard ones. This sequential arrangement and
the transverse momentum influencing the distance measure lead to circular hard jets. In
case of close-by jets the harder jet of both stays circular and the nearby soft jet misses a
lens-shaped region as illustrated in Fig. 5.1. In contrast, kt algorithms with a positive sign
in Eq. 5.4 cluster in the first iteration constituents with small transverse momenta and
merge in the end constituents with highest transverse momenta.
So from first principles these two algorithms do not create overlapping jets. In addition
Figure 5.1: This plot is made from a sample of parton-level events generated with Herwig and
clustered with the anti-kt jet algorithm. It illustrates the active catchment area of the resulting
hard jets and nearby soft jets. Taken from Ref. [33].
they have the advantage of infrared and collinear safety. The optimal radius parameter
to reconstruct jets which have a good momentum reconstruction is a compromise. To
gather all objects emerging (created by hadronisation) from the parton initiating a jet
demands a large jet radius. In consequence of a large jet radius the contamination from the
underlying event increases which counteracts a good momentum reconstruction. Taking
both effects into account the optimal jet radius ranges between 0.4 and 0.6 [81]. In this
analysis, anti-kt jets with distance parameter R = 0.4 are used.
5.1.2 The reconstruction of jet constituents from calorimeter cells
The jet constituents chosen here are topological calorimeter clusters [82] with an energy
E ¡ 0 GeV consisting of a group of calorimeter cells. These dynamically-grown topological
clusters aim to reconstruct the energy of a single particle which deposits its energy in
many calorimeter cells. The advantage of this algorithm is the efficient suppression of
the calorimeter noise. The noise in each calorimeter cell is estimated beforehand as the
absolute value of the energy deposited in the calorimeter cell divided by the root mean
square (RMS) of the energy distribution measured in events triggered at random bunch
crossings.
This cluster forming algorithm is designed to imitate a typical shower development and
leads to clusters with a variable number of cells. The algorithm starts from a seed cell
whose signal-to-noise ratio is above a threshold of 4. Iteratively neighbouring cells which
fulfil a signal-to-noise ratio of 2 are added. Finally, all adjacent calorimeter cells are added
to the existing cluster. The building of topological clusters is finished after a splitting
54
5.1 Jet reconstruction
step in which overlapping showers from close-by particles are separated. The individual
particles that initiated the shower may have produce well-separated local maxima in each
topological cluster. Such local maxima are defined as those clustered cells which satisfy
E ¡ 500 MeV and whose neighbouring cells have all less energy. These local maxima are
used as seeds in a new iteration of cluster building and the original cluster is split into
more topological clusters, one for each local maximum found. At the end of this cluster
building process, each shared cell is added to the adjoining clusters with weights, which
are functions of their energies and distances to the centre of the cluster centroids. The
energy of a topological cluster is equal to the energy sum of all clustered cells belonging
to it. The clusters are assigned a mass of zero and the direction is reconstructed from
the absolute energy-weighted averages of pseudorapidities and azimuthal angles of the
constituent cells.
5.1.3 Jet calibration in ATLAS
The jet energy calibration scheme used in this analysis is called the EM+JES scheme [60].
The reconstructed jets in this analysis have this energy calibration applied. This simple
scheme corrects the jet energy EEM derived at the electromagnetic scale with the help
of correction factors from MC simulation, which are a function of the jet energy and
pseudorapidity. This calibration scheme as simple as it is allows a direct evaluation of
the systematic uncertainties and is referred to as the jet energy scale uncertainty. The
calibration consists of three steps:
Correction due to pile-up: The additional energy reconstructed in jets arising from
pile-up is corrected by subtracting an average amount of energy from each jet. This
energy correction is calculated with the help of two quantities: the average number of jet
constituents xNconstituentsy and the average additional energy Cpileup in each jet constituent.
The latter quantity is a function of the number of reconstructed primary vertices, NPV, the
detector region encoded in η and the bunch spacing. The number of reconstructed primary
vertices is a measure of the number of additional proton-proton interactions in the same
bunch crossing. The spacing between consecutive filled bunches is considered because
events from the previous bunch crossing may have impact on the jet measurement in the
subsequent bunch crossing. This additional energy is measured directly in events selected
by the L1 MBTS trigger from the average energy deposited in a non-noise-suppressed jet
constituent with respect to events with one primary vertex and no additional energy. The
average number of jet constituents which indicates the jet area is measured as a function
of rapidity in data triggered by the single jet triggers. With the help of both quantities
the additional energy in a jet is given by:
Ecorrected measuredT  ET  xNconstituentspηq y CpileuppNPV, η, bunch spacingq. (5.5)
For jets with |y|   2.1 the pile-up correction increases with the number of reconstructed
primary vertices (NPV  2, ..., 5) from approximately 0.2 GeV to a maximum of 2 GeV.
Vertex correction: Calorimeter jets and their constituents are reconstructed using the
geometrical centre of the ATLAS detector as the default. After the event reconstruction
in each event the jet four-momenta are corrected by adjusting the coordinates of each
topological cluster to point to the vertex of the primary hard scatter. The kinematic
observables of the clusters are re-calculated and the jet direction is re-defined. This
55
5 Data reconstruction in ATLAS
correction improves the angular resolution.
Jet energy and direction correction: The final step of the calibration scheme is to
restore the reconstructed jet energy to the mean energy of the truth jet and to correct
direction biases in the jet reconstruction. These may arise from poorly instrumented
detector regions measuring a lower energy than better instrumented ones. This non-
uniformity in the energy measurement biases the direction reconstruction of topological
clusters. This η-correction is derived with the help of simulated events calculating the
shift in the η reconstruction ∆η  ηtruth  ηreco. The size of this correction on the jets
is very small (∆η   0.01) for most of the detector regions except the transition regions
(∆η   0.03) at around |η|  0.8 and |η|  1.3.
The energy calibration is derived from MC simulations on all isolated calorimeter jets
that have an isolated matching truth jet. The isolation of a jet is fulfilled if there is no
other jet with p ¡ 7 GeV within ∆R  1. The EM-scale energy response R  EEMT forEtruth
each matched jet pair is measured in bins of the truth jet energy Etruth and uncorrected
calorimeter jet detector pseudorapidity. The response in each (Etruth,η)-bin is fitted by
a Gaussian distribution to determine the peak position xRy and the average calorimeter
jet energy xEEMy. For every detector region a function F pEEMcalib q of the jet response
is obtained by fitting the points (xEEMy, xRy). This fitted function then determines the
correction factor to relate the measured jet energy in the calorimeter to the hadronic scale:
EM
EEM JES  E  Ep q| . (5.6)F EMcalib E η
The values of the correction factor 1F EMcalibpE q| decrease with higher jet pT and range fromη
about 1.7 for pT = 40 GeV in the central region to 1.2 for pT = 1000 GeV in the end-cap
region. They are illustrated in Fig. D.1 in the appendix. Final jets calibrated with the
EM+JESscheme are saved and input to physics analysis if they fulfil pT ¡ 7 GeV which
approximately corresponds to pEMT ¡ 4 GeV. Information of soft jets below this kinematic
cut are not available. From now on, reconstructed jet quantities, e.g. pT, use implicitly
the EM+JES calibration.
5.2 Tracking
The reconstruction of trajectories from charged particles is the main ingredient to identify
the hard scatter and long-lived hadrons decaying in a significant distance from the hard
scatter. Charged particles produced in a hard scatter emerge from one interaction point.
Their trajectories point back to this point of origin which is called the primary vertex. For
example a decay vertex from a heavy flavour hadron is called a secondary vertex (SV). The
reconstruction of such secondary vertices is described in Section 6.2. A charged particle
traversing the inner detector generates hits along its flight path in each sub-detector. From
these hits tracks are reconstructed and from the final set of tracks primary vertices are
formed.
There are several effects degrading the tracking performance. Due to the high activity
in high-energy proton-proton collisions there may be ambiguities in associating a hit to
a track. The alignment of the inner detector components is crucial for track finding as
well as a realistic description of the material along the flight paths of the particles. A
systematic uncertainty on the modelling of the track reconstruction in simulation is caused
56
5.2 Tracking
by the presence of unaccounted material leading to additional hadronic interactions.
In the following sections, the reconstruction of tracks and of primary vertices is outlined.
In the last section studies on the performance of the ATLAS tracking system with 2010
ATLAS data are presented.
5.2.1 The tracking algorithm
The default tracking algorithm [83] starts from the inner silicon sub-detectors and is
called inside-out track reconstruction. In a pre-processing step the hit information of
the Pixel and SCT detectors are transformed into three-dimensional space-points. These
space-points are processed for seeding the track candidate search. Track seeds are formed
from a combination of space-points. Based on these track seeds, track candidate creation
is started. The track candidate creation involves track fitting and is performed on the hit
information itself because the formation of the space-points in the SCT has an inherent
uncertainty. The located seeds provide a directional information from which the detector
elements for the further search of associated hits to this track candidate are determined.
Successive hits along the track candidate are simultaneously added and fitted by a fitter
formalism [84] to help to predict the next expected hit position.
The next step in the track reconstruction involves the solving of ambiguities between
different tracks. Many track candidates share hits, are incomplete and may even describe
fake tracks. Therefore quality criteria need to be established to rank each track candidate.
Track candidates are refit using a refined reconstruction geometry with a more detailed
material description. Then these are classified by a scoring strategy making use of different
characteristics of a track. In general, missing and shared hits between tracks result in a
downgrading of these tracks and hits are weighted according to the precision of the sub-
detectors. Shared hits are assigned to the track with the higher score, while the remaining
track is refit disregarding this hit. Below a certain quality criterion reconstructed tracks
are excluded from further processing.
Finally, the track reconstructed from the silicon sub-detector information is extended
into the TRT. Two steps are necessary for this: finding compatible sets of TRT hits and
a track refit with the full set of hit information from all three sub-detectors. Given a
track candidate from the Pixel and SCT detectors, the track is extrapolated into the TRT
detector volume. This extrapolation is done over a large distance and within the magnetic
field and is therefore subject to large uncertainties. Therefore the search window for TRT
points which are collected for further processing is large. For an associated extension the
track is refit allowing to change the initial silicon track. The original and the new track
are compared using the quality score strategy. The silicon track is kept in case the quality
score is lower for the extended version. Finally, all tracks above a certain minimum ptrackT
are saved. In case of this analysis, all tracks with at least ptrackT ¡ 100 MeV are kept.
5.2.2 Primary vertex finding
The reconstruction of the interaction vertex is based on the reconstruction of charged-
particle tracks as presented in the previous section. The reconstruction of primary vertices
(PV) is done in two steps [85]: a primary vertex finding algorithm identifying vertex candi-
dates and associated reconstructed tracks and a vertex fitting algorithm for reconstructing
the vertex position and the corresponding error matrix. With the help of an identified
primary vertex the associated tracks are refit constraining their point of origin. Tracks
57
5 Data reconstruction in ATLAS
entering the primary vertex reconstruction are subject to the following quality requirements:
 ptrackT ¡ 150 MeV,
 |dBS0 |   4 mm,
 σpdBS0 q   5 mm,
σpzBS 0 q   10 mm,
 at least 4 hits in the SCT detector,
 at least 6 hits in the silicon detectors.
Here dBS and zBS0 0 denote the transverse and longitudinal impact parameters respectively
of tracks with respect to the centre of the luminous region, so-called beam-spot (BS), with
their corresponding uncertainties σpdBS0 q, σpzBS0 q from the track fit. A detailed description
of the beam-spot determination can be found in[86]. Impact parameters are defined by
the distance between the point of closest approach to a point of interest in the transverse
plane and along the z-axis for the transverse and longitudinal impact parameter respec-
tively. The impact parameters are shown in Fig. 5.2 with respect to the primary vertex.
The sign of zPV0 is given by the distance between zPV and zSV in the ATLAS coordinate
system. The sign of dPV0 is given by the geometrical relation between these unit vectors
signpdPV0 q  pp̂ d̂q  L̂, where p̂ is the unit vector pointing in direction of the transverse
momentum of the track, d̂ is the unit vector pointing from the primary vertex to the
point of closest approach and L̂ the unit vector in direction of the angular momentum
of the particle’s trajectory in the magnetic field. The selection cuts based on the impact
parameters are meant to remove a large fraction of tracks originating from secondary
interactions. The luminous region is on a regular basis determined during data taken
by the distribution of the primary vertices reconstructed and is archived in a database.
In the final reconstruction this recorded information is utilised to calculate the impact
parameters.
The vertex finding starts by selecting all tracks compatible with the interaction region and
the quality criteria listed above. The iterative vertex finding approach then continues by
searching for a vertex seed. A vertex seed is a global maximum in the distribution of z coor-
dinates of the tracks with respect to the point of closest approach to the beam-spot centre.
The vertex position is determined by the adaptive vertex fitting algorithm [87] taking into
account the seed and the associated tracks around it. This fitter is a robust χ2-based
fitting algorithm which handles outlying tracks by down-weighting their contribution to
the vertex progressively. Tracks incompatible with the vertex by more than approximately
7σ in transverse and longitudinal directions are able to be used as new vertex seeds. This
procedure is repeated until no new vertices are found or the list of reconstructed tracks
is empty. The measurement of the beam-spot constrains the available seeds and reduces
the number of outliers in the reconstruction of the primary vertex. Consequently the
constraint on the primary vertex to be in agreement with the beam-spot reduces beam-
related background and backgro°und from cosmic particles. The reconstructed vertices are
ordered in descending order by pptrackT q2, which is strongly correlated to the total number
of tracks at the vertex. The hard-scatter vertex is distinguished from soft interactions by
the higher average ptrackT of its tracks and correspondingly the primary vertex at top of the
list is selected.
58
5.2 Tracking
Jet axis
Jet axis
a) b)
y
Track Track
Secondary Secondary
vertex vertex
θ
d
0 zPVsinθ0  
Beam x z zSV PV z
Primary vertex
zP V = z -z
0 PV SV
  
Figure 5.2: Definition of the impact parameters with respect to the primary vertex: a) transverse
and b) longitudinal impact parameter.
5.2.3 Measurements of tracking performance
This section presents a selection of measurements on the performance of the tracking system
relevant to this analysis. The track and vertex reconstruction depend on correct alignment
information, detector geometry and material description which makes a thorough check on
their description necessary. These performance studies which began with the measurement
of cosmic particles improved the understanding of the detector and consequently the
tracking performance. The first measurement of tracking properties in collisions was done
with data selected by the minimum bias triggers [88]. The tracks from charged particles in
the kinematic range |η|   2.1 and ptrackT ¡ 500 MeV are selected in a data sample triggered
by the single-arm minimum-bias trigger and ensured data quality. The events are required
to have one primary vertex consistent with the beam-spot and at least one good quality
track. A good track needs to satisfy the following criteria:
 ptrackT ¡ 500 MeV,
 a minimum number of silicon detector hits,
 transverse and longitudinal impact parameters calculated with respect to the event
primary vertex |dPV|   1.5 mm and |zPV0 0 |  sin θ   1.5 mm.
The impact parameter cuts are used to remove secondary interactions mostly due to
hadronic interactions, photon conversions and decays of long-lived particles. Fig. 5.3 shows
that the average number of silicon hits on tracks as a function of pseudorapidity is well
described by the simulation.
The following performance study [90] has grown more mature and uses data-driven methods
to derive systematic uncertainties. It extended the considered tracks to the full acceptance
range of the inner detector of |η track|   2.5 and lowered the ptrackT threshold cut for the
track reconstruction. This updated study has refined their track selection cuts, for details
refer to [90]. The track reconstruction efficiency was estimated from simulation and the
59
5 Data reconstruction in ATLAS
(a) (b)
F?igure 5.3: The number of hits measured in the silicon detectors with the ATLAS detector at
s = 7 TeV: a) Pixel, b) SCT is compared to Pythia prediction with the older ATLAS tune
MC09 [89]. The data corresponds to an integrated luminosity of 6.8 µb1. Taken from Ref. [88].
level of agreement between data and simulation was determined to derive a systematic
uncertainty. This efficiency is defined as
Nmatchedpptrack, ηq
 pptracktrack T , ηq  reco Tp , (5.7)N ptrackgen T , ηq
where ptrackT and η are generated particle properties. N
matched
reco is the number of recon-
structed tracks matched to a generated charged particle and Ngen is the number of generated
charged particles as a function of ptrackT and η. The association between a reconstructed
track and a generated charged particle uses a matching algorithm in angular space with
matching parameter ∆R   0.15. The resulting track reconstruction efficiency is shown
in Fig. 5.4. The rise of the efficiency with increasing ptrackT is due to an indirect minimum
ptrackT requirement on the tracks and a minimum number of detector layers, which are
passed through, coming from the minimum numbers of silicon hits allowed.
The imperfect description of the detector, in particular the material budget, leads to the
main systematic uncertainty which needs to be considered.
Two data-driven methods are used to determine the agreement between simulation and
data concerning the material distribution [90]. The first method reconstructs the invariant
mass of K0s mesons decaying into oppositely charged pions, the second compares track
lengths in data and simulation. For the most accurate description both methods are
combined. The first method is most sensitive at small radii, while the other method
probes the detector volume beyond the Pixel detector. The comparison of the data to MC
simulations with different material budgets determines the level of unaccounted material
in the inner detector.
The track length method validates the material description in MC by studying the rate
at which tracks which were found in the Pixel detector can be extended into the SCT
detector. The comparisons between MC simulations with different material descriptions
and data indicate the level of imperfection of the material description beyond the Pixel
detector.
The considered decay products of K0s mesons undergo ionisation and multiple scattering
when traversing the inner detector. The reconstruction of the invariant mass (width and
60
5.2 Tracking
?
Figure 5.4: The track reconstruction efficiency as a function of ptrackT for s = 7 TeV is
derived from non-diffractive (ND) minimum bias MC 1. The efficiency is shown for the following
phase space cuts: the number of charged particles in the event n ¥ 2, ptrackch T ¡ 100 MeV and
|η track|   2.5. The statistical errors are shown as black lines, the total errors as green shaded
areas. Taken from Ref. [90].
mean) as a function of radius in data and MC should have been equally biased by ionisation
and hadronic interactions. The peak and the width of the invariant mass spectra is fitted
and the fitted K0s mass relative to the nominal sample as a function of radius is determined.
Fig. 5.5 shows the resulting behaviour of the fitted mass ratio with respect to the nominal
sample. In data the mass is in very good agreement with the nominal simulation sample
for small radii, but with increasing radii data exhibits a negative slope.
The agreement between data and nominal MC simulation varies in each detector region.
Minimum Bias Events ( s=900 GeV)
500
MC (nominal) ATLAS Preliminary
499 MC (10%)
MC (20%)
498
497
496
495
494
|η| < 1.5
493
3
10 102 10
Radius [mm]
Figure 5.5: Fitted K0s mass ratios as a function of the decay radius for data an?d various MC
simulations with Pythia relative to the nominal MC sample. Data was taken at s = 900 TeV
and corresponds to the full data set from 2009 LHC running (400000 events). The K0s candidates
are required to have a decay radius within the bin boundaries. The two pions are not allowed to
have silicon hits before the decay radius and at least one silicon hit in every following layer. The
marker’s errors are statistical only. The vertical dashed lines indicate radial positions of material
in the Inner Detector barrel. Taken from Ref. [91].
Whereas the barrel is very well described, the transition region shows small deviations
1Non-diffractive (soft inelastic) processes are modelled from low-pT lowest-order perturbative QCD 2 Ñ 2
scatters.
61
K0 mean [MeV]
S
Beam Pipe
Pixel Layer-0
Pixel Layer-1
Pixel Layer-2
SCT Layers
5 Data reconstruction in ATLAS
in both methods which are covered by 10% uncertainty (∆10%) on the Pixel and SCT
detector material. In the K0s invariant mass measurement the unaccounted material
between the Pixel and SCT detector is described by the data over MC ratio of the track
length measurement (∆track length ratio). The end-caps show fairly high deviations in the
track length method which is accounted for by a 20% increase in material in the gap
between Pixel and SCT detector (∆20%gap) in combination with the 10% uncertainty on
the Pixel and SCT detector material. The deviations in the track reconstruction efficiency
∆material between the nominal and MC samples with extra material, which show the best
agreement between data and MC, are taken as systematic uncertainty:
∆materialpK0s q ∆10% `∆track length ratio, (5.8)
∆materialptrack lengthq ∆10%  ∆20%gap. (5.9)
The final systematic uncertainty selected is given by the more conservative choice between
these data-driven methods, and is summarised in Table 5.1. With these methods the
systematic uncertainties arising on tracking related observables are obtained. The resulting
systematic uncertainties are given in Table 5.1.
Systematic uncertainty on tracking efficiency
|η track|   1.3 1.3   |η track|   1.9 1.9   |η track|   2.3 2.3   |η track|   2.5
2% 3% 4% 7%
Table 5.1: Summary of the tracking efficiency systematics due to material interactions for
tracks above 500 MeV [90].
5.3 Muon reconstruction
This section describes briefly the reconstruction of muons originating from semi-leptonic
decays of b- and c-hadrons, so-called soft muons. The term soft refers to the rather low
momentum of these muons compared to those coming from the decay of heavy particles
(such as Z or W ). More details on the general muon reconstruction can be found in [92].
Soft muons are reconstructed with the help of both the muon system and the inner detector.
The combination of these two systems improves the momentum resolution and reduces
the mis-identifications of muons. Muons in this collection are reconstructed using two
complementary methods:
 Combined muon: a standalone muon spectrometer track is associated to an inner
detector one on the basis of a χ2 match. The combined track parameters are
determined from either a statistical combination of both tracks or a complete refit
of the full track.
 Tagged muon: a reconstructed inner detector track identifies a tagged muon if the
track extrapolated to the muon spectrometer, using detailed information about the
material and the magnetic fields, can be associated with a track segment in one or
more muon chambers.
62
5.3 Muon reconstruction
The combination of these methods increases the performance of the muon identification at
low pT because the latter algorithm identifies muons which do not have enough energy to
cause hits in the full spectrometer. The reconstruction efficiency for combined muons in
2010 ATLAS data is about 98%.
For the reconstruction of the muons two chains are available:
 Chain 1: the reconstruction begins locally in each muon chamber by the search for
straight line track segments in the bending plane pointing to the centre of ATLAS.
Track segments are extended to the next station to build search roads. A minimum
of two track segments in different muon stations are required to be able to form a
muon track. These tracks can be statistically combined to an inner detector track
using matching cuts to build a combined track. Unused segments found by this
process are used to tag extrapolated inner detector tracks and so to reconstruct
tagged muons.
 Chain 2: on the full muon spectrometer a track pattern recognition algorithm
performs independent transforms on both the bending and non-bending projections.
The segment finding is seeded from patterns in the two projections. A track candidate
is formed from segments compatible with a curved track and belonging to the same
pattern. Segments from the outermost chambers seed a track fit with all segments
in the next chambers closer to the interaction point. Combined muons are obtained
by fitting the full track consisting of the standalone muon track and the associated
inner detector track. Tagged muons can be found with the help of all track segments
build by the pattern recognition process.
63

6 Bottom-tagging in ATLAS
The identification of jets with bottom-flavours (b-tagging) takes advantages of several
properties of bottom-hadrons as discussed in Section 3.1.4. The identification relies on
the precise measurement of charged tracks in the inner detector of ATLAS and on the
reconstruction of muons in the muon spectrometer. The relevant jet information for
b-tagging purposes is the jet direction. Only jets fulfilling pT ¡ 15 GeV and which are
within the inner detector acceptance (|η|   2.5) are subject to the b-tagging algorithm.
These jets are called taggable jets. The strategy of labelling jets in MC simulation to be a
b-jet, c-jet or light jet was presented in Section 3.1.
6.1 Bottom-tagging algorithms
Each b-tagging algorithm produces a weight distribution where the heavy flavours are
visually separated from other flavours. In the simplest case the b-jet identification is an
one-dimensional selection cut along this distribution. After this selection cut the remaining
jets are called b-tagged. To estimate the performance of a b-tagging algorithm the following
quantities are defined:
The b-tagging efficiency btag is defined as the fraction of taggable jets labelled as b-jets
which are tagged by the b-tagging algorithm under study:
 #pb-jet&b-taggedqbtag #p . (6.1)b-jetq
The b-tagging rejection Rbtag is defined as the inverse of the mistag rate mistag which
is given by the fraction of taggable jets not labelled as b-jets which are tagged by the
b-tagging algorithm under study:
1   #pno b-jet&b-taggedqmistag
Rbtag #p . (6.2)no b-jetq
The mistag rate of light jets light (of c-jets c) is given by the fraction of taggable light-jets
(c-jets) which are tagged by the b-tagging algorithm under study:
 #plight-jetpc-jetq&b-taggedqlightpcq #plight-jetp qq . (6.3)c-jet
The b-tagging purity fpur is defined as the fraction of b-tagged-jets which are also
labelled a b-jet:
 #pb-jet&b-taggedqfpur #p . (6.4)b-taggedq
These three performance estimators are dependent on the data sample used and on
the kinematic cuts applied. The performance estimated from simulation of b-tagging
algorithms is strongly depended on the MC generator, its incorporated heavy flavour
65
6 Bottom-tagging in ATLAS
description and on the detector description. Therefore the b-tagging algorithms require a
dedicated data-driven calibration. Based on this calibration each analysis has to obtain
their b-tagging efficiency and purity.
The spatial algorithms, the secondary vertex tagger and the impact parameter taggers,
which use tracks and subsequently reconstructed vertices, are the most powerful ones and
the first choice for an analysis. The soft lepton taggers are very important because their
overlap to the spatial algorithms is minimal. The most important realisations for this
analysis of a secondary vertex tagger, impact parameter tagger as well of the soft lepton
tagger are discussed in the following. Their usage is preferred due to their robustness,
simplicity and on an uncomplicated validation with data. This is because the algorithms
are based on well-measurable distributions and do not involve complicated mathematical
methods. Consequently their performance is limited. However, the usage and validation
of more advanced techniques is on-going. Among these techniques are the combination of
individual taggers and the extension to two-dimensional discriminant distributions and
the validation of a multivariate approach and a neural network.
6.2 Secondary vertex tagger
The b-tagging algorithm discussed in this section is the main tool in this analysis. It
reconstructs the displaced vertex from a b-hadron decay with the help of tracks which are
significantly displaced from the primary vertex [93]. A heavy-flavour hadron decay within
a jet and the resulting secondary vertex with its tracks is shown in Fig. 6.1. This secondary
vertex is reconstructed from tracks associated to a jet with an angular matching requiring
∆R   0.4. Tracks, which can be associated by ∆R   0.4 to two jets, are assigned to
the closest one. Tracks which fulfil the criteria listed in Table 6.1 are used in the vertex
finding. These selection cuts are different to other impact parameter based taggers due to
a SV0-specific optimisation.
The reconstruction of the secondary vertex starts by building all two-track vertices
Selection cuts
ptrackT ¡ 0.5 GeV
|dPV0 |   2 mm
|zPV0 sin θ|   2 mm
σpdPV0 q   1 mm
σpzPV0 q   5 mm
χ2/DoF   3
Number of Pixel hits ¥ 2
Number of SCT hits ¥ 4
Number of silicon hits ¥ 7
Table 6.1: Track selection requirements used by the SV0 tagging algorithm. dPV0 and z
PV
0
are the impact parameters of the track in the transverse plane and the longitudinal direction
respectively. They are derived with respect to the reconstructed primary vertex. The χ2/DoF
denote the property of the track fit. DoF stands for the number of degrees of freedom.
66
6.2 Secondary vertex tagger
Jet Axis
Secondary Vertex
Decay Length
Track
Primary Vertex
Impact
Parameter
Figure 6.1: Illustration of a heavy flavour hadron decay within a jet. The distance between
a secondary vertex (SV) and the primary vertex (=decay length) indicates the presence of a
long-lived particle. The secondary vertex is reconstructed from tracks which are significantly
displaced from the primary vertex. Taken from Ref.[93]
considering only tracks not compatible with the primary vertex by requiring the three-
dimensional impact parameter significance L{σpLq with respect to the primary vertex
to be bigger than 2.3. In addition the sum of the impact parameter significance of the
two tracks has to be greater than 6.6. Furthermore the quality of the vertex fits must be
good (χ2   4.5) and the vertices must all be incompatible with the primary vertex.The
remaining two-track vertices are probed whether their mass is consistent with a K0s meson,
a Λ0 baryon or a photon conversion or whether their radius is consistent with the radius
of one of the three Pixel detector layers (material interactions). If any of the former
criteria holds the vertex is removed. Finally for each jet, the tracks from the two-track
vertices, which survived the selection cuts, are combined and fitted to a single secondary
vertex. Iteratively the vertex fit removes the track with the largest χ2 contribution until
the fit probability of the vertex is greater than 0.001, the vertex mass is less than 6 GeV
and the largest χ2 contribution from any track is 7 or less. Tracks which failed the
selections during the building of the vertices are re-considered in the vertex fit and if
suitable re-incorporated into the selection. The resulting discriminatory variable, called
SV0 weight, is the three-dimensional signed decay length significance LSV{σpLSVq of the
secondary vertex. The sign of LSV{σpLSVq is given by the sign of the projection of the
decay length vector on to the jet axis. The uncertainty σpLSVq is the quadratic sum of the
uncertainty from the secondary vertex fit and the uncertainty from the primary vertex.
A jet is considered b-tagged if it contains a secondary vertex, reconstructed with the SV0
tagging algorithm, with a SV0 weight greater than 5.85: this is the operating point that
yields a 50% b-tagging efficiency in simulated tt̄ events. The SV0 weight distribution of
the leading jets with pT ¡ 40 GeV and |y|   2.1 in simulation using a QCD dijet sample
is shown in Fig. 6.2. The single contributions from different flavoured jets are drawn
stacked on top of each other. This tagging-algorithm is well-understood and robust. Its
performance is decreased due to tracking related effects like material interactions and
pattern-recognition problems near the jet core where the track density is the highest.
67
6 Bottom-tagging in ATLAS
×103
1000 Pythia: b-jets
Pythia: c-jets
Pythia: light jets
800 MC stat. unc.
600
400
200
0
-50 -40 -30 -20 -10 0 10 20 30 40
SV0 weight
Figure 6.2: The SV0 weight which is identical to the three-dimensional signed decay length
significance LSV{σpLSVq is shown obtained from Pythia QCD simulation. Events with at least
two jets fulfilling pT ¡ 40 GeV and |y|   2.1 are selected. Jets originating from b-hadrons
compared to other other flavours tend to have larger significances. The single contributions are
drawn stacked on top of each other.
6.3 Impact parameter tagger
The jet probability b-tagging algorithm (JetProb) [94] uses the transverse impact parame-
ters of all tracks fulfilling certain quality cuts. This algorithm will be used to investigate a
possible systematic due to the choice of the b-tagging algorithm. For b-tagging purposes
the sign of the impact parameters of tracks associated to a jet are re-calculated to reflect
the lifetime. The transverse and longitudinal impact parameters are shown in Fig. 5.2.
In context of flavour tagging the sign of these are determined by the sign of the scalar
product of the jet direction vector and the vector pointing from the primary vertex to
the point of closest approach. All reconstructed tracks are subject to resolution effects.
The experimental resolution produces positive and negative signs randomly distributed
for tracks originating from the primary vertex. But long-lived particles produced in the
primary vertex tend to generate decay products with positive signs.
The tracks are associated to a jet with a pT-dependent angular matching in ∆R   A(pT).
5
The association cut is given by A(p )  0.239 e1.221.6410 pT{ MeVT . The functional form
is optimised to associate the majority of decay products even at low jet pT and to reproduce
the collimation of jets with increasing jet pT. Consequently the cut is loosened for low pT
due to the more isotropic behaviour of the decay products and tightened for increasing
pT. For this b-tagging algorithm an accurate measurement of the impact parameters is
essential. Therefore, the track selection includes the requirement that each selected track
contains a hit in the innermost tracking layer, the so-called b-layer. Due to its small radius,
it provides the most valuable tracking information to derive the impact parameters. The
tracks associated to a jet are selected if they fulfil the criteria listed in Table 6.2. In
addition two-track vertices formed from these selected tracks (cf. Section 6.2) compatible
with long-lived particles, photon conversions and material interactions are identified and
the corresponding tracks rejected. The signed transverse impact parameter significance is
shown in Fig. 6.3 for all tracks considered by the JetProb tagging algorithm obtained from
Pythia simulation for light, c- and b-jets. The tagging algorithm compares all signed
impact parameter significances d0{σpd0q of the selected tracks in a jet to a resolution
function R for prompt tracks. In order to calculate the probability Ptrack for one track i
68
NNuummeerr  ooff  jjeettss  ((aarrbbiittrraarryy  uunniittss))
6.3 Impact parameter tagger
Selection cuts
ptrackT ¡ 1 GeV
|dPV0 |   1 mm
|zPV0 sin θ|   1.5 mm
Number of Pixel hits ¥ 2
Number of b-layer hits ¥ 1
Number of silicon hits ¥ 7
Table 6.2: Track selection requirements used by the impact parameter tagging algorithm. dPV0
and zPV0 are the impact parameters of the track in the transverse plane and the longitudinal
direction respectively. They are derived with respect to the reconstructed primary vertex.
108 Pythia: b-jets
Pythia: c-jets
107 Pythia: light jets
MC stat. unc.
106
105
104
103
102
10
-140 -30 -20 -10 0 10 20 30 40
d0/σ(d )0
Figure 6.3: The signed transverse impact parameter significance d0{σpd0q of all tracks considered
by the JetProb tagging algorithm in simulated QCD events obtained from Pythia. The jets are
selected with the requirements pT ¡ 40 GeV and |y|   2.1. The single contributions are drawn
stacked on top of each other.
that its origin is the primary vertex, the» following quantity is calculated:|di i0{σ pd0q|
Ptrack i  Rpxqdx. (6.5)
8
The resolution function is determined from experimental data with the help of tracks with
negative impact parameters, which are dominated from light-flavour jets and reflect the
experimental resolution smearing of the impact parameter. The negative side of the signed
transverse impact parameter distribution is symmetrised around zero and fitted to build
the resolution function R. The jet probability Pjet, which discriminates between b-jets
and light jets, is the combination of individual probabilities Ptrack of the N tracks with
positive transverse impact parameters and is given as follows:
N1̧
  p ln P
k
0q
Pjet P0 , (6.6)
 k!k 0
where
N¹1
P0  Ptrack i . (6.7)
k0
69
AArrbbiittrraarryy  uunniittss
6 Bottom-tagging in ATLAS
The individual track probabilities Ptrack are multiplied to form the product P0. The jet
probability Pjet, called JetProb weight, is calculated from the product P0 weighted by a
factor dependent on the track multiplicity. The JetProb weight reflects the probability that
a jet contains no tracks originating from a decay of a long-lived particle. A light jet would
correspondingly have a probability near 1. The distribution  log10pJetProb weightq of
the JetProb tagging weight is shown in Fig. 6.4. In this parametrisation the light jets are
accordingly localised around zero. With the JetProb algorithm jets are b-tagged if they
fulfil  log10pJetProb weightq ¡ 3.25. This is the operating point for the JetProb tagging
algorithm that yields a 50% b-tagging efficiency in simulated tt̄ events. This operating
point is compatible with the SV0 weight cut at 5.85.
Pythia: b-jets
Pythia: c-jets
7 Pythia: light jets10 MC stat. unc.
106
105
1040 1 2 3 4 5 6 7 8 9 10
-Log (JetProb weight)
10
Figure 6.4: The JetProb weight as a function of  log10pJetProb weightq shown of the leading
jets with pT ¡ 40 GeV and |y|   2.1 in dijet events are shown obtained from QCD Pythia
simulation. The single contributions are drawn stacked on top of each other.
6.4 Soft muon tagger
The soft lepton tagging algorithm [64] takes advantages of the presence of a lepton (=
muon or electron) within a jet originating from a semi-leptonic decay of a b-hadron. The
usage of muons is preferred over electrons due to the higher background in the electron
sample from QCD, the larger acceptance of the muon reconstruction and deficiencies in the
electron reconstruction caused by dead material and the poor performance of the transition
region between barrel and end-cap cryostats. The requirement of the presence of a muon
limits the bottom-flavour identification by the semi-leptonic branching ratio, however, this
method provides a complement method which is mostly statistically independent from
the more effective lifetime taggers discussed above. Because of this the soft muons are
extensively used for cross-calibration of the lifetime taggers which is presented later (cf.
Section 8.2.1).
The key objects for this algorithm are the reconstructed muons [92]. Muons are associated
to the closest jet in angular space which fulfils ∆R   0.5 in the event. Additionally, the
following requirements are made to the muons:
 |dPV0 |   4 mm,
70
NNuummbbeerr  ooff  jjeettss  ((aarrbbiittrraarryy  uunniittss))
6.5 Summary
pmuon T ¡ 4 GeV,
 Matching between the muon spectrometer and inner detector tracks χ2{ndof   10.
ndof stands for the number of degrees of freedom.
This tagging algorithm uses as discriminant the prelT variable which is the momentum of
the muon transverse to the combined muon-jet axis, where the jet axis is corrected for
the presence of the muon, shown in Fig. 6.5. If more than one muon is associated to
the jet, the muon with the highest transverse momentum is chosen. The muons from
muon muon-jet axis
prel
T
pmuon
jet
  
Figure 6.5: Illustration of the momentum of the muon transverse to the combined muon-jet
axis: prelT .
bottom decays have a significantly larger transverse momentum relative to the jet axis
than muons from light hadron decays. Fig. 6.6 presents this behaviour obtained from
QCD Pythia simulation, where b-jets tend to have a broad prelT distribution with the
centre shifted to higher prelT values. These different shapes of the p
rel
T distributions are used
in an one-dimensional likelihood ratio to discriminate b-jets from c- and light jets. The
likelihood ratio uses the normalised variable prelT /(p
rel
T +0.5 GeV). For each jet with the
help of the muon with the highest transverse momentum the likelihood ratio is given by:
0  Lpprel b T |bqQ
0light  LpprelT |
, (6.8)
lightq
where 0b (
0
light) is the fraction of b-jets (light jets) that contain a muon satisfying the
selection cuts and LpprelT |bq (LpprelT |lightq) is the probability density function for a b-jet
(light jet). The discriminating power of the prelT variable is diminishing with increasing jet
pT due to the stronger collimation of the jets. This causes the muon to be almost collinear
with the jet axis and the prelT distributions start to match very strongly.
6.5 Summary
The taggers presented in detail in the former sections are chosen due to their robustness.
The default b-tagging algorithm in the analysis is the SV0 tagging algorithm. A possible
71
6 Bottom-tagging in ATLAS
Figure 6.6: The prelT distribution for b-, c- and light-flavour jets obtained by QCD Pythia sim-
ulation. The distributions are all normalised to unit area. Jets are considered with pT ¡ 25 GeV
and |η|   2.5 and the combined muon track has to satisfy the selection cuts in Table 6.1. Taken
from Ref. [95].
dependence of the measured cross section on the tagging algorithm is checked with the help
of the JetProb algorithm. The working point of 50% b-tagging efficiency in simulated tt̄
events is used for both lifetime taggers. Correspondingly a jet is b-tagged if the SV0 weight
is bigger than 5.85 or if  log10pJetProb weightq is bigger than 3.25. Their estimated
performance from tt̄ events is shown in Fig. 6.7. The light-jet rejection is presented
as a function of the tagging efficiency for jets with pT ¡ 20 GeV and |η|   2.5. The
light-jet rejection is decreasing with increasing b-tagging efficiency. An efficiency increase
is achieved by lowering the selection cut and correspondingly selecting more jets which
do not contain a bottom-flavoured hadron. The advantage of the robustness of the SV0
and JetProb tagging algorithm is achieved at the expenses of a low light-jet rejection
with respect to the advanced tagging algorithms. The high-performance taggers SV1,
IP3D, JetFitter and their combinations IP3D+SV1 and IP3D+JetFitter can achieve a
higher light jet rejection of the order of nearly 2000 at 50% b-tagging efficiency. The
SV1 tagger takes advantages of further secondary vertex properties with discriminating
power like the invariant mass of the charges tracks in the secondary vertex. The SV1
weight is a the outcome of a likelihood ratio which takes into properties of the secondary
vertex and their correlation. On the other is the IP3D tagger the advanced version of the
JetProb tagger and utilises the two-dimensional distribution of the signed transverse and
longitudinal impact parameter significances. The IP3D tagger is also based on hypothesis
tests with a likelihood ratio. The JetFitter algorithm combines the information from the
SV1 tagger with the decay length significance evaluated with the help a more advanced
fitting algorithm. For more details on the advanced methods please refer to [64, 96]. At
the chosen working point of 50% in the simulated tt̄ sample the SV0 algorithm corresponds
to a light-jet rejection of about 300 which means that for every 300 light-jets one is
mis-identified as a b-jet. The light-jet rejection of the JetProb algorithm is approximately
150, one light-jet out of 150 is mis-identified as a b-jet. The rejection power of a b-tagging
algorithm rapidly decreases with rising jet pT. This degradation is caused by the track
reconstruction. The track density increases with the jet pT due to the higher activity
and stronger collimation of the jet which enhances the overlap between tracks and the
72
6.5 Summary
probability of mis-reconstruction. Therefore a light jet can more easily fake tracks with a
significant lifetime causing the light-rejection power to be deteriorated. On the other hand
also the b-tagging efficiency is a function of jet pT. Firstly the efficiency increases at low
pT (approximately 20 to 100 GeV), stays approximately constant and is degraded at high
jet pT (approximately 300 GeV). Slower b-hadrons generate more isotropic decay products,
these may fail to be associated to the corresponding jet or to fulfil the track selection cuts
(e.g. ptrackT ¡ 1 GeV) of the b-tagging algorithm in question. With increasing jet pT and
hence increasing b-hadron pT the decay products are boosted in direction of the b-hadron.
This increases the fraction of tracks from decay products to be associate with the jet and
this simply increases the efficiency. The degradation of the efficiency at high jet pT is
caused by the track reconstruction deficiencies which also decrease the light-jet rejection.
Figure 6.7: Light-jet rejection as a function of the b-jet tagging efficiency for the early tagging
algorithms (JetProb and SV0) and for the advanced algorithms, based on simulated tt̄ events
from the MC@NLO generator [56]. Details on the advanced algorithms SV1, IP3D, JetFitter
and their combinations can be found in [64, 96]. Taken from Ref. [96].
73

7 Data and event selection
After giving a description of the detector, the definition of jets and the methods to identify
bottom-flavoured jets, the following chapter presents details on the data samples, data
cleaning and the event and trigger selection of the analysis. Starting from the trigger
system which selects data events online, basic quality requirements on detector level
determine the integrated luminosity available for the analysis. Subsequently on event level
the reconstructed objects which are subject to this analysis undergo cleaning cuts. Finally,
from the sample of reconstructed jets (containing all flavours), in the following called
inclusive jets, the jets with bottom-flavoured content are extracted and serve as basis for
the cross section measurement.
7.1 Data samples and quality
The data sample which is a?vailable for this analysis contains proton-proton collisions at
a centre-of-mass energy of s = 7 TeV recorded from March to October 2010 with the
ATLAS detector. It corresponds to a total integrated luminosity of L=45.01.5 pb1.
This data sample is divided into distinct periods A to I corresponding to time periods with
constant accelerator configuration (cf. Section 4.2) and detector operation. The analysed
sample is selected with the help of the hardware-based calorimeter jet triggers. The early
data periods A to F only make use of the lowest trigger level (L1). With increasing
luminosity L1 triggers with lower jet energy thresholds were prescaled starting from period
C. Finally, the more advanced jet algorithms on the Level-2 (L2) trigger level have become
the default selection criteria starting from period G (except for the unprescaled jet trigger
with lowest jet energy threshold). In order to maximise the available integrated luminosity
different jet triggers are used to cover the entire jet pT spectrum. The chosen trigger
strategy ensures that the event selection by the single jet trigger is nearly 100% efficient.
To ensure the quality of the events hardware-based and analysis-based quality criteria are
used. The hardware-based criteria requires that the LHC delivers stable beams with a beam
energy of 3.5 TeV. The second criterion is the operation of the ATLAS detector or of chosen
detectors components with nominal setup, e.g. magnets, inner detector, calorimeter and
muon system. If these basic selection criteria are met, an offline analysis-based inspection
of a standard set of distributions leads to a data quality assessment for each individual
sub-detector, trigger and each type of reconstructed physics object. In the end the final
result stated in five different colours (green, yellow, red, grey and black) of each data
quality inspection is recorded in a condition database. For details see Appendix C and [97].
The green colour indicates that a sub-system performed with no major problems. For
this analysis good data quality is required on detector and analysis level for the tracking,
calorimeter and muon system and for the jet triggers. A complete list of requirements
is presented in Appendix C. The total integrated luminosity with good data quality is
33.91.2 ( 34) pb1 which is a fraction of about 72% of the total recorded luminosity.
Table 7.1 and Table 7.2 show an overview of the available integrated luminosities with good
75
7 Data and event selection
data quality per data period and single jet trigger. The luminosities have a systematic
uncertainty of 3.4% [61] and include possible prescales of the trigger items.
Period L1 J5 L1 J10 L1 J15 L1 J30 L1 J55 L1 J75 L1 J95
A 0.3 0.3 0.3 0.3 0.3 0.3 0.3
B 7.7 7.7 7.7 7.7 7.7 7.7 7.7
C 7.9 8.2 8.2 8.2 8.2 8.2 8.2
D 10.1 67.5 278.7 278.7 278.7 278.7 278.7
E 2.9 19.6 223.4 965.2 965.2 965.2 965.2
F 1.4 9.2 8.3 666.1 1741.2 1741.2 1741.2
Total 30.4 112.6 526.6 1926.2 3001.3 3001.3 3001.3
Table 7.1: Overview of total integrated luminosities of the L1 single jet triggers with good data
quality in nb1 for data periods A to F.
Period L2 j15 L2 j25 L2 j30 L2 j45 L2 j70 L2 j90 L1 J95
G 1.0 10.9 35.8 182.3 5211.7 4476.3 5531.9
H 0.4 4.5 4.5 20.6 435.1 486.0 6939.3
I 0.7 7.5 7.5 33.0 245.1 798.6 18411.4
Total 2.1 22.9 47.9 235.9 5892.0 5761.0 30882.5
Table 7.2: Overview of total integrated luminosities of the L2 single jet triggers and the lowest
unprescaled L1 trigger with good data quality in nb1 for data periods G to I.
7.2 Quality criteria for jets
In a first step the data quality cuts at the detector level ensure a general event quality,
subsequently a dedicated object cleaning at event level is performed to solve remaining
issues. Firstly in the case of reconstructed jets, events with a hard interaction may contain
jets not originating from the collision itself but from background sources. Secondly jets may
be seeded from real energy depositions but located in problematic calorimeter regions [98].
The following sources can create reconstructed jets not associated to the hard interaction,
so-called bad jets:
 Non-collision and cosmic background:
– Beam-gas events, where an interaction happened between a proton in the bunch
and the residual gas within the beam pipe over the length of the ATLAS
detector.
– Muons or pions in the halo of the beam, originating from interactions which
occurred not in the proximity of the ATLAS detector with the material from
technical equipment in and around the beam-line.
76
7.2 Quality criteria for jets
– Cosmic ray muons traversing the ATLAS detector in coincidence with a proton-
proton collision and experiencing catastrophic energy loss.1
 Calorimeter noise:
– Sporadically fake calorimeter signals in the HEC calorimeter can occur. In this
case the neighbouring calorimeter cells around the fake signal have a negative
energy due to the capacitive coupling. The sum of negative energy cells (negE)
is a measure for such fake signals. The reconstructed jets of these signals have
a large energy fraction (fHEC) in the HEC calorimeter and can in addition
be identified with the help of poor signal shapes. The calorimeter quality
(fHECquality) is a measure for the amount of energy contributing to a jet from
cells with a poor signal shape. A poor signal shape is identified by differences
in the sampling with respect to a reference pulse shape.
– Coherent noise induced by noise bursts in the electromagnetic calorimeter
lead to a mis-reconstruction of jets which have a large energy fraction in the
electromagnetic calorimeter (fEM). In addition these cells exhibit a poor signal
shape. The calorimeter quality (fEMquality) is a measure for the amount of
energy contributing to a jet from cells with a poor signal shape. A poor signal
shape is identified by differences in the sampling with respect to a reference
pulse shape.
To reject non-collision and cosmic background jets several properties are checked. The
reconstructed jet time (tjet) deduced from the reconstructed calorimeter cell times weighted
with the square of the cell energies is required to be in agreement with the event time
reported from the trigger. For jets within the tracking acceptance a minimal charged
fraction of the jet’s transverse momentum (fch) has to be measured by tracks associated
to each jet. A minimal energy deposition of each jet has to be reported by the closest
calorimeter (fEM) sub-system to the interaction region. In addition a maximum energy
fraction (fmax) in any single calorimeter layer is imposed on each jet.
To reject non-collision and cosmic background jets in data two quality selections are used:
 Loose selection is designed to conserve more than 99% of the jets originating from
a hard interaction and real energy deposition.
 Medium selection requires stricter quality criteria than the loose selection but
induces a larger inefficiency.
A measurement using inclusive jets requires the medium selection because this selection
is capable to reject and control jets in the high transverse momentum region more efficiently.
In case of a measurement of b-jets the loose selection criteria can be used because a b-tagged
jet and its associated tracks fulfil high quality criteria which exclude any jet originating
from a background source or calorimeter noise.
In addition, jets originating from problematic calorimeter regions are rejected. The two
main issues leading to such jets are:
1With increasing muon energy radiative effects in the energy loss mechanism start to become more
significant. The probability for such a large energy loss in the calorimeter increases, often referred to
as catastrophic.
77
7 Data and event selection
Loose Medium
Had. (fHEC ¡ 0.5 and | fHECquality |¡ 0.5) Loose or
noise or | negE |¡ 60 GeV fHEC ¡ 1 | fHECquality |
Coherent fEM ¡ 0.95 and fEMquality ¡ 0.8 Loose or
EM noise and | η |  2.8 fEM ¡ 0.9 and fEMquality ¡ 0.8 and | η |  2.8
Non-collision | tjet |¡ 25 ns or Loose or
and cosmic (fEM   0.05 and fch   0.05 and | η |  2) | tjet |¡ 10 ns
background or (fEM   0.05 and | η |¥ 2) or (fEM   0.05 and fch   0.1 and | η |  2)
or (fmax ¡ 0.99 and | η |  2) or (fEM ¡ 0.95 and fch   0.05 and | η |  2)
Table 7.3: Selection criteria used to reject jets from background sources. Recommendations are
taken from [98].
 The energy measurement of jets which contain dead or deactivated calorimeter cells
is corrected by extrapolating the energy deposit from the energy in the neighbouring
cells. The energy measurement of jets with a significant fraction of extrapolated
energy fcorr is not trusted and rejected if fcorr ¡ 50%.
 Jets with a large fraction of energy deposition in the scintillators in the gap between
the hadronic calorimeters in the barrel and end-cap fgap are discarded due to the
not-validated calibration of this sub-system if fgap ¡ 50%.
These cuts are established by the analysis of events selected by the L1 MBTS trigger [98].
Jet properties are compared to minimum bias Pythia simulation after successive cleaning
cuts. The power of the cleaning cuts are presented in Fig. 7.1. Events with good data
quality and colliding proton bunches (DQ+Collisions) are selected. The jet pT distribution
is showed for different jet cleaning selections. The underlying jet pT distribution does not
require any cleaning cut and shows a large tail towards high transverse momenta which
is not described by simulation. The two cleaning selections are improving the agreement
between data and simulation until data and simulation sit on top of each other.
7.3 Trigger efficiency and usage concept
The hardware-based calorimeter jet triggers are used to select the events. These are
discussed in detail in Section 4.3.5. The use of prescales, which are larger than 1 to
downscale event rates, deforms the recorded jet pT spectrum. Because of the limited
bandwidth, prescales of triggers with lower jet energy thresholds are larger. Due to
inefficiencies of the trigger with respect to the offline analysis events are lost. In an analysis
these effects of limited efficiencies and rate downscaling must be corrected to restore
the original statistics and properties. To optimise the available event statistics different
triggers are combined to cover different kinematic regions. Here the determination of
the trigger efficiency is presented and subsequently the strategy of the trigger usage is
discussed. This strategy combines triggers according to the trigger efficiencies such that it
provides a fully efficient selection. Consequently, only the downscaling by the prescales
must be corrected for in the analysis which reduces possible systematic uncertainties.
78
7.3 Trigger efficiency and usage concept
Figure 7.1: Inclusive anti-kt jet pT distribution with distance parameter R = 0.4 after successive
cleaning cuts: requiring no jets reconstructed from one noisy hadronic calorimeter cell, rejecting
bad quality jets. The jets are reconstructed at the electromagnetic scale. The prediction from
minimum bias Pythia simulation is superimposed and normalised to the number of jets in data.
The outliers above the transverse momentum of 300 GeV are real jets from one single dijet event.
Taken from Ref. [98].
7.3.1 Trigger efficiency measurement
The trigger efficiency is measured on an event basis with the help of an unbiased event
sample fulfilling the given analysis selections. The efficiency per event is defined as the
probability that the jets in a given event would satisfy the trigger. The trigger efficiency
is determined from data because the trigger is not emulated perfectly in simulation. The
unbiased event sample is selected with the help of a reference trigger. The efficiency of a
trigger as a function of an event property q is given by:
p q  number of events selected by both triggerspqqtrig q . (7.1)
number of events selected by reference triggerpqq
For this analysis the trigger efficiencies for the L1 jet triggers in periods A to F are
determined as well as the trigger efficiencies of the L2 jet triggers in periods G to I. The
efficiencies are determined for jets within the rapidity region |y|   2.1 in events with good
data quality. Furthermore events are selected if they contain a primary vertex with at
least 10 associated tracks (cf. Section 7.4). The trigger efficiencies are always calculated
with respect to jets calibrated with the EM+JES scheme.
Periods A to F: The L1 jet trigger efficiencies are measured with respect to the inde-
pendent L1 MBTS trigger, which provides an unbiased reference sample. The inefficiency
of the L1 MBTS trigger for the events considered is negligible [99]. This method is called
orthogonal trigger method. The trigger efficiency for one L1 JX trigger as a function of
reconstructed jet pT, calibrated with the EM+JES scheme, is given by:
p q  jet pT distribution that passes L1 JX and L1 MBTS criteriatrig,L1 JX pT . (7.2)
unbiased jet pT distribution that passes L1 MBTS
This efficiency is determined for all prescaled triggers and the lowest unprescaled trigger.
A jet trigger efficiency distribution is illustrated in Fig. 7.2 as a function of reconstructed
79
7 Data and event selection
jet pT of a jet trigger imposing a minimum energy requirement in the calorimeter. The
distribution can be described by the shape of a step-function with smoothened turn-on
behaviour (Fermi-function). At a certain point the efficiency reaches a plateau from which
on the trigger is fully efficient. The plateau is defined as the point where the efficiency
reaches over 99%.
The jet trigger efficiencies obtained with the reference trigger L1 MBTS for the data
periods A to F are presented in Fig. 7.3. The efficiencies are plotted and the plateaus are
indicated by the vertical lines. The dashed lines are extracted from a fit to the efficiency
curves. The statistical errors on the trigger efficiencies are obtained by Bayes’ theorem
calculated at 68.3% confidence-level. [100] This method determines the most probable
value of the efficiency given the observed events Ntotal and Npass events out of Ntotal passing
the threshold of the trigger. This probability is given by Bayes’ theorem: the probability
that trig is the true efficiency given Npass and Ntotal events is the product of the probability
of observing Npass events given the efficiency  and the probability of the true efficiency
within the allowed integral with obeying the correct normalisation. The process is assumed
to be binomial and the efficiency values between r0, 1s are equally qualified so that the
most probable value is set to be Npass{Ntotal. From the probability distribution the 68.3%
confidence-level is extracted and used as upper and lower statistical uncertainty. This
method is strictly speaking valid for events with weights equal to one and not applicable
to QCD simulation. The plateau regions extracted from this plot are written down in
Table 7.4.
1
0.8
0.6
0.4
0.2
0
0 10 20 30 40 50 60 70 80
p  [GeV]
T
Figure 7.2: Illustration of a trigger efficiency distribution as a function of reconstructed jet pT.
Periods G to I: For data periods G to I the L2 jet algorithms which are seeded by
L1 were activated. The L2 trigger efficiencies include the L1 trigger efficiencies. The
activation of the L2 jet algorithms and consequently the possible rejection of jets changes
the trigger efficiencies.
Due to the large downscaling of the MBTS triggers, they lack the necessary statistics to
serve as reference triggers. To obtain the L2 trigger efficiencies two different methods were
used:
 Bootstrap method: The unbiased reference sample for each trigger L2 jX (for example
L2 j30) is provided by a lower threshold trigger L2 jXlow (for example L2 j20) which
80
Trigger efficiency ∈trig
7.3 Trigger efficiency and usage concept
1
0.8
0.6
L1_J5
0.4 L1_J10
L1_J15
0.2 L1_J30
L1_J55
0
50 100 150 200 250
p  [GeV]
T
Figure 7.3: Trigger efficiencies for the L1 single jet triggers used in periods A to F for jets with
|y|   2.1. The dashed lines are drawn to guide the eyes.
Trigger Trigger plateau [GeV] Average prescale (A to F)
L1 J5 40 98.79
L1 J10 80 26.66
L1 J15 110 5.70
L1 J30 160 1.56
L1 J55 210 1
Table 7.4: Beginning of trigger plateaus, at which the trigger efficiency reaches over 99%,
expressed in jet pT and the corresponding trigger for data periods A to F. Due to a misconfiguration
in period G which persisted for a short time period L2 j70 recorded a larger fraction of events
compared to the L2 j90.
is on plateau in the region of interest where the higher trigger reaches the plateau:
p q  jet pT distribution that passes L2 jX and L2 jXtrig,L2 jX p lowT . (7.3)
unbiased jet pT distribution that passes L2 jXlow
 Tag-and-probe method: The unbiased reference sample for each trigger L2 jX is
obtained from events which pass any L2 jX. From these events one of the triggered
RoIs and its corresponding offline jet which served as tag jet are removed. The
remaining probe jets are used to measure the trigger efficiency. Each remaining jet
is matched in angular space (∆R   0.4) with an L1 RoI and subsequently with an
L2 RoI:
p q  probe jet pT distribution of jets with a passing L2 jX RoItrig,L2 jX pT . (7.4)
probe jet pT spectrum from any L2 jet trigger
The bootstrap method is the default choice to determine the trigger efficiencies but it has
the disadvantage that it is inapplicable for the lowest single jet trigger. To measure the
trigger efficiency of L2 j15 the tag-and-probe method is used. This method determines
the efficiency per jet, while the bootstrap method returns the efficiency per event. The
efficiency per jet is defined as the probability that a specific jet would satisfy the trigger
81
∈trig
7 Data and event selection
condition. The difference between per event and per jet efficiencies is that while in the
first case all jets in an event that passed the trigger are positively contributing to the effi-
ciency, in the second case only reconstructed jets matched in angular space to a trigger RoI.
The resulting trigger efficiencies for the data periods G to I are presented in Fig. 7.4
as function of reconstructed jet pT, calibrated with the EM+JES scheme. The trigger
efficiencies are plotted in the kinematic range in which the reference trigger is on plateau.
Below the plateau region of the reference trigger the efficiency is biased and unphysical.
The vertical lines indicate the beginning of each plateau. The trigger efficiency obtained
from the tag-and-probe method for L2 j15 does not reach the plateau at 40 GeV. The
subsequent plateaus have not changed with respect to periods A to F. Nevertheless in
context of this dijet measurement the inefficiency of L2 j15 for two jets within |y|   2.1
and pT ¡ 40 GeV is smaller than 0.002. This assumption is checked in the full event
sample recorded. It is evaluated that in every event with two jets above 40 GeV within
|y|   2.1, one of these jets had a L2 RoI which at least 15 GeV. Therefore the trigger
plateaus stay unchanged with respect to periods A to F and are summarised in Table 7.5.
1
0.8
0.6
L2_j15
0.4 L2_j30
L2_j45
L2_j70
0.2 L2_j90
L1_J95
0
50 100 150 200 250 300
p  [GeV]
T
Figure 7.4: Trigger efficiencies for the L2 single jet triggers used in periods G to I for jets with
|y|   2.1. The dashed lines are drawn to guide the eyes.
Trigger Trigger plateau [GeV] Average prescale (A to F)
L2 j15 40 14581.10
L2 j30 80 645.03
L2 j45 110 130.89
L2 j70 160 5.24
L2 j90 210 5.36
L1 J95 ¡ 260 1
Table 7.5: Beginning of trigger plateaus, at which the trigger efficiency reaches over 99%,
expressed in jet pT and the corresponding trigger for data periods G to I.
82
∈trig
7.4 Event selection for cross section measurement
7.3.2 Concept of trigger usage
The concept of trigger usage divides the phase space into distinct regions in terms of
leading jet pT and selects events only by a single trigger in each region, while all other
events are dropped. For the smallest possible statistical uncertainty and a nearly fully
efficient event selection the trigger in each phase space region is used which provides the
largest number of events and is on plateau. These selection criteria are easily deduced
from Table 7.4 and Table 7.5. The starting points of the plateaus of subsequent triggers
determine the phase space divisions. The original statistics of the selected data sample is
restored by applying to each event the weight given by
 prescalewtrig . (7.5)
trig
This weighting corrects for the unphysical properties in data caused by the trigger configu-
ration but the data statistic is artificially increased. The statistical uncertainty on the
data points does not follow Poisson statistics. The statistical error is given as square root
of the sum of wj weight squares.
The measurement of the dijet cross sections starts by determining the number of events
NpM, pTq as a function of dijet mass and leading jet pT. The number of events as a
function of dijet mass and leading jet pT is illustrated in Fig. 7.5. Each division in leading
jet pT is full-efficiently measured by one single jet trigger. Every pT-bin in Fig. 7.5 has its
own trigger luminosity Li which intrinsically includes the rate downscaling by the set of
prescales and trigger efficiency trig,i. The trigger efficiencies for the chosen phase space
regions are set equal to one.
102
>310
10
260-310 1
210-260
10-1
160-210
110-160 10-2
80-110
40-80
-3
0 200 400 600 800 1000 1200 10
bb dijet mass [GeV]
Figure 7.5: Shown is the number of events NpM,pTq as a function of dijet mass and leading
jet pT according to the distinct phase space divisions from the trigger efficiencies.
7.4 Event selection for cross section measurement
Events passing the good data quality criteria and fulfilling the trigger strategy are selected
for further processing. The subsequent offline selection steps which are presented here
include firstly basic collision-event characteristics and the jet object cleaning requirements.
Ultimately analysis-dependent selections on the event topology are made. The complete
event selection is given in the following:
83
leading jet p  [GeV]
T
Arbitrary units
7 Data and event selection
1. Event selection: Each event is required to have a primary vertex which is recon-
structed in agreement with the beam spot measurement (cf. Section 5.2.2) with
at least ten associated tracks to ensure a good primary vertex resolution. The
distribution of the z-coordinate of the primary vertex in simulated data is reweighted
to be in agreement with data (cf. Section 4.4). The width of the zPV distribution is
approximately 6 cm.
2. Jet selection: Within these events reconstructed jets calibrated with the EM+JES
scheme are selected if their transverse momentum is above pT¡ 40 GeV and they
are within the rapidity region |y|   2.1. The single jet trigger with lowest threshold
reaches its plateau at 40 GeV. The limited acceptance in rapidity ensures that the
jets are completely contained in the tracking volume. Hence tracks with dR   0.4 to
the jet axis are fully reconstructed. As the colliding bunches have a spatial width, an
interaction may happen displaced to the centre of the detector, tracks may be lost
from detection by this shift. However, the effect of the width of the zPV distribution
is estimated and found to be negligible (|∆y|   0.02).
3. Cleaning selection: Jets are excluded if they do not fulfil the jet quality criteria
(loose or medium). An event containing a rejected jet is still assumed to be a valid
QCD event.
4. Inclusive dijet selection: Events are discarded if the number of remaining jets
for the analysis is smaller than 2. At this point the event sample is an inclusive dijet
sample.
5. bb̄ dijet selection: The leading jets are selected as bottom-flavour jets by the
chosen b-tagging algorithm if they fulfil the b-tagging weight cut. The b-tagging
selection cuts are summarised in Table 7.6. For convenience in the rest of the analysis,
b-tagged jets refer to SV0 b-tagged jets.
b-tagging algorithm b-tagging weight cut
SV0 5.85
 log10pJetProbq 3.25
Table 7.6: Summary of b-tagging weight cuts in use.
The selection of events in simulation is equivalent to the presented selection steps except
for the data quality requirement, the trigger selection and the jet cleaning cuts. Because
the evaluation of data and jet quality is not applicable to simulated data. Furthermore,
the data is corrected for the trigger downscaling.
Table 7.7 presents the number of events and jets after each selection cut. The trigger
selection cut rejects more than 90% of the events. About 3% of all events are selected as a
dijet event, containing at least two clean jets with pT¡ 40 GeV and |y|   2.1. Finally, the
prescale-corrected number of events with leading jets which are b-tagged is about 250000.
The jet pT distributions after the selection cuts numbered two to four is presented
in Fig. 7.6. Without any jet cleaning in data (cf. Fig. 7.6 (2.)), there is a significant
84
7.4 Event selection for cross section measurement
Number of events Number of jets
Data Quality 2.13108 7.42108
Trigger selection 1.35106 6.70106
Event selection 1.34106 6.67106
Inclusive dijet events 7.74105 1.88106
SV0 b-tagged dijets (5) 256713
Table 7.7: Cut flow summary for events and jets.
excess of jets in data at high jet pT. After the jet cleaning cuts presented in Fig. 7.6
(3.) the comparison between data and Pythia simulation improves as expected from
former studies presented in Fig. 7.1 (taken from Ref. [98]). Finally, the jet pT distribution
of events with at least two clean jets with pT¡ 40 GeV and |y|   2.1 is presented in
Fig. 7.6 (4.). The agreement between data and MC is good. The conventions for the
binning of physical quantities in this analysis with non-uniform bin widths are written
down in Appendix A. The leading and sub-leading jet are referred to as jet 1 and jet 2,
the remaining jets are numerically numbered.
1 1
p  > 40 GeV,|y| < 2.1 Jet cleaning
10-1 T Data 10-1 Data
10-2 (2.) Pythia 10-2 (3.) Pythia
10-3 10-3
10-4 10-4
10-5 10-5
10-6 10-6
10-7 10-7
10-8 10-8
10-9 10-9
0 200 400 600 800 1000 1200 1400 1600 1800 0 200 400 600 800 1000 1200 1400 1600 1800
p  [GeV] p  [GeV]
T T
1
Dijet events
10-1 Data
10-2 (4.) Pythia
10-3
10-4
10-5
10-6
10-7
10-8
10-9
0 200 400 600 800 1000 1200 1400 1600 1800
p  [GeV]
T
Figure 7.6: Jet pT distributions changing with cut flow from cut number 2 (top left) to cut
number 4 (bottom left) as defined on page 83.
85
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11//NN  ddNN//ddpp   [[GGeeVV--11]]
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TT

8 Object understanding and
calibration
In this chapter the event selection presented in the preceding chapter is used to determine
the data sample. In Section 8.1 the description of ATLAS data by the Pythia simulation
is discussed. The focus for this study is on the reconstructed jets and jet related tracking
properties. The simulation helps to determine several important quantities like efficiencies,
calibrations and correction factors. These can only be trusted if a thorough check on the
simulation is performed. Furthermore, possible systematics arising from the uncertainty
on the modelling have to be addressed. In Section 8.2 the b-tagging calibration for the
SV0 and JetProb algorithms are presented. The extracted calibration is extended and
validated to higher jet-pT regions for this measurement. In Section 8.3 the jet energy
scale uncertainty of EM+JES calibrated jets is discussed and the determination of the
uncertainty for b-tagged jets is presented.
8.1 Jet and track properties in data and simulation
This dijet cross section measurement relies on an adequate description of data by the
simulation. The default Pythia samples (cf. 4.4) are used to derive any necessary
correction for the cross section measurement which is not deducible from data. This
section studies the agreement of analysis related properties between data corresponding to
a total integrated luminosity of about 34 pb1 and the Pythia predictions. The event
selection summarised in Section 7.4 is applied to data and to simulated events. This
agreement is quantified by the ratio between data and MC and has to be evaluated taking
statistical uncertainties into account from both samples. With the help of inclusive jets, the
compatibility of the leading-order pQCD calculations for the hard scatter between protons
implemented in the parton shower generator Pythia is investigated. The properties
of tracks from charged particles associated to these jets are discussed because they are
key ingredients for the b-tagging algorithms. Along the selection of b-tagged jets, the
discriminant weight distribution of both lifetime taggers is compared between data and
simulation. In the next step, all b-tagged jets found in the inclusive data sample are
studied and the phase space coverage of the available dataset is illustrated.
8.1.1 Properties of inclusive jets
The production of jets in proton-proton collisions reflect the distinctive signature of short-
distance interactions between the partons in a leading-order picture of the proton. The
leading jets are identified with the partons emerging from the hard scatter. Additional jets
in the event are produced by final- and initial-state radiation, multi-parton interactions
and fragmentation. The following comparisons between data and MC are done separately
for the leading jets and additional jets. The statistical uncertainty on the MC distributions
87
8 Object understanding and calibration
are represented by grey hatched areas. Data and MC distributions are either normalised
to unit area or the MC distribution is normalised to data.
The properties of the selected dijet sample is presented in the following. The event and
object selection for an inclusive jet sample is detailed in Section 7.4. In Fig. 8.1 the
leading jets pT and dijet mass M distributions are presented for reconstructed jets with
|y|   2.1 and pT ¡ 40 GeV. The statistics of the simulated data events for inclusive
jets is high (cf. Section 4.4) and the statistical uncertainty is hardly visible. The jet pT
spectrum (Fig. 8.1(a)) extends to 1.5 TeV and contains 1.5 million jets. The corresponding
measurement of the invariant dijet mass M of these jets in Fig. 8.1(b) covers the phase
space to about 3 TeV. The phase space restrictions cause the unphysical decrement of the
number of events below M   110 GeV. The observed agreement between data and MC
for the inclusive pT and dijet mass distributions is good but it gets worse with increasing
jet pT. The prediction from Pythia tends to underestimate the distribution at high pT
and dijet mass M and consequently overestimates the jets and events in the low pT and
dijet mass range, respectively. This deficiency caused by the limitations to describe the
hard scatter will give rise to a systematic uncertainty in the measurement. With this first
data at a centre-of-mass energy of 7 TeV from the stable running periods of the LHC in
2010, the measurements from the Tevatron on inclusive jets are surpassed [101] already.
The azimuthal and rapidity correlations are determined between the leading jets. At
1
10-1 ∫Ldt = 34 pb-1 Inclusive jets: 10-1 ∫Ldt = 34 pb-1 Inclusive jets:
-2 Data Data10 Pythia 10-2 Pythia
10-3 MC stat. unc. 10-3 MC stat. unc.
10-4
10-5 10
-4
10-6 10
-5
10-7 10-6
10-8 10-7
10-9
0 200 400 600 800 1000 1200 1400 1600 1800 1.50 500 1000 1500 2000 2500 30002
1 1
0
0 200 400 600 800 1000 1200 1400 1600 1800 0 500 1000 1500 2000 2500 3000
p  (leading jets) [GeV]
T dijet mass M [GeV]
(a) Jet pT distribution of leading jets (b) Dijet mass M distribution of leading jets
Figure 8.1: Properties of the leading jets in an inclusive dijet sample in data and QCD Pythia
samples.
leading-order the partons emerging out of the hard scatter are produced back-to-back.
The angular correlation is peaked at ∆φ  π. The angular correlation of the leading jets is
presented in Fig. 8.2(a). Next-to-leading order corrections modify the angular correlation
and populate the lower regions in ∆φ. Pythia models this higher order effects partly
through the parton showers. This approach leads to an adequate description of the shape
of the angular correlations between the leading jets above π{2. Nevertheless, Pythia
underestimates the contributions at regions with low angular separation. In this region
the leading jets, which are selected, originate from a parton pair, which was created in
the parton shower. The unsteady shape of the prediction below ∆φ   1 is caused by the
creation mechanism, namely parton splittings, which are an inefficient procedure from
the statistical point of view. The comparison of the Pythia prediction and data is as
expected (cf. Section 2.3.2). The rapidity correlation (Fig. 8.2(b)) has a maximum at
88
Data/MC 11//NN  ddNN//ddpp   [[GGeeVV
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Data/MC 111///NNN   dddNNN///dddMMM   [[[GGGeeeVVV---111]]]
8.1 Jet and track properties in data and simulation
∆η  0 and follows a falling distribution with increasing |∆η|. This correlation shows a
very good agreement between data and simulation within the statistical uncertainty.
The jet multiplicity and the inclusive pT distribution of the additional jets are shown
0.1
Inclusive jets: ∫Ldt = 34 pb-1 0.09 ∫Ldt = 34 pb-1 Inclusive jets:
-1 Data 0.08 Data10 Pythia 0.07 Pythia
MC stat. unc. MC stat. unc.
0.06
10-2 0.05
0.04
0.03
-3 0.0210
0.01
0
1.50 0.5 1 1.5 2 2.5 3 1.5-4 -3 -2 -1 0 1 2 3 4
1 1
0.5 0.5
0 0
0 0.5 1 1.5 2 2.5 3 -4 -3 -2 -1 0 1 2 3 4
∆φ (leading jets) [rad] ∆η (leading jets)
(a) Angular correlation of leading jets (b) Rapidity correlation of leading jets
Figure 8.2: Angular and rapidity correlation of the leading jets in an inclusive dijet sample.
in Fig. 8.3. Events with exactly 2 jets, fulfilling the cleaning cuts and the phase space
restrictions, make up more than 90% of the selected events. Pythia describes the jet
multiplicity well. Also the pT distribution of additional jets is well reproduced with the
same remarks on the hardness of the distribution as for the leading jets above. Furthermore,
the ∆R distributions between the leading jets and the additional jets show good agreement
between data and MC (see Appendix E).
Concluding the observations made so far, the description of inclusive jets in data with
10
1 ∫Ldt = 34 pb-1 Inclusive jets: 1 ∫Ldt = 34 pb-1 Inclusive jets:
10-1 Data 10-1 Data
10-2 Pythia -2 Pythia
10-3 MC stat. unc.
10 MC stat. unc.
-3
10-4 10
10-5 10-4
10-6 10-5
10-7 10-6
10-8
-9 10-710
10-10 -8
1.5 0 2 4 6 8 10 12 14
10 0 100 200 300 400 500 600 700 800
2
1
0.5 1
0 0
0 2 4 6 8 10 12 14 0 100 200 300 400 500 600 700 800
Jet multiplicity p  (jets 3 and 4) [GeV]
T
(a) Jet multiplicity in inclusive dijet sample (b) pT spectrum of additional jets
Figure 8.3: Description of the jet multiplicity and pT distribution of the additional jets in an
inclusive dijet sample.
the leading-order parton shower generator Pythia is good. The deficiencies confirm the
expectations from Section 2.3. The underestimation of high pT jets has to be taken into
account in the systematics.
89
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Data/MC 111///NNN   dddNNN///dddppp    [[[GGGeeeVVV
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8 Object understanding and calibration
8.1.2 Properties of tracks associated to jets
As was seen, the scattering process of the proton constituents and its kinematics is well
described by pQCD and the default generator in this analysis. The structure of the jets
generated in the fragmentation process is more complex. With the help of the b-tagging
track selection cuts presented in Table 6.2 used in the JetProb tagger, the modelling
of charged tracks associated to jets is studied. The b-tagging track selection requires
well-measured tracks and is designed to reject fake tracks as well as tracks from long-lived
particles or material interactions.
Hadronisation produces particles with limited transverse momentum with respect to the
22 ×10
6 ×106
40
20 Inclusive jets: Inclusive jets:35
18 Data Data
16 Pythia 30 Pythia
14 MC stat. unc. 25 MC stat. unc.
12
10 ∫Ldt = 34 pb-1 20 ∫Ldt = 34 pb-1
8 15
6 10
4
2 5
0 0
0 5 10 15 20 25 0 5 10 15 20
1.5 1.5
1 1
0 5 10 15 20 25 0 5 10 15 20
Number of tracks (leading jets) Number of quality tracks (leading jets)
(a) All reconstructed tracks (b) b-tagging quality tracks
Figure 8.4: Track multiplicities for differently selected tracks associated to a jet: (a) all
reconstructed tracks considered, (b) only b-tagging quality tracks considered.
parton direction. With increasing transverse momentum of the jet a large fraction of
transverse momentum of the jet is concentrated in the jet core and the jet gets more
collimated. The contribution of perturbative QCD radiation becomes more significant and
counteracts the collimation. Accordingly, the average track multiplicity increases with jet
pT. As studies have shown, jets are in general broader in data than in MC [102]. The
track multiplicity for the leading jets predicted by Pythia and compared to data is shown
in Fig. 8.4. This figure presents the multiplicities for an unrestricted and for the b-tagging
track quality selections. The multiplicities in Fig. 8.4(a) are almost identical, whereas for
the b-tagging track selection they are almost 5% lower for data than for MC. The stricter
b-tagging selection presented in Fig. 8.4(b) rejects tracks and the average track multiplicity
decreases. The modelling of the track multiplicity is dependent on the description of the
tracking system in simulation and on the hadronisation which is strongly dependent on
the chosen phenomenological model.
The transverse impact parameter and its significance distributions for tracks associated to
a jet and fulfilling the b-tagging selection cut is presented in Fig. 8.5. This distribution is
the basis for the lifetime tagger JetProb and the measurement of the impact parameters is
essential for finding secondary vertices. It has to be emphasised that the Pythia prediction
is in excellent agreement with data. This implies several facts: It can be deduced that
the disagreement in the track multiplicities are rather caused by the imperfection of
the physics tune (cf. Section 2.3.1) than from the modelling of the track reconstruction.
Furthermore, the pattern recognition in a high-density environment like the jet core is
90
Data/MC NNuummbbeerr  ooff  jjeettss
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8.1 Jet and track properties in data and simulation
∫Ldt = 34 pb-1 Inclusive jets: ∫Ldt = 34 pb-1 Inclusive jets:1 Data 1 Data
Pythia Pythia
10-1 MC stat. unc. 10-1 MC stat. unc.
10-2 10-2
10-3 10-3
10-4 10-4
1.4-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.-410 -8 -6 -4 -2 0 2 4 6 8 10
1.2 1.2
1 1
0.8 0.8
0.6 0.6
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -10 -8 -6 -4 -2 0 2 4 6 8 10
d0 (leading jets) [mm] d0/σ(d ) (leading jets)0
(a) Transverse impact parameter (b) Transverse impact parameter significance
Figure 8.5: The reconstructed transverse impact parameter and its significance are presented
for tracks associated to a jet and fulfilling b-tagging quality cuts.
well reproduced by the simulation as well as the hit sharing among tracks. In Fig. 8.5(b)
the ratio data/MC shows that there is a slight disagreement between data and MC of
about 20% at high |d0{σpd0q| indicating that the simulated distribution is slightly narrower.
From the perfect agreement of the transverse impact parameter distribution, it can be
concluded that this slight disagreement comes from the resolution modelling of the primary
and secondary vertex. This can be caused by small residual misalignments in the detector
(not perfectly described by the simulation) or differences in the primary vertex resolution.
In Appendix E Fig. E.3 the longitudinal impact parameter distribution can be found.
Finally, the reconstructed transverse momentum of tracks associated with a jet and fulfilling
-1 ∫Ldt = 34 pb-1 Inclusive jets:10 Data
10-2 Pythia
MC stat. unc.
10-3
10-4
10-5
10-6
30 50 100 150 200 250 300 350 400 450 500
2
1
0
0 50 100 150 200 250 300 350 400 450 500
ptrack (leading jets) [GeV]
T
Figure 8.6: Reconstructed transverse momentum distribution of tracks associated with a jet and
fulfilling b-tagging quality cuts.
b-tagging quality cuts is studied. These cuts require a minimum transverse momentum of
the tracks, this ensures that mainly tracks are selected from a hard process rather than
from the underlying event. In Fig. 8.6 it can be seen that the transverse momentum of
tracks reconstructed in data and MC agrees well and describes an exponentially falling
spectrum.
The deviations in the track multiplicity are due to the imperfection of the modelling
of the complex processes during fragmentation. The input variables for the b-tagging
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8 Object understanding and calibration
algorithms are very well described by the simulation. The performance of the tagging
algorithms will therefore be well reproduced by simulation. The discrepancy between the
b-tagging efficiency and mistagging rate in data and MC will be small. Nevertheless, as the
performance of the b-tagging algorithm depends on the fraction of transverse momentum
of the jet carried by charged tracks and neutral particles, as well as the track multiplicity
and track and vertex resolutions, a b-tagging calibration is necessary.
8.1.3 Properties of b-tagged jets
The discriminant weight distributions produced by the SV0 and JetProb taggers are
presented and compared to simulated events separated into the different jet categories:
b-jets, c-jets and light-jets. The pmuonT spectrum of the identified soft muon with highest
transverse momentum is studied as a function of jet pT. Finally, properties of identified
b-tagged jets with the SV0 tagging algorithm are examined and the covered phase space is
illustrated.
To identify b-jets, the weight distributions, which are presented in Fig. 8.7, are used. Jets
on which these b-tagging algorithms failed to find a secondary vertex or to calculate a jet
probability are excluded. This failure can have a diversity of reasons. There are no tracks
available for the algorithms, the secondary vertex fit is not successful or the likelihood
function is undefined for the impact parameter measured. Consequently, the number of
jets with no failure in MC is reweighted to the number of jets with no failure in data.
The sample of jets shown by the SV0 weight distribution and by the JetProb are not
identical, but do have a sizable overlap (¿50%). The description of the weight distribution
by Pythia is in remarkable agreement within 10% with data especially in the region
above the b-tagging selection cut of 5.85 which marks the 50% efficiency in the simulated
tt̄ sample.
In the reconstruction of the jets based on the calorimeter, identified muons are not taken
107
6 Data ∫Ldt = 34 pb-1 ∫Ldt = 34 pb-1 Data10 Pythia: b-jets Pythia: b-jets
105 Pythia: c-jets 7 Pythia: c-jetsPythia: light jets 10 Pythia: light jets
104 MC stat. unc. MC stat. unc.
103 106
102
10 105
1
10-1-350 -40 -30 -20 -10 0 10 20 30 40
1.50 1 2 3 4 5 6 7 8 9 10
2 1
1
0 0.5
-50 -40 -30 -20 -10 0 10 20 30 40 0 1 2 3 4 5 6 7 8 9 10
SV0 weight (leading jets) JetProb weight (leading jets)
(a) SV0 b-tagging algorithm (b) JetProb b-tagging algorithm
Figure 8.7: Discriminant weight distribution of the b-tagging algorithms SV0 and JetProb for
the taggable, leading jets. The single contributions are drawn stacked on top of each other.
into account and the escaping neutrinos carry away part of the b-hadron’s energy. In case
of a semi-leptonic b-hadron decay with a branching ration of about 10% the transverse
momentum loss due to the escaping muon is on average 10% according to Pythia. These
detector effects need to be corrected for and therefore the modelling of the hadron decay
92
Data/MC NNNuuummmbbbeeerrr   ooofff   jjjeeetttsss
Data/MC NNuummbbeerr  ooff  jjeettss
8.1 Jet and track properties in data and simulation
is of interest. The pmuonT spectrum of identified soft muons with respect to the beam axis
in data (cf. Section 6.4) compared to the simulation indicates how well the hadron decay
is described in terms of the fraction of momentum carried by the muon and respectively
by the neutrino. The distributions of the transverse momenta in simulation of the soft
muons in Fig. 8.8 as a function of jet pT show reasonable agreement with data.
The sample of b-tagged jets in the following has applied the calibration derived in
Ldt = 34 pb-1 Ldt = 34 pb-1
10-1
∫ Data -1 ∫ Data10
Pythia Pythia
10-2 MC stat. unc. 10-2 MC stat. unc.
10-3 10-3
10-4 10-4
10-5 10-5
40 10 20 30 40 50 60 70 80 90 40 20 40 60 80 100 120
3 3
2 2
1 1
0 0
0 10 20 30 40 50 60 70 80 90 0 20 40 60 80 100 120
pmuon [GeV] pmuon [GeV]
T T
(a) Jet pT: 80-110 GeV (b) Jet pT: 210-260 GeV
Figure 8.8: Subset of muon pT distributions for different pT ranges according to trigger plateaus:
(a) jets with pT between 80 and 110 GeV, (b) jets with pT between 210 and 260 GeV.
10-1
10-2 ∫Ldt = 34 pb
-1 b-tagged jets:
Data
10-3 Pythia
10-4 MC stat. unc.
10-5
10-6
10-7
10-8
10-90 100 200 300 400 500 600 700 800 900 1000
2
1
0
0 100 200 300 400 500 600 700 800 900 1000
p  (leading jets) [GeV]
T
Figure 8.9: The transverse momentum distribution of the leading jets from events with double
b-tagged leading jets.
Section 8.2. The properties of the b-tagged jets used to measure the dijet cross section are
presented in Figs. 8.9 and 8.10. The b-tagged dijets are a sub-sample of the inclusive jets
presented in Fig. 8.1(b). The transverse momentum spectrum extends to 900 GeV and
the MC sample each bin is separated into three contributions: mistagged light- and c-jets
and correctly tagged b-jets. Among all b-jets only a fraction dependent on the b-tagging
efficiency is identified. The spectrum is reasonably well described by the simulation. The
same is true for the φ and η distributions of b-tagged jets in Fig. 8.10. In case of the η
distribution it has to be taken into account that rapidity and pseudorapidity are not the
same. Therefore, the phase space restriction to the rapidity region below 2.1 is smeared
93
mmuuoonn --11
Data/MC 11//NN  ddNN//ddpp   [[GGeeVV ]]
TT
Data/MC 111///NNN   dddNNN///dddppp    [[[GGGeeeVVV
---111]]]
TTT
11//NN  ddNN//ddppmmuuoonnData/MC   [[GGeeVV
--11]]
TT
8 Object understanding and calibration
0.2 0.2
0.18 ∫Ldt = 34 pb-1 b-tagged jets: 0.18 ∫Ldt = 34 pb-1 b-tagged jets:
0.16 Data 0.16 Data
0.14 Pythia 0.14 Pythia
MC stat. unc. MC stat. unc.
0.12 0.12
0.1 0.1
0.08 0.08
0.06 0.06
0.04 0.04
0.02 0.02
0 0
-3 -2 -1 0 1 2 3 -2 -1 0 1 2
2 2
1 1
0 0
-3 -2 -1 0 1 2 3 -2 -1 0 1 2
φ [rad] η
(a) φ distribution (b) η distribution
Figure 8.10: Distribution of the number of b-tagged jets as a function of (a) φ and (b) η from
events with double b-tagged leading jets.
at the acceptance limits in terms of pseudorapidity. These distributions also reveal the
deficiency of the available simulation events, the available statistic is not sufficient. This
raises important issues for this analysis, as can be seen later.
In summary, the studies presented justify that the simulated events can be used as a baseline
to derive the necessary corrections and systematics for this cross section measurement.
The few remaining deficiencies in the simulation modelling have to be taken into account
in systematic uncertainties. The final remark is that the presented studies focus on certain
important issues in the context of this analysis. This good agreement cannot be extended
blindly onto other aspects. In the next sections the primary properties and uncertainties
of the b-tagging algorithms and the jet energy measurement are discussed, which are the
main focus for this measurement.
8.2 Calibration of bottom-tagging algorithms
The performances of the tagging algorithms SV0 and JetProb in data and simulation are
not identical for the reasons we have seen in the former section. Several effects cause
differences between data and MC. Simulated resolutions differ from data due to poorly
understood geometrical effects which are not modelled in the simulation. A small fraction
of the inner detector modules is disabled from time to time. The estimated performance in
the simulation depends on the modelling of fragmentation and the description of charged
tracks, so consequently on the tune used in the simulation. The measurement of the
b-tagging efficiency and mistag rate in data is translated into scale factors that correct the
b-tagging performance in simulation to that observed in data:
data data b lightκ , κ  . (8.1)b sim light simb light
Because both the b- and c-hadrons are long-lived hadrons, it is assumed for the moment
that b- and c-tagging efficiencies show a similar behaviour. These scale factors have the
advantage of universality in the sense that are applicable to differently selected analysis
samples with different event topologies. With the help of the scale factors the efficiency and
94
Data/MC 111///NNN   dddNNN///dddφφφ   [[[rrraaaddd---111]]]
Data/MC 111///NNN   dddNNN///dddηηη
8.2 Calibration of bottom-tagging algorithms
mistag rate can be deduced with the help of simulation. The scale factors are determined
as a function of jet pT and η for the reasons presented in Section 6.5. Several methods
are available to derive the scale factors. Their applicability is mostly dependent on the
available statistics.
The calibration of the efficiency used in this analysis (see Section 8.2.1), due to the limited
statistics, is making use of the semi-leptonic decays of b-hadrons into muons. With the
help of the soft muons (pmuonT ¡ 4 GeV) and the measured prelT distribution the scale
factors can be determined. This method is referred to as the prelT method. As discussed in
Section 6.4 this method breaks down at transverse momenta of the jets of about 150 GeV.
The extension of the calibration and its validity for this cross section measurement are
presented in Section 8.2.2. Methods favoured in case of high statistics, which are also
applicable for high pT jets, are using tt̄ events where the event selections make use of
semi-leptonic and dilepton signatures in the tt̄ decay channels.1
The mistag rate is determined with the help of two methods which are performed on
an inclusive jet sample. The use of the inclusive jet sample makes both methods less
dependent on statistical effects. The so-called SV0 mass method measures with the help
of the reconstructed mass distribution of secondary vertices the fraction of light-jets before
and after applying the tagging cut and the efficiency calibration. The negative tag method
relies on the fact that the impact parameter or the decay length from light-jets due to
the finite resolution of the tracking system is measured as originating in front or behind
the primary vertex with respect to the jet axis. This mis-measurement occurs equally
distributed in each direction. With the help of the negative side of the impact parameter or
the decay length distribution the amount of mistakenly tagged light-jets can be estimated.
The difference in the measured and simulated negative tail of the impact parameter and
the decay length distribution are corrected by the mistagging scale factor. The results of
both independent methods are combined in order to give the best possible estimation and
to cover the largest possible kinematic region.
8.2.1 Calibrating the lifetime tagging algorithms
For all methods, distributions in simulation, which are known to disagree with data, are
reweighted to reflect the measured distribution to reduce the impact of them on the
systematics. The primary vertex zPV distribution is reweighted in the same manner as
shown in Section 4.4. In addition the inclusive jet pT spectrum as presented in Fig. 8.1(a)
is harder in data than in simulation and this discrepancy is corrected for by a bin-by-
bin reweighting in the simulation samples used for the scale factor determination. The
calibration is done for anti-kt jets with a radius R = 0.4 and a minimum pT of 20 GeV
and within the rapidity |y|   2.5. Events are selected if their primary vertex consists of
more than 9 tracks. The following sections go into detail on the efficiency and mistag
calibration [103].
1The top(antitop)-quark decays almost 100% into W+b(b̄). In semi-leptonic signatures one of the
W -bosons decayed into a lepton-pair and the other into a quark-antiquark pair, in dilepton signatures
both decayed into a lepton-pair.
95
8 Object understanding and calibration
8.2.1.1 Efficiency calibration with muons
In the prelT method events are collected using the single jet triggers (cf. Sections 4.3.4.1
and 4.3.5) with an additional requirement that a reconstructed muon is spatially matched
to the jet object. prelT distributions are constructed for b-,c, and light-jets with the help
of data and MC. From the prelT distributions for each jet flavour templates are derived
which describe the shape of the distributions. These templates are used in a likelihood fit
which adjusts the relative contributions such that their sum best describes the prelT shape
in data. The fraction of b-jets is determined from the prelT distributions in data before
the SV0 b-tagging requirement (fb) shown in Fig. 8.11(a) and afterwards (f
tag
b ) shown in
Fig. 8.11. The corresponding prelT distribution requiring the JetProb tagging selection cut
can be found in Appendix F Fig. F.1. The b-tagging efficiency is then derived from
tag tag
datab 
fb N
 , (8.2)fb N
where N and N tag are the total number of jets in those samples. The data sample, which
(a) Before b-tagging (b) After SV0 b-tagging cut
Figure 8.11: Example of a template fit in data to the prelT distribution before b-tagging (a) and
after the SV0 b-tagging cut (b) at 50% b-tagging efficiency. The template fit is performed on all
jets. Uncertainties shown are for data statistics only. The discrepancies between the data and
the sum of the templates are fully covered by the systematic uncertainties on the template shapes.
Taken from Ref. [103].
is used to perform the fit, has the additional requirement to contain at least one jet with a
decay length significance (SV0 weight) bigger than 1 (tag) in order to increase the heavy-
flavour content in the sample. The corresponding tag jet is discarded for the efficiency
measurement and the fit is making use of the probe jet. This requirement diminishes the
light-flavour content and is used to minimise the dependency on the modelling and the
knowledge on the angular resolution of the prelT variable in light-jets.
The b- and c-flavour templates are derived from Pythia simulation. The light-jet template
is derived from a data sample dominated by light-jets. This data sample contains only
events in which no jet is b-tagged by the IP3D+SV1 tagger using a working point with
80% b-tagging efficiency derived in simulated tt̄ events (see Fig. 6.7).
Systematic uncertainties affecting this measurement have either a direct impact on the prelT
96
8.2 Calibration of bottom-tagging algorithms
distributions or indirectly by changing the sample compositions or their kinematics. The
uncertainties are evaluated by repeating the prelT template fits on data with the modified
template distributions. Three sources of systematic uncertainties can be identified: the
jet measurement, systematics from the method itself and simulation related uncertainties.
The uncertainty of the jet energy measurement is affecting the prelT sample composition
and kinematics. Systematics arising from the method are the limited statistics available
to build the templates, the template modelling and the usage of MC derived templates
for the b- and c-flavours. Furthermore, it is assumed that the result of this calibration
method is also approximately valid on hadronically decaying b-hadrons. The validity of this
assumption is dependent on the description of track multiplicity in hadronically decaying
b-hadrons in simulated data. The difference between data and MC when comparing the
muon and the inclusive jet sample is taken as systematic uncertainty and this causes a
sizable uncertainty. Uncertainties caused by the imperfection of modelling the data by
the Pythia simulation are evaluated by reweighting the corresponding variables to agree
with data. In this case the b-hadron direction and the low region of the muon pT spectrum
are not perfectly described. Finally, uncertainties in the simulation concerning branching
ratios of semi-leptonic decays, b-fragmentation, modelling of the kinematics of b-hadron
decays and the fraction and modelling of bb̄ pairs from gluon splitting are assessed with
the help of the simulation.
Table F.1 and Table F.2 in Appendix F summarise the different contributions in detail.
More details on the mentioned evaluation of the uncertainties are given in Ref. [103].
The resulting scale factors for the SV0 tagger using the 50% efficiency working point and
their uncertainties are given in the following:
20   pT   30 GeV : 0.85 0.06 (stat)  0.09 (syst)
30   pT   60 GeV : 0.91 0.03 (stat)  0.07 (syst)
60   pT   90 GeV : 0.88 0.04 (stat)  0.03 (syst)
90   pT   140 GeV : 0.88 0.09 (stat)  0.08 (syst)
The detailed numbers for the corresponding working point of the JetProb tagger can be
looked up in Appendix F. The scale factor for c-jets is assumed to be the same as that
for b-jets but with the uncertainty doubled. Dedicated studies are needed to constrain
the c-tagging properties further but are not available at the moment. Both scale factors
are illustrated in Fig. 8.12 as a function of jet pT up to 140 GeV. The scale factors for
both taggers are all close to one in all bins of jet pT. The relative total uncertainty ranges
from 4% to 14%. The largest contributions to the systematic uncertainties come from the
jet energy measurement, the template statistics and the uncertainty from the assumption
of the validity of the calibration on hadronically decaying b-hadrons. The systematic
uncertainty on the b-tagging efficiency is large ( 6  20%) and affects the dijet cross
section measurement significantly. In prospects of much larger available statistics from
LHC operation in 2011 and 2012, this uncertainty can be reduced greatly with the help of
the calibration method using tt̄ events. Furthermore, the calibration can be improved by
reducing the jet energy scale uncertainty and by increasing the knowledge on properties of
b-fragmentation and decay.
97
8 Object understanding and calibration
(a) SV0 tagger for SV0 weight ¡ 5.85 (b) JetProb tagger for JetProb weight ¡ 3.25
Figure 8.12: The b-tagging efficiency scale factors from the prelT method as a function of jet pT
for the SV0 tagger (a) and the JetProb tagger (b) using the 50% efficiency working point from
simulated tt̄ events. Taken from Ref. [103].
8.2.1.2 Calibration of the mistag rate
The calibration measurements for the mistag rate use an inclusive jet sample selected by
the single jet triggers. The mistag rate is the fraction of jets originating from light-jets
which are tagged by the b-tagging algorithm.2 The mistag calibration is derived as a
function of the jet pT and rapidity. Two independent methods are used which are combined
to give the final result.
SV0 mass method: Similar to the prelT method, from a discriminant variable, which
separates the different flavours, templates are constructed and with their help the fraction
of light-jets retained after the b-tagging selection is determined. In this case the templates
are constructed from the invariant mass of the charged particles associated to the sec-
ondary vertex, denoted as SV0 mass. An SV0 mass distribution is shown in Fig. 8.17. The
templates are derived from simulation and fitted to the experimental data after having
applied the b-tagging selection cut. The fits determine the fraction of flavours in the
b-tagged sample. With the help of the efficiency calibration the number of heavy flavours
Ntag
(b and c) before the tagging selection can be calculated from: N  pb,cqpb,cq . The numberpb,cq
of light-jets in the data sample before tagging is obtained by subtracting the other flavours
from the total number of jets: Nlight  Ndata  Nb  Nc. The mistag rate for light-jets
measured in data is given by:
N tag lightlight . (8.3)
Nlight
Negative tag method: A jet is considered as negatively b-tagged if it fulfils the inverse
relation, for example SV0 weight ¤ 5.85. The mistag rate light (as defined in Section 6.1)
is estimated by the negative tag rate neginc of the inclusive jet sample. Both rates would be
identical, if the negative part of the distribution used for flavour discrimination is identical
for all jet flavours and the tagging distribution for light-jets was perfectly symmetric
2Jets originating from u, d or s quarks or from gluons are jointly referred to as light-jets.
98
8.2 Calibration of bottom-tagging algorithms
around zero (see Fig. 8.7). Therefore, the following corrections have to be applied in order
to correct for these discrepancies. The negative tag rate consists of contributions from b-,
c- and light-jets. Firstly, the negative tag rate for b- and c-jets differs from the negative
tag rate for light-jets. This is because resolution effects on heavy-flavour jets which have
measurable lifetimes cause a sign flip of the discriminating variable and this increases the
negative tag rate with respect to the light mistag rate. The negative tag rate has to be
neg
corrected with a factor k  lighthf neg   1. Secondly, the negative tag rate misses the effectsinc
of material interactions and long-lived particles included in the light mistag rate. The

negative tag rate has to be corrected with a factor k  lightll neg ¡ 1. In summary, to extractlight
the light mistag rate from the negative tag rate two corrections factors, which are derived
from simulation, need to be considered:
mistagp  q  neglight inc  khfkll. (8.4)
Systematics: Sources of systematic uncertainties on both methods are instrumental
effects and uncertainties on the modelling of physics by MC. Both sources cause either
modified shapes of the templates or modifications in the correction factors khf or kll.
The uncertainty by the simulation statistics, the uncertainty on the b-tagging efficiency
calibration and the uncertainty on the fraction of jets containing long-lived particles or
material interactions are considered as systematic uncertainties in both methods. For the
SV0 mass method also the uncertainties on the shape of the constructed templates are
taken into account. Discrepancies in the modelling of the track multiplicity and impact
parameter resolutions are corrected by reweighting MC to fit data and to evaluate the
impact. The resulting relative systematic uncertainties are included in Appendix F. In
addition the dependency of the scale factors on the data periods are derived to account
for changes in the trigger configuration (for example trigger prescale) and changes in the
pile-up conditions. The observed shifts in the resulting scale factors are taken into account
in the final result and a systematic uncertainty contributing between 10% and 40% is
assigned.
Combination of both methods: For the jet pT bins above 200 GeV only the negative
tag method is used due to the available statistics in data and simulation. For each data
period the scale factors of both analyses, which show good overall agreement, are combined
under the assumption of uncorrelated uncertainties. The final scale factor is derived taking
the shifts between the data periods into account in the following way:
data{sim data{sim
κdata{sim ppTq 
maxpκlight ppTqq  minpκlight ppTqq , (8.5)
light 2
p data{simp qq p data{simwhere max κlight pT and min κlight ppTqq denote the maximum and minimum scale
factor obtained from the average scale factor of both methods over the data periods. The
uncertainty, which is the observed spread of scale factors over the data periods, covering the
data period dependence is added in quadrature to the systematic uncertainties described
above. The combined mistag scale factors and their uncertainties are given in Table 8.1 and
illustrated in Fig. 8.13(a) for the SV0 tagging algorithm at the 50% b-tagging working point.
The corresponding results are summarised in detail for the JetProb algorithm in Table F.7
and illustrated in Fig. 8.13(b). The mistag calibration scale factors are in agreement with
unity within their systematic uncertainty. The major systematic uncertainties arise from
the data period dependency of the scale factors, the simulation statistics, the uncertainties
99
8 Object understanding and calibration
Jet pT [GeV]
40-60 60-90 90-140 140-200 200-300 300-500
|η|   1.2
1.00.2 1.10.1 0.90.1 1.10.1 1.30.3 0.90.5
1.2   |η|   2.1
1.20.2 1.00.2 1.00.2 1.00.3 0.90.6 21
Table 8.1: The mistag rate scale factors for the SV0 tagger for the selection cuts yielding
50% efficiency in tt̄ events as function of jet pT and |η|. The quoted uncertainties include the
statistical and systematic uncertainties.
(a) (b)
Figure 8.13: The mistag scale factors after combining the results from the SV0 mass and
negative tag method for the SV0 tagging algorithm (a) and the JetProb tagging algorithm (b) for
the selection cuts yielding 50% efficiency in tt̄ events for |η|   1.2 (green) and 1.2   |η|   2.5
(black). Taken from Ref. [103].
on the impact parameter resolution and from the variations in the fractions of long-lived
particles and material interactions in jets. The total uncertainties on the scale factor range
from approximately 30% at 40 GeV to 10% for intermediate jet pT and are dominated
by systematic uncertainties. The total uncertainty in the high-pT region approximately
amounts to 50%.
8.2.2 Extension of the calibration and validation
The b-tagging calibration with 2010 ATLAS data yielded scale factors close to one with
total uncertainties in the range between 5% and 50%. The efficiency scale factors do not
show any dependence within the uncertainty on jet pT or rapidity. This is the justification
to extend the b-tagging efficiency calibration for this cross section measurement to higher
kinematic regions. If necessary, additional systematic uncertainties have to be addressed.
The calibration corrects for effects concerning the track and vertex resolutions and includes
systematic uncertainties which are determined by reweighting simulation to fit data and
100
8.2 Calibration of bottom-tagging algorithms
×106 ×106
40 40 < p  < 140 GeV 50 40 < p  < 140 GeVT T
35 Data Data
30 Pythia: b-jets 40 Pythia: b-jets
Pythia: c-jets Pythia: c-jets
25 Pythia: light-jets 30 Pythia: light-jets
20 MC stat. unc. MC stat. unc.
15 20
∫Ldt = 34 pb-1 ∫Ldt = 34 pb-110
10
5
0 0
0 2 4 6 8 10 0 2 4 6 8 10
2 2
1 1
0 0
0 2 4 6 8 10 0 2 4 6 8 10
 Number of pixel hits  Number of  shared pixel hits
(a) 40 GeV   pT   140 GeV (b) 40 GeV   pT   140 GeV
×103 ×103
400
140 < p  < 300 GeV 450 140 < p  < 300 GeV
350 T
Data 400
T
Data
300 Pythia: b-jets 350 Pythia: b-jets
250 Pythia: c-jets 300 Pythia: c-jets
Pythia: light-jets 250 Pythia: light-jets200 MC stat. unc. MC stat. unc.
200
150
∫Ldt = 34 pb-1 150100 ∫Ldt = 34 pb
-1
100
50 50
0 0
0 2 4 6 8 10 0 2 4 6 8 10
2 2
1 1
0 0
0 2 4 6 8 10 0 2 4 6 8 10
 Number of pixel hits  Number of  shared pixel hits
(c) 140 GeV   pT   300 GeV (d) 140 GeV   pT   300 GeV
Figure 8.14: Distribution of the number of pixel hits on tracks in different kinematic regions,
for both hit categories: (a,c) all hits, (b,d) shared hits. The tracks are considered by the SV0
tagging algorithm of b-tagged jets. Simulated data is normalised to the number of b-tagged jets in
data. The single contributions are drawn stacked on top of each other.
by examining the uncertainties on the simulation modelling. The ansatz to extend the
calibration is to apply the last measured scale factor to jets with pT ¡ 140 GeV and to
double the systematic uncertainty. The agreement between data and simulation is checked
between the kinematic regions which are already validated with respect to the calibration
discussed in the former section and the kinematic regions beyond. In the following the
calibration is extended as explained above and the properties and description of b-tagged
jets are studied in detail.
The properties of the tracks, associated to b-tagged jets fulfilling the event selection
and subject to the SV0 tagging algorithm, are investigated depending on the jet pT.
Compared are the following regions: 40 GeV   pT   140 GeV, 140 GeV   pT   300 GeV
and pT ¡ 300 GeV. Important to the validity of the b-tagging calibration is the probabil-
ity and properties of shared hits because they play an important role in degrading the
b-tagging performance. They mostly influence the impact parameter distribution in the
tails (cf. Fig. G.1). Hit sharing in the pixel detector is especially critical to b-tagging
performance. A track with shared hits, denoted as shared track, is defined by having
at least one shared hit in the pixel or at least two shared hits in the SCT detector. A
track without shared hits is referred to as good track. The hit multiplicities measured
101
Data/MC NNNNuuuummmmbbbbeeeerrrr    ooooffff    jjjjeeeettttssss Data/MC NNNNuuuummmmbbbbeeeerrrr    ooooffff    jjjjeeeettttssss
Data/MC NNNNuuuummmmbbbbeeeerrrr    ooooffff    jjjjeeeettttssss Data/MC NNNNuuuummmmbbbbeeeerrrr    ooooffff    jjjjeeeettttssss
8 Object understanding and calibration
0.16
∫Ldt = 34 pb-1 40 < p  < 140 GeV 0.5 ∫Ldt = 34 pb-1 140 < p  < 300 GeVT T
0.14 Data Data
Pythia: b-jets Pythia: b-jets
0.12 Pythia: c-jets 0.4 Pythia: c-jets
Pythia: light-jets Pythia: light-jets
0.1 MC stat. unc. MC stat. unc.
0.3
0.08
0.06 0.2
0.04
0.1
0.02
0 0
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
∆R between track and jet axis ∆R between track and jet axis
(a) (b)
0.9
∫Ldt = 34 pb-1 p  > 300 GeVT
0.8 Data
Pythia: b-jets
0.7 Pythia: c-jets
0.6 Pythia: light-jets
MC stat. unc.
0.5
0.4
0.3
0.2
0.1
0
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
∆R between track and jet axis
(c) pT ¡ 300 GeV
Figure 8.15: Distribution of the fraction of tracks with shared hits in b-tagged jets as a func-
tion of their distance ∆R to the axis of the jet. Presented are three kinematic regions: (a)
40 GeV   pT   140 GeV, (b) 140 GeV   pT   300 GeV and (c) pT ¡ 300 GeV. The single
contributions are drawn stacked on top of each other.
in the pixel detectors for both track categories as a function of the jet pT are shown
in Fig. 8.14. The hit multiplicities for the upper most kinematic region is included in
Appendix G. On average a track consists of 3 pixel hits of which most are not shared
between different tracks. These three space points measured at very small radii from the
interaction point are essential for b-tagging. The hit multiplicities for the other inner
detector subsystems are included in Appendix G. In general a track also consists of 8 SCT
hits and 34 hits in the TRT. The distribution of the number of shared hits for the b-layer,
the pixel and SCT detector is peaked at zero for all jet pT ranges. The agreement between
simulation and data is very good in general, the number of shared hits is well modelled.
There is no significant discrepancy between the calibrated region (Fig. 8.14 top) and the
region with the extended calibration (Fig. 8.14 bottom). To validate that the simulation
correctly reflects the degradation of the b-tagging performance in the higher kinematic
regions, the increase of the fraction of shared hits as a function of their distance from
the axis (transverse profile) of the jet in angular space is studied. Besides the frequency
and distribution of tracks with shared hits among the sub-systems in the inner detector,
this transverse profile is important. The prediction of Pythia for the fraction of shared
hits in tracks associated to b-tagged jets is compared to data in Fig. 8.15. It is clearly
102
FFrraaccttiioonn  ooff  ttrraacckkss  wwiitthh  sshhaarreedd  hhiittss
FFrraaccttiioonn  ooff  ttrraacckkss  wwiitthh  sshhaarreedd  hhiittss
FFrraaccttiioonn  ooff  ttrraacckkss  wwiitthh  sshhaarreedd  hhiittss
8.2 Calibration of bottom-tagging algorithms
∫Ldt = 34 pb-1 110 GeV < M < 370 GeV ∫Ldt = 34 pb-130000 370 GeV < M < 850 GeVData 1000 Data
Pythia: b-jets Pythia: b-jets
25000 Pythia: c-jets Pythia: c-jetsPythia: light jets 800 Pythia: light jets
MC stat. unc. MC stat. unc.
20000
600
15000
400
10000
5000 200
0 0
0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 45 50
SV0 weight SV0 weight
(a) (b)
Figure 8.16: SV0 weight (decay length significance) distribution of b-tagged jets in events where
the leading jets are both b-tagged in bins of reconstructed dijet mass: (a) 110 GeV  M   370 GeV
and (b) 370 GeV   M   850 GeV. The single contributions are drawn stacked on top of each
other.
visible that the fraction of tracks with shared hits is larger for tracks closer to the axis
of the jet. These distributions also reflect the fact that the light-jet rejection is strongly
dependent on the jet pT. The fraction of mistagged light-jets is heavily increasing in each
subsequent kinematic region. The fraction of shared hits among the tracks associated to a
jet is more than doubled between subsequent kinematic regions. The fraction increases
from about 10% to 60% at ∆RÑ 0 with increasing jet pT bin. This effect is well modelled
by the simulation in the region covered by the b-tagging calibration as well as in the region
probed above 140 GeV.
The former paragraph discussed the entire sample of b-tagged jets, the next distributions
focus on the properties of b-tagged jets in events where the leading jets are both b-tagged
and which are used in the cross section measurement. The SV0 weight distribution of
these b-tagged jets is presented in Fig. 8.16 in bins of reconstructed dijet mass M . The
dijet mass bins approximately represent the kinematic regions with validated calibra-
tion (110 GeV   M   370 GeV) and the kinematic region subject to this validation
(370 GeV   M   850 GeV). In contrast to the fraction of light-jets and c-jets remaining
in Fig. 8.15 the requirement of a double b-tag in events improves the purity and the
fraction of light-jets is reduced. In the higher mass region the number of events is strongly
decreased, but the overall agreement between data and simulation is good. The mass of
the reconstructed secondary vertex among those b-tagged jets is presented in Fig. 8.17.
These templates nicely demonstrate the discriminating power of the secondary vertex
mass.
Each b-tagged jet is a single entry in the histogram, namely two entries per event. But
these figures cannot show the correlation between the b-tagged jets nor is it possible to
extract the number of signal events for the bb̄ cross section measurement. The SV0 mass
of light-jets peaks in general below 1 GeV, whereas c- and b-jets contain a secondary
vertex with an average mass of 2 GeV. Both discussed quantities, the SV0 weight and
the SV0 mass distribution separated into different mass regions, are well described by the
simulation. Both distributions are important for the cross section measurement. The SV0
mass is well modelled because the tracking in simulation can be trusted. In Appendix G
103
NNuummbbeerr  ooff  jjeettss
NNuummbbeerr  ooff  jjeettss
8 Object understanding and calibration
several additional cross checks are shown including the description of jets with a SV0
weight below 5.85 which also consolidates the validity of the calibration for jets with
pT ¡ 140 GeV.
In summary, the cross section measurement makes use of the b-tagging efficiency calibration
60000 1800
∫Ldt = 34 pb-1 110 GeV < M < 370 GeV ∫Ldt = 34 pb-1 370 GeV < M < 850 GeV
Data 1600 Data
50000 Pythia: b-jets Pythia: b-jets
Pythia: c-jets 1400 Pythia: c-jets
Pythia: light jets Pythia: light jets
40000 MC stat. unc. 1200 MC stat. unc.
1000
30000
800
20000 600
400
10000
200
0 0
0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14
SV0 mass for b-tagged jets (double tag) [GeV] SV0 mass for b-tagged jets (double tag) [GeV]
(a) 110 GeV   M   370 GeV (b) 370 GeV   M   850 GeV
Figure 8.17: The distribution of the invariant mass of the charged tracks in the secondary
vertex in events where both leading jets are b-tagged. The single contributions are drawn stacked
on top of each other.
extended for jets with a transverse momentum higher than 140 GeV. The validity of this
assumption is proven by the cross checks presented. It can be estimated that doubling the
systematic uncertainty is sufficient and conservative enough. In Section 9 it will shown that
an extension of the mistag scale factors is not necessary and that they are not of concern
to the cross section measurement. But the extension of the mistag scale factors is included
in the histograms presented. Furthermore, in the following description of systematics for
the analysis the extension is addressed once more and, if necessary, additional systematic
uncertainties have to be assigned.
The resulting calibration scale factors are the following:
20   pT   30 GeV : 0.85 0.06 (stat)  0.09 (syst)
30   pT   60 GeV : 0.91 0.03 (stat)  0.07 (syst)
60   pT   90 GeV : 0.88 0.04 (stat)  0.03 (syst)
90   pT   140 GeV : 0.88 0.09 (stat)  0.08 (syst)
pT ¡ 140 GeV : 0.88 0.09 (stat)  0.16 (syst)
8.3 Jet energy scales and resolution
The algorithms used to obtain the four-momenta of jets and the calibration to correct jet
energies at the hadronic scale have already been presented. The precision of this established
energy scale determines the accuracy of many measurements. A jet energy scale uncertainty
of 1% which is the goal of ATLAS in the long term results in an uncertainty of about 10%
on the jet cross section in the intermediate pT range. For this analysis, the inclusive jet
104
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NNuummbbeerr  ooff  jjeettss
8.3 Jet energy scales and resolution
energy scale uncertainty ranges from approximately 2% to 4% for jets within |η|   2.1 and
between pT ¡ 40 GeV and pT   800 GeV. The following section discusses this uncertainty
and its origin as well as the determination of the jet energy resolution with a data-driven
method. In principle, the jet energy uncertainty depends on the initial parton type by
which a jet was initiated. This arises from the different fragmentation behaviour of different
parton types. However, it is not derived separately for each parton type since in the data
this is a priori unknown. In Section 3.1.3 it was already presented that the fragmentation
of b-jets is harder compared to light-quark and gluon jets. Due to the presence of the
b-hadron the particle composition in such jets differs with respect to the majority of jets
on which the energy scale uncertainty has been derived from. To obtain an estimate of
an additional uncertainty on b-jets a data-driven method is tested making use of tracking
information.
8.3.1 Inclusive jet energy scale uncertainties
The jet energy scale (JES) uncertainty [60] for inclusive jets which are calibrated with the
EM+JES calibration scheme (cf. Section 5.1.3) is determined as function of jet pT and η.
It is estimated from combinations of data-driven techniques [104], a single pion test-beam
measurement [105] and analyses based on MC simulations. Details on the nominal Pythia
MC samples, on which the calibration is derived from, are given in Section 4.4. The sources
of the systematic uncertainties and their effect on the response (cf. Eq. 5.2) of EM+JES
calibrated jets are discussed. The systematic uncertainty has the following contributions:
 The uncertainty due to the calibration method.
 The uncertainty due to the calorimeter response.
 The uncertainty due to the detector simulation.
 The uncertainty due to the physics model and parameters embedded in the MC
event generators.
 The uncertainty due to the relative calibration of jets with |η| ¡ 0.8.
Calibration method: After applying the EM+JES calibration scheme on the sample
on which the calibration is derived from, small deviations from unity in the response R
(cf. Eq. 5.2) at low pT remain (non-closure). The reconstructed jets are therefore not
completely restored to particle level. Firstly, this is caused by the assumption in the
EM+JES calibration that each constituent in a jet needs the same average compensation.
Secondly, the calibration does not distinguish between jet energy and momentum, any jet
with a non-zero jet mass is slightly distorted in transverse momentum by the EM+JES
energy calibration. The systematic uncertainty due to the non-closure is taken as the
largest deviation of the response from unity between energy and pT.
Calorimeter response: The jet energy response and the scale uncertainty is derived
from the response and the uncertainty of the single particles interacting in the calorimeters
which contribute to a jet. With the help of the simulation the energy deposited in each
calorimeter cell can be linked to the initiating particles. The uncertainties for charged
hadrons are measured by:
 The measurement of the single hadron energy in a cone around an isolated track
with respect to the track momentum (E over p measurement) in the momentum
range from 0.5   ptrack   20 GeV.
105
8 Object understanding and calibration
 The measurement of the response of single charged pions of a momentum between
20 and 350 GeV in the combined test-beam performed in 2004, where a full slice of
the ATLAS calorimeter has been assembled.
The absolute electromagnetic energy scale is established using Z Ñ ee decays for the
electromagnetic calorimeters and using the energy loss of minimally ionising muons in
the Tile calorimeter. The uncertainty found on this electromagnetic scale is considered
for all other particles in the jets not covered by the E over p measurement. Additional
uncertainties which are taken into account are related to the calorimeter acceptance, the
uncertainties for particles with ptrackT ¡ 400 GeV and uncertainties connected to neutral
hadrons.
Detector simulation: Uncertainties due to the detector simulation are caused by the
modelling of the electronic noise and the material description in the simulation.
As described in Section 5.1.2, the topological clusters are reconstructed using the signal-
to-noise ratio of calorimeter cells. Hence, the mis-modelling of the noise in the simulation
can lead to differences in shape and in the appearance of fake clusters. The noise in
the calorimeters is time-dependent due to for example small instabilities in the voltage
supply, whereas the noise injected in the simulation is not. Electronic noise in the ATLAS
calorimeters is dependent on the architecture of the calorimeter. In the electromagnetic
calorimeters the noise is of the order of 10 to 100 MeV, in the hadronic calorimeters the
noise is of the order of 100 to 600 MeV.
Therefore, the modelling of noise cannot completely reflect the noise in data. This effect
is estimated by using the RMS of the noise measured in data to reconstruct jets from
topological clusters in simulation. The maximum observed change in the jet response
between the nominal sample and the modified sample is used to estimate the uncertainty
on the jet energy measurement.
The jet calibration was derived using the geometry simulated in the nominal MC sample
(cf. Section 4.4). Generated MC samples with variations in the material budget are studied.
In general, the data-driven analyses are not directly affected by this because they use
reconstructed data. Nevertheless the track selection in the E over p measurement and
all particles not included in the data-driven E over p measurement with p ¡ 20 GeV are
affected by discrepancies in the material description.
Physics modelling in the event generator: The contribution to the jet energy scale
uncertainty from the modelling of the fragmentation, the underlying event and different
MC models are obtained with the help of the following samples:
 Alpgen+Herwig+Jimmy: The Alpgen generator [106] interfaced with Herwig
and Jimmy is used to determine the contributions to the uncertainty arising from
differences in the modelling of the hard process generation and the soft physics
modelling. For these samples an MC10 tune is used with the CTEQ6L1 parton
distribution [11]. Compared to the nominal Pythia simulation, this sample is
different in every single generation step: modelling of the multi-parton interactions,
the parton shower, the fragmentation model and the underlying event.
 Perugia2010 tune: Besides the MC10 tune, the Perugia tunes [107, 108] are inde-
pendent tunes which are derived from recent hadron collider data. Adjustments to
final-state radiation, to the production of particles with strangeness and to measure-
ments of jet fragmentations are included. This tune is used to mainly investigate
effects of soft physics modelling.
106
8.3 Jet energy scales and resolution
The jet response for each sample is determined and the ratio of the nominal response
to the response for each of the two samples is used to estimate a systematic uncertainty.
Intercalibration: The JES uncertainty for forward jets in the end-cap and forward
regions (|η| ¡ 0.8) is determined using the uncertainty from central jets (|η|   0.8) from
the single particle response and from the systematic variations of the MC simulations. The
uncertainty is transferred into the forward region with the help of transverse momentum
balance in dijet events. The events used require at least one central jet. Events are
selected for this dijet balance method, if they posses a perfect back-to-back dijet topology
|φ1φ2| ¡ 2.6. In case of an additional jet, the transverse momentum carried by this third
jets is restricted to a small fraction of the average transverse momentum of the leading
EM   pT,1 pjets p T,2T,3 15% . The central jet is exploited to measure the forward jet’s relative2
response. The following effects contribute to the total jet energy scale uncertainty for
forward jets:
 Deviations between the relative jet response in data and simulation are considered
in the systematic uncertainty by adding those in quadrature.
 The total uncertainty from the reference jets are kept as baseline.
As part of the jet energy calibration, a correction to each jet is applied to correct for
the additional energy contributed by pile-up interactions. To estimate the remaining
uncertainty in the jet energy scale after this correction the following studies are done: the
effect of variations in the trigger selection on the average additional energy Cpileup in each
jet constituent is studied, the construction of the jet correction from the average number
of jet constituents xNconstituentspηq y is validated, jets formed from charged particle tracks
(ptrackT ¡ 0.5 GeV and |η|   2.5) which are input to the anti-kt algorithm are matched
to calorimeter jets to measure the variations in the corrected calorimeter jet energies
as a function of the number of primary vertices NPV, the non-closure of the correction
at the constituents level is evaluated as a function of the number of primary vertices
N .3PV Beyond the limited coverage of the track-jets, the dijet balance method is also
here used to transfer the uncertainty in the more forward regions. The total systematic
uncertainty from the pile-up correction is a function of NPV and is the quadratic sum of
all uncertainties.
Summary of the jet energy scale uncertainty: The total uncertainty on the jet
energy scale is the quadratic sum of all individual contributions. In the central region
(|η|   0.8), the uncertainty as function of jet pT and |η| is composed from:
 The final non-closure uncertainty which is accounting for the uncertainty on the
calibration procedure is the maximum deviation from unity between the energy and
pT response.
 The calorimeter response uncertainty is estimated from the propagation of single
particle uncertainties to the jets.
 Contributions to the uncertainties using Monte-Carlo samples with a systematic
variation are accounted for as described in the following:
The ratio between the response in the sample Rvar with the corresponding variation
3These are so-called track-jets. They are insensitive to pile-up effects and can therefore be used as
reference objects to study the pile-up correction.
107
8 Object understanding and calibration
and the response in the nominal sample Rnom is used as follows to estimate the
deviations caused by systematic variation:
∆ pp , ηq    Rvarp

pT, ηq
JES T 1 R pp , ηq 
 . (8.6)
nom T
This deviation is determined for the energy as well as for the pT response. The
final contribution to the JES uncertainty is given by the larger deviation in either
response to the final JES systematic uncertainty due to the specific systematic effect:
∆JESppT, |η|q  maxp∆E pp , ηq,∆pTJES T JESppT, ηqq. (8.7)
In addition the uncertainties from the material description are adjusted. The
uncertainty estimated from additional material in the inner detector for the E over p
measurement is scaled by the average fraction of particles forming the jet that are
within the acceptance p   20 GeV. The uncertainty from the additional material
in front of the calorimeter for particles not covered in the E over p measurement is
scaled by the average fraction of such particles within a jet.
For each (pT, η)-bin, the uncertainty contributions from the calorimeter, the jet cal-
ibration non-closure, and systematic Monte-Carlo simulation variations are added in
quadrature. Furthermore, for jets in the regions beyond |η| ¡ 0.8, the intercalibration
contribution is added in quadrature to the total JES uncertainty with the exception of
the non-closure term that is taken from the specific η-region. The contribution to the
uncertainty due to additional proton-proton interactions is added event-by-event, because
it depends on the number of primary vertices in the event. In the following the JES
uncertainties assume only one single interaction in the event. For jets with pseudorapidity
|η|   2.1 and one additional interaction the pile-up uncertainty is less than 2% and
monotonically decreasing with jet pT. The uncertainty increases with each additional
pile-up vertex, with four vertices the uncertainty is overall less than 6%.
This uncertainty derived on a QCD inclusive jet sample reflects the specific composition
of gluon- and quark-initiated jets in QCD. Differences in the event topology from this
mixture can lead to a dependence on the jet energy scale. Such analyses like the one
presented have to account for these differences due to a different jet flavour mixing.
Finally, the fractional jet energy scale systematic uncertainty and the individual contribu-
tions are shown for two selected pseudorapidity regions in Fig. 8.18. The jet energy scale
uncertainty which is the baseline for jets considered in this analysis is between 2% and 4%.
This does not include the uncertainty from the pile-up correction. The uncertainty from
the non-closure for all pseudorapidity regions and jets with pT ¡ 30 GeV is smaller than
1%. The uncertainty is driven in the high-pT region by the uncertainty on the calorimeter
response from the single particle response and adds 1.5% up to 4% to the uncertainty.
The uncertainty from the noise modelling in MC is negligible for jets with pT ¡ 45 GeV
and from the detector modelling well below 1% for all kinematic regions. At low pT the
uncertainty from the MC modelling accounts for approximately a constant contribution of
1.5% and decreases with increasing jet pT. In summary, the maximum uncertainties in
different η regions is presented using representative jet transverse momenta of 20, 200 and
1.5 TeV.
108
8.3 Jet energy scales and resolution
0.12 0.12
Anti-k  R=0.4, EM+JES, 0 ≤ | η | < 0.3, Data 2010 + Monte Carlo QCD jets Anti-k  R=0.4, EM+JES, 1.2 ≤ | η | < 2.1, Data 2010 + Monte Carlo QCD jets
t t
0.1 ALPGEN+HERWIG+JIMMY Noise Thresholds 0.1 ALPGEN+HERWIG+JIMMY Noise Thresholds
JES calibration non-closure PYTHIA Perugia2010 JES calibration non-closure PYTHIA Perugia2010
Single particle (calorimeter) Additional dead material Single particle (calorimeter) Additional dead material
0.08 Total JES uncertainty 0.08 Intercalibration Total JES uncertainty
0.06 0.06
ATLAS ATLAS
0.04 0.04
0.02 0.02
0 0
3 3 3 3
30 40 102 2×102 10 2×10 30 40 102 2×102 10 2×10
p jet [GeV] p jet [GeV]
T T
(a) in the barrel region (b) in the end-cap region
Figure 8.18: Fractional jet energy scale systematic uncertainty as a function of pT for jets
in the pseudorapidity region 0.3   |η|   0.8 in the calorimeter barrel (a) and in the region
1.2   |η|   2.1 in the calorimeter end-cap. The total uncertainty is shown as the solid light
shaded area. The individual sources are also shown together with uncertainties from the fitting
procedure if applicable. Taken from Ref. [60].
8.3.2 Jet energy resolution
The energy smearing of particles and correspondingly for jets of fixed energy is due to
the limited energy resolution σpEq{E of the calorimeters from fluctuations inherent in the
development of showers, and by instrumental and calibration limits. For jets an additional
aspect influences the resolution. The particle composition within the jet has an impact
on the total jet energy resolution. Fluctuations in the shower development are due to
the probabilistic nature of interactions of the particles in the jet with?the calorimeter
material. This statistical process improves with increasing energy (91{ E). An energy-
independent term due to instrumental effects contributes to the energy resolution (91{E)
and a constant term is limiting the resolution at very high energies due to non-linearities
and non-uniformities. The total energy resolution is consequently given by:
σ  ?a ` b ` c, (8.8)
E E E
where a, b and c are determined by the calorimeter parameters. In analogy the transverse
momentum resolution is defined and is for simplicity also referred to as jet energy resolution.
8.3.2.1 Resolution of inclusive jets
For the jet energy measurement the knowledge on the jet energy resolution is important
as it defines the dijet mass resolution. The currently applied EM+JES calibration is not
designed to improve the energy resolution of the jets. The calibration only shifts the
average response of jets closer to unity. The modelling of the jet energy resolution in
simulation has to be validated using data-driven methods in order to be able to correct
these smearing effects for the cross section measurement.
The jet energy resolution in data is measured using the transverse momentum balance of
the leading jets in QCD dijet events [109]. At leading order the transverse momentum
109
Fractional JES systematic uncertainty
Fractional JES systematic uncertainty
8 Object understanding and calibration
Maximum fractional JES Uncertainty
η region
pT = 20 GeV 200 GeV 1.5 TeV
0   |η|   0.3 4.1% 2.3% 3.1%
0.3   |η|   0.8 4.3% 2.4% 3.3%
0.8   |η|   1.2 4.4% 2.5% 3.4%
1.2   |η|   2.1 5.3% 2.6% 3.5%
2.1   |η|   2.8 7.4% 2.7%
Table 8.2: Summary of the maximum EM+JES jet energy scale systematic uncertainties for
different pT and η regions from the Monte-Carlo simulation based study for anti-kt jets with
R  0.4. Taken from Ref. [60].
of the two jets in a dijet topology is conserved. An asymmetry between the transverse
momenta of the two leading jets AppT,1, pT,2q is defined as
p q  pT,1  pT,2A pT,1, pT,2   . (8.9)pT,1 pT,2
The asymmetry is described by a Gaussian distribution and is sensitive to the jet energy
resolution. The relation between the Gaussian σ of the asymmetry distribution and the
relative jet resolution for jets in the same rapidity region is given by:
a
σpp q2   σpp q2 T,1 T,2  ?σ
?
p
σ TA x   y ñ
σp
2σ TA  . (8.10)
pT,1 pT,2 2pT pT
p  p
The average pT of the dijet system is given by p
avg  T,1 T,2T . To be less sensitive to soft2
radiation effects and to enrich the events with back-to-back configurations, the following
selection cuts are required: the number of jets in the event is required to be smaller than
4, ∆φpleading jetsq ¡ 2.6 and the transverse momentum of the possible third jet has to
be smaller than 10 GeV at the electromagnetic scale. A subset of measured asymmetries
for inclusive jets with |y|   1.2 is given in Fig. 8.19. The data and simulation prediction
are overlaid and found to be in reasonable agreement. The asymmetry has the shape of a
Gaussian distribution and each distribution is fitted to extract σA. In order to correct
for effects due to the presence of additional soft jets not detected in the calorimeter or
not reconstructed by the jet reconstruction, the asymmetry is recomputed allowing for a
third jet with a series of allowed p values pEMT T,3   {5,7,8,10,15,30} GeV. The fitted σ of
the asymmetry as a function of the threshold value on the third jet is fitted with a straight
line to extrapolate down to pT,3 Ñ 0. This extrapolation gives a data-driven estimate on
the expected resolution on an ideal dijet topology. The dependence of the asymmetry
on the presence of a third jets is presented by two examples in Fig. 8.20. These figures
show the relative resolution extracted from the asymmetry distributions as a function of
threshold value pT,3. The asymmetry in each jet pT region is recalculated for these six
threshold values: 5, 7, 8, 10, 15 and 20 GeV. A soft radiation correction factor is obtained
from the ratio between the extrapolated value at pT,3 Ñ 0 and the value at 10 GeV. This
110
8.3 Jet energy scales and resolution
0.14 avg avg40 GeV < p < 60 GeV Inclusive jets: 0.3 210 GeV < p < 260 GeV
Inclusive jets:
T T
0.12 |y|<1.2 Data |y|<1.2 Data
Pythia 0.25 Pythia
0.1
0.2
0.08
0.15
0.06
0.04 0.1
0.02 0.05
0 0
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1
Asymmetry A Asymmetry A
(a) (b)
Figure 8.19: Asymmetry distributions for inclusive jets with |y|   1.2 as defined in Eq. 8.9 for
two different pavgT bins: (a) 40   pavgT   60 GeV, (b) 210   pavgT   260 GeV.
correction is then applied to the measurement satisfying pT,3   10 GeV:
pσpp q{p q
 T T pT,3Ñ0 GeVKsoft p . (8.11)σppTq{pTqpT,3Ñ10 GeV
The correction factor is a rising function of pavgT and converges for high transverse momenta
towards 1. Over the full range, it takes values between 0.8 and 1. If, due to statistics,
the correction factor should marginally become bigger than one, it is forced to one. The
resulting fitted transverse momentum resolutions are presented in Fig. 8.21. The shape
of the resolutions obtained in data and simulation are in agreement. The lower parts of
Fig. 8.21 show the differences between the resolutions obtained from data and simulation.
The dotted lines indicate a 10% difference. The resolution in data is underestimated by
about 10%. With the help of the fitted resolution curves it is estimated that this tendency
continues for jets with pT ¡ 300 GeV. More detailed studies of the resolution on ATLAS
0.25 0.25
avg avg
110 GeV < p < 160 GeV Inclusive jets: 110 GeV < p < 160 GeV Inclusive jets:
T T
0.2 |y|<1.2 Data 0.2 1.2≤|y|<2.1 Data
Pythia Pythia
0.15 0.15
0.1 0.1
0.05 0.05
0 0
0 5 10 15 20 25 30 0 5 10 15 20 25 30
pEM [GeV] pEM [GeV]
T,3 T,3
(a) |y|   1.2 (b) 1.2   |y|   2.1
Figure 8.20: Fitted resolution extracted from the asymmetry distributions as a function of the
threshold value applied on pT,3 for the pT region : (a) |y|   1.2, (b) 1.2   |y|   2.1. Only
statistical uncertainties are shown.
111
σ(p )/p
T T 1/N dN/dA
σ(p )/p
T T 1/N dN/dA
8 Object understanding and calibration
0.3
0.2
Inclusive jets: Inclusive jets:
0.25 0.18
Data 0.16 Data
0.2 Pythia 0.14 Pythia
0.12
0.15 0.1
0.08
0.1
0.06
0.05 0.04
0.02
0 0
0 50 100 150 200 250 300 350 400 0 50 100 150 200 250 300 350 400
1.2 1.2
1 1
0.8 0.8
0 50 100 150 200 250 300 350 400 0 50 100 150 200 250 300 350 400
pavg [GeV] pavg [GeV]
T T
(a) |y|   1.2 (b) 1.2   |y|   2.1
Figure 8.21: Jet momentum resolution measured using the dijet balance in QCD events as a
function of pavgT between 40 and 300 GeV. The soft radiation effects are corrected. The dashed
lines in the lower plots indicated a deviation of 10%.
data can be found here [109]. The pT difference measured with the dijet balance is not
only due to the resolution affects in the detector but also includes energy losses in the
reconstruction of each jets due to the showering and fragmentation (so-called out-of-cone
effects). With the help of the simulation this effect can be corrected for but this does
not change the relative deviation of about 10% between data and simulation. Such a
correction effects the lower pT region more strongly and yields a correction factor of about
10% for jets around 40 to 60 GeV.
The resolution embedded in the ATLAS simulation measured from the jet response
of reconstructed jets matched to particle jets for an inclusive jet sample is presented
in Fig. 8.22. The resolution is identified with the standard deviation of the Gaussian
distributions of the jet response. This resolution derived from the simulation is not
expected to be in perfect agreement with the outcome of the dijet balance method which
is corrected for soft radiation and energy losses due to the showering. This is because
the jets entering in the jet response calculation are taken from all event topologies. With
the help of the resolution extracted from simulation in Fig. 8.22 pseudo-experiments will
later be used to estimate the uncertainty arising from the mis-modelling of the jet energy
resolution in simulation. The jet resolution in simulation is degraded conservatively by
10% which is the outcome of the dijet balance measurement for all rapidity and kinematic
regions.
8.3.2.2 Resolution of jets with heavy-flavour content
Due to the limited statistics detailed studies on the basis of the dijet balance method for
b-tagged jets are not possible. The uncertainty covering the deviation in the resolution
between data and simulation from inclusive jets is already conservative. There is no
evidence that this deviation is much larger or different for b-jets therefore the knowledge
from the dijet balance method is transferred to b-tagged jets. The resolution of b-jets
is extracted from simulation the same way as discussed for the inclusive jet sample
and presented in Fig. 8.23. The dashed lines represent the outcome of a fit describing
the resolution curve with Eq. 8.8. The bin sizes used in the dijet mass cross section
measurement are chosen accordingly to the dijet mass resolution to contain approximately
112
Data/MC σσ((pp ))//ppTT TT
Data/MC σσσ(((ppp )))///pppTTT TTT
8.3 Jet energy scales and resolution
0.15
0.14
Pythia:
0.13
Inclusive jets
0.12
0.11
0.1
0.09
0.08
0.07
0.06
0.05
0 100 200 300 400 500 600 700 800
ptruth [GeV]
T
Figure 8.22: Jet momentum resolution as a function of ptruthT derived from simulation. The
jets entering in this calculation fulfil the same requirements as for the jet response calculation.
The error bars reflect the uncertainties on the fit parameter.
95% (=2σ) of the reconstructed events. Details on this binning are given in Appendix A.
With the help of the resolution of b-jets shown in Fig. 8.23(a) the uncertainty on the dijet
cross section will be evaluated using pseudo-experiments. The resolution of b-jets is similar
to the resolution of inclusive jets in the low pT region. At around 300 GeV the resolution at
calorimeter level of b-jets is better than for inclusive jets. At about 800 GeV the resolution
for b-jets is about 15% better. Due to the dominating presence of gluon-initiated jets, the
resolution of inclusive jets is worse than that of jets from heavy-quarks. Gluon-initiated
jets tend to produce more particles (The colour charges predict that the probability of
gluon emission of a gluon relative to that of a gluon emission off a quark is  9 .) which
4
are also softer compared to particles in quark-initiated jets. This already leads to an effect
in the resolution due to the statistical nature of a shower development. Moreover, slower
particles tend to bend more in a magnetic field. Therefore gluon-initiated jets are wider
and may be subject to higher losses in the jet reconstruction because particles are bent
outside the area of the jet algorithm.
The inclusion of non-interacting particles into the resolution determination has the effect
of degrading the jet pT resolution as shown in Fig. 8.23(b). The distribution of the relative
difference between reconstructed jet energy Ereco and simulated true energy Etruth has
approximately a Gaussian shape. The inclusion of non-interacting particles enhances
the negative tail and makes the distributions more asymmetric. A Gaussian core is still
retained. In the worst case the resolution is degraded by about 25% in the high pT region.
8.3.3 Energy scale uncertainties of jets with heavy-flavour content
For this cross section measurement of b-jets with the help of the SV0 tagging algorithm, an
additional jet energy scale uncertainty is derived with the help of tracking information in
data. The tracks are calibrated independently from the calorimeter and serve as reference
objects. This uncertainty is strictly speaking only valid for SV0 b-tagged jets. The total
jet energy scale uncertainty is given by:
Total JES uncertainty  inclusive JES uncertainty` b-jet JES uncertainty. (8.12)
113
σ(p )/p
T T
8 Object understanding and calibration
0.15 0.15
0.14 Pythia: 0.14 Pythia:
0.13 Inclusive 0.13 b-jets (NI)
0.12 b-jets 0.12 b-jets
0.11 Fit 0.11 Fit
0.1 0.1
0.09 0.09
0.08 0.08
0.07 0.07
0.06 0.06
0.05 0.05
0 100 200 300 400 500 600 700 800 0 100 200 300 400 500 600 700 800
ptruth [GeV] ptruth [GeV]
T T
(a) (b)
Figure 8.23: Jet pT resolution as a function of p
truth
T derived from simulation. The jets entering
in this calculation fulfil the same requirements as for the jet response calculation. (a) Inclusive
and b-jets are compared at calorimeter level, (b) b-jets are compared at calorimeter level and at
particle level including non-interacting particles (NI). The error bars reflect the uncertainties on
the fit parameter.
All b-jets are treated equally, irrespective of their decay mode and calibrated with the
EM+JES scheme. The missing energy carried away by neutrinos and muons is not corrected
for directly in the energy measurement. But this correction is performed in a single step
where the energy of the calorimeter jet is corrected with the help of the energy of the
matched particle jet in simulation including the energy of the neutrino and the muon.
In the course of these studies, the jet response of b-jets and b-tagged jets is compared to
understand the impact of the EM+JES calibration. This is followed by the studies aiming
to obtain an additional uncertainty on the jet flavour for this analysis.
8.3.3.1 Jet energy response of jets with heavy-flavour content
The jet pT response (cf. Eq. 5.2) is calculated as a function of the transverse momentum
of the particle jet for each subset of jet flavours. The impact of the EM+JES calibration
is studied because the calibration constants are driven by the flavour mixture of the
QCD sample. To obtain the jet pT response, reconstructed jets are matched to truth jets
requiring ∆R   0.4. If a reconstructed or truth jet fails an isolation criteria, namely that
another jet with pEMT ¡ 7 GeV is found within ∆R   1, this jet pair is discarded. The
response in a given ptruthT bin is obtained by fitting a Gaussian distribution and identifying
the response as the Gaussian mean from the fit. The behaviour of the jet pT response
of b-jets compared to the inclusive response is presented in Fig. 8.24. The errors on the
obtained response values are given by the uncertainty on the Gaussian mean from the fit
result and reflect the available statistics in each jet flavour sample. The response presented
in Fig. 8.24(a) is calculated from particle jets which represent the calorimeter level (cf.
Section 5.1). The response is calculated from the default Pythia samples for truth jets
with ptruthT ¡ 20 GeV and |y|   2.1.
The response of the inclusive QCD jet sample shows deviations from unity of less than
1% and gives rise to the non-closure uncertainty contribution presented in Section 8.3.1.
The response of the light-jet sample in which the light-quark and gluon-initiated jets are
joined is in almost perfect agreement with the inclusive sample as expected. These two
114
σ(p )/p
T T
σ(p )/p
T T
8.3 Jet energy scales and resolution
samples have the largest overlap and the contribution of the other heavier quark initiated
jets in the inclusive sample is at the per cent level.
The response of the c- and b-jets can be understood when separating the inclusive sample
into gluon- and quark-initiated jets. The fragmentation properties of gluon jets cause
that the correction to restore gluon jets to hadronic scale has to be much larger than for
quark jets. Gluon jets show a larger track multiplicity and a broader jet shape compared
to quark jets. These properties can also be used to distinguish between quark- and
gluon-initiated jets. Therefore the energy of the light-quark jets in the inclusive sample is
as overcompensated as the one from the c- and b-jets (cf. Fig. D.2 and [110]). The b-jet
response rises to 2% above the inclusive response and decreases with increasing transverse
momentum of the particle jet. This behaviour is driven by the EM+JES correction factor
shown in Fig. D.1. At about 400 GeV the response of quark initiated jets dominate the
correction factors in the EM+JES calibration and the b-jet response reaches the inclusive
response and ranges between 0.99 and 1. The same holds for the response of c-jets. In case
of particle jets which also include muons and neutrinos (cf. Section 5.1) as in Fig. 8.24(b)
the response of jets initiated from quarks with an appreciable branching ratio into muons
and neutrinos (b- and c-quarks) is reduced to approximately 3% for b-jets. This is because
the particle jet’s momentum in the denominator of the response is enlarged with respect
to the detectable energy in the calorimeters. The response of the inclusive and light-jet
sample change within a few per mill with respect to the particle jets excluding muons and
neutrinos.
In the following, the impact of the b-tagging requirement on the b-jets is studied.
1.05 1.05
1.04 Pythia: 1.04 Pythia:
inclusive inclusive
1.03 b-jet 1.03 b-jet
1.02 c-jet 1.02 c-jet
1.01 light-jet 1.01 light-jet
1 1
0.99 0.99
0.98 0.98
0.97 0.97
0.96 0.96
0.95 0.95
0 200 400 600 800 1000 1200 0 200 400 600 800 1000 1200
ptruth [GeV] pNI [GeV]
T T
(a) Calorimeter level (b) Particle level (NI)
Figure 8.24: Average simulated jet response (of jets calibrated with EM+JES scheme) for
different jet flavours as a function of ptruthT ¡ 20 GeV ((a)) and pNIT ¡ 20 GeV ((b)) for all jets
within |y|   2.1. The transverse momentum pNIT in simulation is calculated using in addition
the momenta from the neutrinos and muons. The error bars represent the error obtained by the
Gaussian fit and approximately reflects the statistics of each jet flavour.
The selection of b-jets using charged tracks might bias the jet energy scale due to the
selection of a well measurable subset of b-jets with a specific fragmentation. The first
separation into different sub-samples is done using the SV0 tagging algorithm in Fig. 8.25(a).
These sub-samples contain different mixtures of jet flavours. The response of the not-
tagged and inclusive sample is as expected identical. The sample of b-tagged jets is
approximately composed of about 50% b-jets. The composition varies between different pT
115
response R
response R
8 Object understanding and calibration
1.05 1.05
1.04 Pythia: 1.04 SV0 weight > 5.85 Pythia:
1.03 inclusive 1.03 light-jets
1.02 not b-tagged jets 1.02 c-jets
1.01 b-tagged jets 1.01 b-jets
1 1
0.99 0.99
0.98 0.98
0.97 0.97
0.96 0.96
0.95 0.95
0 200 400 600 800 1000 1200 0 200 400 600 800 1000 1200
ptruth [GeV] ptruth [GeV]
T T
(a) (b)
Figure 8.25: Average simulated jet response (of jets calibrated with EM+JES scheme) for
different jet samples selected with the b-tagging selection cut as a function of ptruthT ¡ 20 GeV
for all jets within |y|   2.1. (a) Jets are separated by the b-tagging selection cut. (b) b-tagged
jets are in addition separated into their jet flavour. The error bars represent the error obtained
by the Gaussian fit and approximately reflects the statistics of each jet flavour.
bins. Nevertheless, the b-tagged sample exhibits roughly the same behaviour as the sample
of b-jets in Fig. 8.24(a). The rise at the beginning of the pT spectrum is damped and the
response reaches more rapidly unity. This is due to the mistagged light jets whose fraction
is increasing with pT. In the data-driven methods the jet energy scale of a b-tagged sample
is studied as well as that of b-tagged samples with enriched and depleted b-jet fractions
and their agreement is discussed. The response of these b-tagged jets is again split into
their jet flavours in Fig. 8.25(b). The response of mistagged light jets starts at 96% and
rises up to 99% in the high pT region. This behaviour indicates that the tagging algorithm
selects among the light-jets a significant subset of jets which show a reduced response
in the EM+JES calibration. This can be explained by the fact that mistagged light-jets
with a significant signed decay length significance are more likely to be faked by light-jets
with an increased track multiplicity. This implies that a larger part of the jet’s energy
is contained in charged particles and therefore hadrons, whose reconstructed energy is
intrinsically lower and rises slowly with increasing ptruthT . But it is very important to note
that tagged b-jets in Fig. 8.25(b) and b-jets in Fig. 8.24(a) show an identical response
within the uncertainty of the Gaussian fit as well as the c-jets. In conclusion the ability
to tag a b-jet and reconstruct a secondary vertex from charged tracks does not alter the
energy scale. This is the foundation to study the properties of b-jets with the aid of a
sample of b-tagged jets.
8.3.3.2 Jet energy scale uncertainty of jets with heavy-flavour content
The aim is to extract the additional jet energy scale uncertainty which accounts for the
differences in fragmentation of jets with bottom-flavour content. The data-driven method
chosen uses the total momentum of charged particles associated with the jet measured in
the inner detector. A track is associated to a jet if ∆Rptrack, jetq   0.4, where track param-
eters are evaluated at the distance of closest approach to the primary vertex. It is examined
how well Monte-Carlo describes b-tagged jets and their associated tracks in the data. The
tracking system is independently calibrated with respect to the calorimeters and can be
116
response R
response R
8.3 Jet energy scales and resolution
used as an independent estimate of the jet energy scale. The transverse momentum of
a jet is compared to the total transverse mom°entum measured in tracks associated to the jet:| p~ track
r  T |trk . (8.13)
pT
This ratio determines the calorimeter jet energy scale for jets contained in the tracking
coverage. Depending on the jet selection, it is be separated between rtrk with inclusive
jets and b-tagged jets. This measurement uses jets with 20 GeV   pT   600 GeV. The
L1 MBTS trigger provides the low pT jet measurement between 20 and 40 GeV, referred
to as minimum bias data. The remaining jets are selected using the single jet triggers
as explained in Section 7.3, referred to as jet trigger data. Tracks are selected with the
following criteria, where d0 and z0 are calculated with respect to the primary vertex:
ptrackT ¡ 1 GeV, Npixel ¥ 1, NSCT ¥ 6,
|dPV|   1.5 mm, |zPV0 0 sin θ|   1.5 mm. (8.14)
Each considered jet contains at least one single quality track. These selection cuts are in
good agreement with the b-tagging quality cuts. To ensure that the track matching to the
jet is not ambiguous, jets are required to be separated by a distance ∆R ¡ 0.8, if they
are not, only the harder jet is retained. The harder jet is well-defined as it was shown
in Section 5.1.1.2 and circular whereas the softer one is deformed. This analysis is split
up in two y-bins: |y|   1.2 and 1.2   |y|   2.1. To quantify the agreement between data
and simulation further, the track multiplicity Ntrk and the distribution of the transverse
momentum measured in charged particles dtrk,Jet as a function of the distance r from the
centre of the jet are studied in Fig. 8.26 and Fig. 8.27. The dtrk,Jet distribution is calculated
from the sum of the transverse momenta of all tracks which lie within the annulus between
r and r  ∆r: °
p q  ° 1 d track1d r r¤r  r ∆r pTtrk,Jet . (8.15)
Ntrk 0¤r1 0.4 p
track
T ∆r
The track multiplicity and the dtrk,Jet distributions are presented for b-tagged jets between
40 GeV   pT   60 GeV. The conclusions made from these plots also hold for the inclusive
jet sample and the other rapidity region. The reference event selection in this jet pT region
uses the jet trigger but if statistics allow the corresponding measurement is also presented
using data selected by the L1 MBTS trigger. The agreement of both trigger selections
indicate that there is no bias associated with the trigger used. The distributions are
normalised to the same area. The track multiplicity presented in Fig. 8.26(a) is reasonably
well described. On average a b-tagged jet between 40 GeV   pT   60 GeV contains 6
quality tracks. The distribution of the number of tracks gets broader with increasing jet
pT and the mean track multiplicity increases. At around 400 to 600 GeV on average a
jet contains about 16 tracks but there are also jets with 40 tracks measured. The mean
track multiplicity in data and simulation as a function of jet pT agrees within about 5% as
shown in Fig. 8.26(b). The level of agreement is independent from the transverse momenta
of the jet. The distribution of the transverse momenta as a function of the distance
from the centre of the jet is presented for b-tagged jets with 40 GeV   pT   60 GeV in
Fig. 8.27(a). Within r   0.1 from the jet axis the largest transverse momentum fraction is
found. The fraction decreases with increasing distance from the jet axis. The simulation
117
8 Object understanding and calibration
reproduces the transverse momentum flow. The average distance of the highest transverse
momentum fraction as a function of jet pT is presented in Fig. 8.27(b). With higher
transverse momentum of the jet this distance decreases as expected due to the collimation
of the jets. Conservatively, the level of agreement is estimated to be at most 20%. The
simulation predicts for pT ¡ 100 GeV a smaller mean distance than observed in data.
However, this again indicates that the density of the charged particles and transverse jet
shape is well modelled. Furthermore, it can be concluded that the transverse spread of
the jets and the loss of tracks at the edge of the tracking coverage is under control.
The estimation of the total jet energy scale uncertainty for b-jets utilises the rtrk distribu-
1 30
40 GeV<p <60 GeV Pythia: b-tagged jets Pythia b-tagged jets
T Jet trigger data
Jet trigger data 25
Minimum bias data
10-1 Minimum bias data ± 5% rel. difference
20
10-2 15
10
10-3
5
10-4 00 5 10 15 20 25 30 35 40 20 30 40 102 2×102
Ntrk p  [GeV]T
(a) (b)
Figure 8.26: The charged track multiplicity distribution for 40 GeV   pT   60 GeV and rapidity
range |y|   1.2 is presented in (a) for b-tagged jets. The mean track multiplicity as a function of
jet pT for b-tagged jets is shown in (b).
1 0.3
Pythia: b-tagged jets Pythia b-tagged jets
40 GeV<p <60 GeV Jet trigger data
T Jet trigger data 0.25 Minimum bias data
10-1 Minimum bias data ± 20 rel. difference
0.2
10-2 0.15
0.1
10-3
0.05
10-4 00 0.1 0.2 0.3 0.4 0.5 20 30 40 102 2×102
r p  [GeV]T
(a) (b)
Figure 8.27: The distribution of the fraction of transverse momentum observed in charged
particles as a function of the distance from the centre of the jet for b-tagged jets and (a)
40 GeV   pT   60 GeV and rapidity range |y|   1.2 and in (b) the corresponding mean value of
this distribution as a function of jet pT.
tions in simulation and data. The rtrk distribution for b-tagged jets with 60 GeV   pT   80 GeV
118
ddttrrkk,,JJeett 11//NN  ddNN//ddNNttrrkk
〈〈  rr  〉〉 〈〈  NN   〉〉ttrrkk
8.3 Jet energy scales and resolution
0.7
Pythia:
nominal
scale 0.94
0.65 scale 0.96
scale 1.04
scale 1.06
0.6
0.55
0.5
0.45
102
p  [GeV]
T
Figure 8.28: Sensitivity of the mean rtrk from simulation to variations of the jet energy scale
by 4 and 6%.
for both rapidity regions are presented in Fig. 8.29. The missing rtrk distributions for
b-tagged jets as well as the complete set of distributions of the inclusive jet sample are
included in Appendix H. The agreement between data and simulation is excellent. The rtrk
variable can become larger than 1 in the tails due to problems in the patter recognition
in the track finding. From these rtrk distributions the mean and the statistical error of
the mean value are obtained as a function of jet pT. Typical rtrk mean values are around
0.5 to 0.7. The rtrk distributions get broader with increasing jet pT and extend to rtrk
values of almost two for the highest measured kinematic range. To demonstrate the
1 1
60 GeV<p <80 GeV Pythia: b-tagged jets 60 GeV<p <80 GeV Pythia: b-tagged jets
T T
Jet trigger data Jet trigger data
10-1 Minimum bias data 10-1 Minimum bias data
10-2 10-2
10-3 10-3
10-4 -40 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
rtrk rtrk
(a) |y|   1.2 (b) 1.2   |y|   2.1
Figure 8.29: rtrk distributions for b-tagged jets with 60 GeV   pT   80 GeV for both rapidity
regions.
sensitivity of the total transverse momentum measured in the tracking system to the jet
energy scale, variations of 4% and6% to the jet energy scale are applied in simulation
and the mean rtrk distribution is recalculated. The rtrk distributions as a function of jet pT
with shifted jet energy scales are presented in Fig. 8.28. A 6% shift in the jet energy scale
results in an approximately 9% variation in the mean of the rtrk distribution. It can be
concluded that the level of agreement between the jet energy scale in data and simulation
can be determined with the help of the tracking system. Its sensitivity is reflected in the
119
11//NN  ddNN//ddrrttrrkk
〈 r  〉
trk
11//NN  ddNN//ddrrttrrkk
8 Object understanding and calibration
mean rtrk distributions in data and simulation. Therefore the correspondence of the jet
energy scale is quantified using the double ratios for the corresponding jet selections applied:
rxrtrk(incl)ys
R Datartrk,inclusive  rx ys , (8.16)rtrk(incl) MC
rxrtrk(b-jet)ys
R Datartrk,b-jet  rx . (8.17)rtrk(b-jet)ysMC
An identical jet energy scale in data and simulation results in an Rr ,X distributiontrk
close to unity. Therefore it is possible to constrain the energy scale and to determine the
uncertainty. In addition it is possible to determine the uncertainty on the jet energy scale.
The systematic uncertainties on the Rr ,inclusive distribution are a direct validation of thetrk
jet energy scale uncertainties presented in Section 8.3.1. A detailed study on inclusive jets
can be found in [111]. The goal is to derive an additional uncertainty for b-tagged jets
taking recourse to the uncertainty on inclusive jets. This can be achieved with the aid of
the following distribution:
1  RrR trk,b-jet . (8.18)
Rrtrk, inclusive
Remaining systematics on R1 estimate the uncertainty contribution arising from the
heavy-flavour fragmentation. Together with the well founded inclusive jet energy scale
uncertainty in Section 8.3.1, the total jet energy scale uncertainty needed for the cross
section measurement can be estimated then with the help of Eq. 8.12 by identifying the
b-jet JES uncertainty with the systematic uncertainty derived on R1.
The systematic uncertainties on Rr and R arise either from tracking relatedtrk,inclusive rtrk,b-jet
uncertainties, jet related uncertainties and from the simulation modelling. In addition the
b-tagging calibration and uncertainty needs to be evaluated for Rr ,b-jet. All contributionstrk
considered are assumed to be uncorrelated. The systematic uncertainties are described in
the following:
1. Simulation modelling: The dependency of the rtrk distribution on the simulation is
examined with the help of the Herwig++ generator which incorporates a different
shower and especially a different fragmentation model (cf. Section 2.3). The variation
observed in the rtrk distribution between Pythia and Herwig++ samples are
symmetrised and taken as a systematic uncertainty. Due to the insufficient statistics
of the Herwig++ samples concerning the b-tagging selection, the variations on
rrtrk(b-jet)sMC are fitted with a constant function.
2. b-tagging calibration: For the Rr ,b-jet measurement the b-tagging scale factors fortrk
the efficiency and mistag rate are varied correlated within their systematic uncertainty
in simulation. The rtrk distribution is re-evaluated and the resulting shifts are added
in quadrature to the systematic uncertainty for Rrtrk,b-jet.
3. Material description: The knowledge of the tracking efficiency modelling in simulation
was evaluated in detail [91], shortly presented in Section 5.2.3 and summarised in
Table 5.1. The systematic uncertainty on the tracking efficiency for isolated tracks
with ptrackT ¡ 500 MeV increases from 2% for central tracks to 4% for tracks in the
end-cap region. The resulting effect on rtrk is rapidity-dependent and leads to a 2%
uncertainty for |y|   1.2 and a 3.1% uncertainty for 1.2   |y|   2.1.
120
8.3 Jet energy scales and resolution
4. Tracking in jet core: High track densities in the jet core influence the tracking
efficiency due to shared hits, fake tracks and lost tracks. From previous studies in
Section 5.2.3 it was concluded that the effects of shared hits and the number of fake
tracks is well described in simulation whereas the loss of tracks is not well understood.
As already described in Eq. 5.7 reconstructed tracks are associated to a truth track
and vice versa. A relative systematic uncertainty of 50% conservatively estimates
the effect of the loss of efficiency using pseudo-experiments. The average inefficiency
in each jet pT bin is estimated from simulation by counting the reconstructed and
matched tracks associated to a jet with pT ¡ 1 GeV and the corresponding generated
tracks with pT ¡ 1 GeV. For each jet the variation in terms of percentages in°
ptrack
the ratio ° T,recomatched is determined by a random generator deciding according to thepT,gen
relative uncertainty of 50% if a truth track should be added or discarded from
the denominator. The relative shift in the ratio rtrk is added in quadrature to the
systematic uncertainty.
5. Jet resolution: The jet energy resolution in simulation is about 10% better than
in data (cf. Fig. 8.21). The resolution in simulation is degraded according to
this maximum deviation for all pT and rapidity bins. The effect of a resolution
improvement is estimated by the variation in case of the degradation. In pseudo-
experiments a random energy that corresponds to a resolution smearing of 10% is
added (or subtracted) to each jet. The resulting average shift on the rtrk distribution
is evaluated and added in quadrature to the systematic uncertainty.
The total systematic uncertainties for inclusive and b-tagged jets are presented for both
rapidity regions in Figs. 8.30 and 8.31. The systematic uncertainty for inclusive jets
is between 2% and 6%. With increasing pT the uncertainty decreases and is maximal
in the lowest pT bin. The systematic uncertainty arising from the tracking in the jet
core is negligible for the lower rapidity bin and rises to about 1% for the rapidity region
between 1.2   |y|   2.1. The uncertainty based on the material description is constant
as a function of jet pT and is the largest contribution at pT ¡ 50 GeV. The behaviour
of the uncertainty based on the jet resolution smearing and the generator modelling is
similar. Both contributions decrease to less than 1% with increasing pT and make up the
largest part of the uncertainty in the lower kinematic regions. In the course of the studies
detailed in [111] the uncertainty on rtrk from pile-up is negligible and to a large extent
this uncertainty will cancel out for the measurement of R1. Most of the description of the
systematic uncertainties on the Rr ,inclusive can be transferred to the fractional systematictrk
uncertainties of Rr ,b-jet in Fig. 8.31. The systematic uncertainty is between 3% andtrk
5%. In addition the uncertainty from the b-tagging calibration adds about 2% at most
to the uncertainty. Finally, Figs. 8.32 and 8.33 present the measurement of Rrtrk,inclusive
and Rr ,b-jet. Both measurements show that the jet energy scale in data and simulationtrk
agree within systematic uncertainties. The agreement is of the level of 2% for inclusive
jets and b-tagged jets with |y|   1.2 and 4% for b-tagged jets in the outermost rapidity
region. The dotted lines in both figures indicate this agreement. With the help of the
tracking information the jet energy scale predicted by the simulation is validated and an
independent scale uncertainty is obtained.
Two further cross checks provide confidence in the estimation of the jet energy scale
uncertainty of b-tagged jets. The estimation of this additional uncertainty is based on the
fact that b-jets which are capable of being b-tagged do not show a systematic difference
121
8 Object understanding and calibration
0.1 0.1
0.09 Total Sys. UncertaintyInclusive jets, |y|<1.2 b-tag. calibration 0.09
Inclusive jets, 1.2<|y|<2.1 Total Sys. Uncertainty
b-tag. calibration
0.08 Anti-k  R=0.4 EM+JES Simulation 0.08
Anti-k t R=0.4 EM+JES Simulation
t Jet resolution s=7TeV,  ∫Ldt=34 pb-1 Jet resolution0.07 s=7TeV,  ∫Ldt=34 pb-1 Material description 0.07 Material description
0.06 Tracking in jet core 0.06 Tracking in jet core
0.05 0.05
0.04 0.04
0.03 0.03
0.02 0.02
0.01 0.01
0 0
30 40 50 60 102 2×102 30 40 50 60 102 2×102
p  [GeV] p  [GeV]
T T
(a) |y|   1.2 (b) 1.2   |y|   2.1
Figure 8.30: The fractional systematic uncertainties on Rr ,inclusive as a function of jet ptrk T
for (a) |y|   1.2 and (b) 1.2   |y|   2.1.
0.1 0.1
0.09 Total Sys. Uncertainty Total Sys. Uncertaintyb-tagged jets, |y|<1.2 b-tag. calibration 0.09 b-tagged jets, 1.2<|y|<2.1 b-tag. calibration
0.08 Anti-k t R=0.4 EM+JES
Simulation 0.08 Anti-k  R=0.4 EM+JES Simulation
Jet resolution t Jet resolution
0.07 s=7TeV,  ∫Ldt=34 pb-1 Material description 0.07 s=7TeV,  ∫Ldt = 34 pb-1 Material description
0.06 Tracking in jet core 0.06 Tracking in jet core
0.05 0.05
0.04 0.04
0.03 0.03
0.02 0.02
0.01 0.01
0 0
30 40 50 102 2×102 30 40 50 102 2×102
p  [GeV] p  [GeV]
T T
(a) |y|   1.2 (b) 1.2   |y|   2.1
Figure 8.31: The fractional systematic uncertainties on Rr ,b-jet as a function of jet pT fortrk
(a) |y|   1.2 and (b) 1.2   |y|   2.1.
in their energy response. To study this, the fraction of b-jets among the b-tagged jets
is changed and the agreement between data and simulation is checked. The following
sub-samples are used for reasons presented in Section 8.2.2: SV0 mass ¥ 1.5 GeV and SV0
mass   1.5 GeV. The former sample has an enhanced fraction of b-jets and the latter is
depleted. The ratio of the mean value of rtrk in data and simulation is presented for both
sub-samples in Fig. 8.34. It can be seen that both selections either enhancing or depleting
the fraction of b-jets in the sample are in agreement with unity within the systematic
uncertainties. The level of agreement is identical to the one found in the full sample.
This affirms that the relation found in simulation between Fig. 8.24(a) and Fig. 8.25(b) is
valid. Furthermore, as muons from a semi-leptonic decay of a bottom-flavoured hadron are
reconstructed as charged tracks it is possible to use an additional selection on soft muons
in the sample of b-tagged jets to ascertain the relation between the jet energy response
of b-jets on calorimeter level and particle level. The transverse momentum of the soft
muon was already studied in Section 8.1.3 and was found to be in agreement between data
and simulation. Relating the mean rtrk values between data and simulation for b-tagged
122
FFrraaccttiioonnaall  SSyysstteemmaattiicc  UUnncceerrttaaiinnttyy FFrraaccttiioonnaall  SSyysstteemmaattiicc  UUnncceerrttaaiinnttyy
FFrraaccttiioonnaall  SSyysstteemmaattiicc  UUnncceerrttaaiinnttyy FFrraaccttiioonnaall  SSyysstteemmaattiicc  UUnncceerrttaaiinnttyy
8.3 Jet energy scales and resolution
1.4 1.4
Inclusive jets, |y|<1.2 Jet trigger data Inclusive jets, 1.2<|y|<2.1 Jet trigger data
1.3 1.3
Anti-k t R=0.4 EM+JES Minimum bias data Anti-k t R=0.4 EM+JES Minimum bias data
1.2 s=7TeV,  ∫Ldt=34 pb-1 1.2 s=7TeV,  ∫Ldt=34 pb-1
 ± 2.0%  ± 2.0% 
1.1 1.1
1 1
0.9 0.9
0.8 0.8
20 30 40 102 2×102 20 30 40 102 2×102
p  [GeV] p  [GeV]
T T
(a) |y|   1.2 (b) 1.2   |y|   2.1
Figure 8.32: The ratio of the mean value of rtrk in data and simulation for inclusive jets as a
function pT for (a) |y|   1.2 and (b) 1.2   |y|   2.1.
1.4 1.4
Jet trigger data Jet trigger data
b-tagged jets, |y|<1.2 b-tagged jets, 1.2<|y|<2.1
1.3 Minimum bias data 1.3 Minimum bias data
Anti-k t R=0.4 EM+JES Sys. Uncertainty Anti-k t R=0.4 EM+JES Sys. Uncertainty
1.2 s=7TeV,  ∫Ldt=34 pb-1 1.2 s=7TeV,  ∫Ldt=34 pb-1
 ± 2.0%  ± 4.0% 
1.1 1.1
1 1
0.9 0.9
0.8 0.8
20 30 40 102 2×102 20 30 40 102 2×102
p  [GeV] p  [GeV]
T T
(a) |y|   1.2 (b) 1.2   |y|   2.1
Figure 8.33: The ratio of the mean value of rtrk in data and simulation for b-tagged jets as a
function pT for (a) |y|   1.2 and (b) 1.2   |y|   2.1.
with a soft muon the energy scale can be tested further for the impact of the neutrino. In
Fig. 8.35(a) the impact of the muon can be seen in the change of the slope of the mean
value distribution. The fraction of energy carried by charged tracks is increased due to
the presence of the muon. The mean rtrk value at small pT is increased by a factor of
approximately 50%. At 500 GeV the increase shrinks to about 9%. Within the statistical
errors and a 2% relative difference data and simulation mean values agree with each other.
In addition to rule out any opposing effect on the full rtrk measurement, the mean values of
rtrk as a function of pT for the selection with a veto on a soft muon is shown in Fig. 8.35(b).
The mean values are similar to the ones from the full measurement as the events with a
soft muon are rather rare as the statistical errors have indicated in Fig. 8.35(a). The level
of agreement is also of the order of 2% or better.
For the calculation of the systematic uncertainties on R1 the following arguments are
considered:
1. Simulation modelling: The deviation between R1 calculated from data and Pythia
and R1Herwig++ calculated from data and Herwig++ simulation are the basis of
123
RRrr ,,bb--jjeett  ==  〈〈  rr   〉〉   //  〈〈  rr   〉〉 RR   ==  〈〈  rr   〉〉   //  〈〈  rr 〉〉ttrrkk ttrrkk ddaattaa ttrrkk MMCC rr ttrrkk,,iinncclluussiivvee ttrrkk ddaattaa ttrrkk MMCC
RRrr ,,bb--jjeett  ==  〈〈  rr   〉〉   //  〈〈  rr   〉〉 RRrr ,,iinncclluussiivvee  ==  〈〈  rr   〉〉   //  〈〈  rr 〉〉ttrrkk ttrrkk ddaattaa ttrrkk MMCC ttrrkk ttrrkk ddaattaa ttrrkk MMCC
8 Object understanding and calibration
1.3 1.3
1.25 SV0 mass > 1.5 GeV Jet trigger data 1.25 SV0 mass < 1.5 GeV Jet trigger data
1.2 Minimum bias data 1.2 Minimum bias data
1.15  ± 2.0% 1.15  ± 2.0% 
1.1 1.1
1.05 1.05
1 1
0.95 0.95
0.9 0.9
0.85 0.85
20 30 40 102 2×102 20 30 40 102 2×102
p  [GeV] p  [GeV]
T T
(a) SV0 mass ¥ 1.5 GeV (b) SV0 mass   1.5 GeV
Figure 8.34: The ratio of the mean value of rtrk in data and simulation for b-tagged jets with
|y|   1.2 separated into two sub-samples: (a) SV0 mass ¥ 1.5 GeV and (b) SV0 mass   1.5 GeV.
the systematic uncertainty. The remaining deviations reflect the uncertainty due
to the different fragmentation as the contributions from the underlying event and
the parton shower cancel out. Due to the limited statistics in case of the b-tagging
selection the deviations are fitted with step functions with disjunctive intervals. The
intervals are chosen to describe the behaviour of the deviations. The first interval is
between 20 GeV and 40 GeV where the difference to the Herwig++ prediction is
significant. The second interval is between 40 GeV and 600 GeV and is the important
kinematic range for the cross section measurement.
2. b-tagging calibration: The b-tagging calibration uncertainty is propagated to R1.
3. Material description: This uncertainty on isolated tracks is coming from an external
measurements and the uncertainties on Rr ,inclusive and Rr ,b-jet are fully correlatedtrk trk
and cancel.
4. Tracking in jet core: It is assumed that both uncertainties are fully correlated and
to first order cancel. This assumption is exactly valid for high pT jets; for low pT
jets the second order deviations are estimated to be about 0.1%.
5. Jet resolution: It is assumed that both uncertainties are fully correlated and to first
order cancel. This assumption is exactly valid for high pT jets; for low pT jets the
second order deviations are estimated to be about 0.2%.
The significant systematic uncertainties on R1 are due to the modelling in simulation
and the b-tagging calibration. Both are added in quadrature. The results on R1 and the
fractional systematic uncertainties are presented in Fig. 8.36 and Fig. 8.37. The jet energy
scale of b-tagged jets relative to the scale of inclusive jets is in agreement to the level of 2%
and 2.5% for jets with |y|   1.2 and 1.2   |y|   2.1 respectively. Within the statistical and
systematic uncertainties the energy scale of b-tagged jets with respect to inclusive jets is in
agreement with unity. The uncertainty from the simulation modelling is almost dominating
in each pT and rapidity region. The systematic uncertainty is between 2% and 4%. The
focus for this analysis is on the interval between 40 GeV and 600 GeV. An additional
uncertainty for b-tagged jets is estimated with the help of charged tracks relating the total
124
〈〈  rr   〉〉   //  〈〈  rr 〉〉
ttrrkk ddaattaa ttrrkk MMCC
〈〈  rr   〉〉   //  〈〈  rr 〉〉
ttrrkk ddaattaa ttrrkk MMCC
8.3 Jet energy scales and resolution
1 0.85
Pythia b-tagged jets Pythia b-tagged jets
Jet trigger data 0.8b-tagged jets with b-tagged jets without Jet trigger data
0.9 Minimum bias data 0.75 Minimum bias datasoft muon ± 2% rel. difference soft muon ± 2% rel. difference
0.8 0.7
0.65
0.7 0.6
0.55
0.6
0.5
0.5 0.45
0.4
20 30 40 102 2×102 20 30 40 102 2×102
p  [GeV] p  [GeV]
T T
(a) Jets with an soft muon (b) Jets without a soft muon
Figure 8.35: The mean value of rtrk in data and simulation for b-tagged jets with |y|   1.2
separated into two sub-samples: (a) b-tagged jets with an soft muon and (b) b-tagged jets without
a soft muon.
transverse momentum in charged particles to the transverse momentum of a jet measured
in the calorimeter. The uncertainty on the fitting parameters for estimating the simulation
modelling uncertainty show a sensitive to the fit result of  0.2%. To be conservative and
cover fitting systematics, an overall constant jet energy scale uncertainty contribution for
b-tagged jets is set to 2.5%. Furthermore, the jet energy scale is proven to be in agreement
between data and simulation. It is expected that differences from fragmentation become
less important at high jet pT, therefore it is justified to safely extrapolate the additional
2.5% jet energy scale uncertainty to higher pT regions for this analysis. In Table 8.3 a
summary of representative values of the systematic uncertainty on the jet energy scale
uncertainty for b-jets is given deduced from the systematic uncertainty on the jet energy
scale uncertainty for inclusive jets and the discussed R1 measurement.
1.4 1.4
Jet trigger data Jet trigger data
b-tagged jets, |y|<1.2 b-tagged jets, 1.2<|y|<2.1
1.3 Minimum bias data 1.3 Minimum bias data
Anti-k t R=0.4 EM+JES Syst. Uncertainty Anti-k t R=0.4 EM+JES Syst. Uncertainty
s=7TeV,  ∫Ldt=34 pb-11.2 1.2 s=7TeV,  ∫Ldt=34 pb-1
 ± 2.0%  ± 2.5% 
1.1 1.1
1 1
0.9 0.9
0.8 0.8
20 30 40 102 2×102 20 30 40 102 2×102
p  [GeV] p  [GeV]
T T
(a) |y|   1.2 (b) 1.2   |y|   2.1
Figure 8.36: The ratio R1 (Eq. 8.18) calculated from inclusive and b-tagged for (a) |y|   1.2
and (b)1.2   |y|   2.1. The dashed lines indicate the estimated agreement between data and
simulation.
125
RR''==  RRrr ttrrkk,,bb--jjeett//RRrr ttrrkk,,iinncclluussiivvee 〈〈  rr   〉〉
ttrrkk
RR''==  RRrr ,,bb--jjeett//RRttrrkk rr ttrrkk,,iinncclluussiivvee 〈〈  rr   〉〉
ttrrkk
8 Object understanding and calibration
JES Uncertainty [%]
pT [GeV]
0   |η|   0.3 0.3   |η|   0.8 0.8   |η|   1.2 1.2   |η|   2.1
40 4.2 % 4.0 % 4.2 % 4.9 %
60 3.5 % 3.4 % 3.7 % 3.7%
80 3.3 % 3.5 % 3.6 % 3.6 %
110 3.2 % 3.5 % 3.5 % 3.6 %
160 3.4 % 3.4 % 3.6 % 3.6 %
210 3.3 % 3.5 % 3.6 % 3.7 %
260 3.3 % 3.5 % 3.6 % 3.7%
310 3.3 % 3.4 % 3.5 % 3.6 %
400 3.3 % 3.5 % 3.6 % 3.7 %
500 3.5 % 3.5 % 3.6 % 3.7 %
600 3.5 % 3.6 % 3.7 % 3.8 %
800 3.6 % 3.8 % 3.9 % 4.0 %
1000 3.8 % 3.9 % 4.0 % 4.2 %
Table 8.3: Summary of the EM+JES jet energy scale systematic uncertainties for b-jets for
different pT and η regions for anti-kt jets with R  0.4.
126
8.3 Jet energy scales and resolution
0.1 0.1
0.09 Total Sys. Uncertainty Total Sys. Uncertaintyb-tagged jets, |y|<1.2 0.09 b-tagged jets, 1.2<|y|<2.1
0.08 Simulation SimulationAnti-k t R=0.4 EM+JES
0.08
b-tag. calibration Anti-k t R=0.4 EM+JES b-tag. calibration
0.07 s=7TeV,  ∫Ldt=34 pb-1 0.07 s=7TeV,  ∫Ldt=34 pb-1
0.06 0.06
0.05 0.05
0.04 0.04
0.03 0.03
0.02 0.02
0.01 0.01
0 0
20 30 40 102 2×102 20 30 40 102 2×102
p  [GeV] p  [GeV]
T T
(a) |y|   1.2 (b) 1.2   |y|   2.1
Figure 8.37: The fractional systematic uncertainties for R1 calculated from inclusive and
b-tagged jets for (a) |y|   1.2 and (b)1.2   |y|   2.1.
127
FFrraaccttiioonnaall  ssyysstteemmaattiicc  uunncceerrttaaiinnttyy
FFrraaccttiioonnaall  ssyysstteemmaattiicc  uunncceerrttaaiinnttyy

9 The cross section measurement
This chapter explains the dijet cross section measurement and describes the methods
used to obtain it. The previous chapters have introduced the physical objects and the
approaches to properly define and reconstruct them (cf. Section 5). The event and object
selection suitable for the cross section measurement has been discussed in Section 7. The
adequacy of the simulation has been thoroughly studied and the most important systematic
uncertainties arising from it have been identified and quantified in the previous chapter.
In the next section the definitions of the cross sections and the terminology used in the
context of the measurement are given. In Section 9.2 the corrections and corresponding
systematic uncertainties for all experimental effects are presented. Finally, the dijet
cross sections which are at this point corrected to particle level are presented and the
systematic uncertainties summarised. The final cross sections are directly comparable to
NLO predictions.
9.1 Cross section definition
The event and jet selection as well as the trigger selection was presented in Section 7 and
is the basis for the cross section measurement. Jets are reconstructed using the anti-kt
algorithm with resolution parameter R = 0.4 and calibrated with the EM+JES scheme.
The relatively long lifetime of hadrons containing a b-quark is exploited to obtain a jet
sample enriched in b-jets. A jet is identified as a b-jet if the decay length significance (SV0
weight) is above 5.85.
The bb̄ dijet cross section is measured for the leading and sub-leading jets in the event as
a function of the invariant mass M , the azimuthal angle difference ∆φ and the angular
variable χ  exp |y1  y2| of the dijet system for jets with pT ¡ 40 GeV and |y|   2.1.
The cross section as a function of dijet mass is plotted only above the minimum mass
where the measurement is no longer biased by the pT phase space cut on the leading jets.
Therefore the measurement begins above a dijet mass of 110 GeV. The spectrum below
this mass is very sensitive to the jet energy scale uncertainty and is also omitted for all
other cross section measurements. The angular variable χ was motivated in Section 2.1.4.
The dijet cross section as a function of χ is measured up to a maximum value of χ   30
and an additional acceptance cut is set on 1 |y1   y2|   1.1 to reject events where both2
jets are boosted into the forward or backward direction. This acceptance cut is illustrated
in Fig. I.1. The dijet cross section as function of the angular variable χ is measured in
two different mass regions: 110 GeV   M   370 GeV and 370 GeV   M   850 GeV. The
definitions of the cross sections are given by:
129
9 The cross section measurement
 dσ  1  Pbb̄ Cunf  NpMq
dM ∆M sel  clean   , (9.1) bb̄  trig M L
dσ  1  P bb̄  Cunf   Np∆φq    , (9.2)d∆φ ∆φ sel clean bb̄ trig ∆φ L
d2σ  1  Pbb̄  Cunf   Npχ,Mq . (9.3)
dχdM ∆χ∆M  sel  clean  bb̄  trig χ,M L
The trigger efficiency trig has been studied in Section 7.3 and was proven to be identical
to 1.0 for the trigger selection chosen. The luminosity L used in the measurement has
been presented in Tables 7.1 and 7.2, and the corresponding systematic uncertainty was
discussed in Section 4.2 and amounts to 3.4%. N denotes the number of events measured
as a function of dijet mass, azimuthal difference and angular variable χ. The binning of the
cross section in these variables is given in Appendix A. The binning in terms of dijet mass
is motivated by the dijet mass resolution as discussed in Section 8.3.2. The binning of
the angular and azimuthal variables is explained later in this chapter. The event selection
efficiency sel and the jet cleaning efficiency clean are studied in the following and possible
systematic uncertainties arising from them are discussed. The identification of b-jets using
the b-tagging algorithm SV0 requires two corrections to the measurement. Firstly, the
b-tagging efficiency bb̄ has to be evaluated using the b-tagging calibration and applied to
correct the number of b-tagged jets to the number of b-jets in data. Secondly, the number
of b-tagged jets needs to be corrected for the additional mistagged jets in the jet sample
with the help of the b-tagging purity Pbb̄. Both corrections bear systematic uncertainties
which need to be evaluated. The correction factors discussed so far take values between
zero and one. The final correction factor Cunf not bound between zero and one corrects
for detector efficiencies and resolutions in a single step. This correction is obtained from
a bin-by-bin unfolding method using simulated events from Pythia. All these factors
are derived separately as a function of dijet mass, ∆φ and χpMq from simulated events
for the different measurements. For readability this is omitted in its usual form in the
cross section definitions above, only the vertical lines with the corresponding subscripts
are given as indicators.
On the basis of the dijet cross section measurement of b-jets, the ratio to inclusive dijets
as a function of dijet mass is calculated. The following cross section definition for inclusive
dijet cross section is used:

dσ 1 C inclincl   unf
incl  incl  incl 
  NinclpMq . (9.4)dM ∆M sel clean trig LM
The cross section ratio is then defined as:

dσbb̄{dM  P  C
bb̄ incl incl incl 
bb̄ unf  sel  clean  trig  Nbb̄pMq{ , (9.5)dσincl dM C incl bb̄ bb̄unf  sel  clean  bb̄  bb̄  NinclpMqtrig M
where dσbb̄{dM is identical to dσ{dM in Eq. 9.1 and the corresponding correction factors
are given an additional superscript to track their origin.
130
9.2 Correction factors and systematic uncertainties
9.2 Correction factors and systematic uncertainties
This section presents the corrections applied to the cross section measurement to correct to
particle level for comparison to NLO predictions and discusses the systematic uncertainties
on the measurement.
9.2.1 Event and jet cleaning selection
The event selection efficiency is determined with the help of the simulated sample of
inclusive jets. The inclusive jet sample is obtained using the same selection cuts without
requiring the b-tagging cuts. It is a nearly perfect representation of the kinematic properties
of a b-tagged jet sample with the important advantage of more statistics. Also later on if
applicable the inclusive jet sample is used as representative sample to evaluate the effect
of systematic uncertainties. The efficiency is calculated from the number of events as a
function of dijet mass without and with requiring at least ten tracks associated to the
primary vertex but keeping the remaining selection cuts in place (cf. Section 7.4). The
event selection efficiency is the bin-wise ratio between these two numbers of events. The
error on the event selection efficiency from simulation is calculated from binomial error
calculation. The result of this calculation is presented as (1- sel). The inefficiency is
shown in Fig. 9.1(a) as a function of inclusive dijet mass. The event selection efficiency
is above 99.9% for 110 GeV   M   1000 GeV. The fluctuations in the inefficiency are
caused by the statistics in the simulated samples. The efficiencies as functions of ∆φ and
χ exhibit as expected the same behaviour. A primary vertex is unambiguously defined by
a minimum of three tracks. With increasing jet pT the number of tracks associated to a jet
is also increasing. Therefore a measurement using jets with pT lower than 40 GeV would
have a higher inefficiency due to the minimum number of tracks required. On average one
jet between 40 and 60 GeV already contributes 6 tracks. Hence, it does not surprise that
the inefficiency is small. The impact on the cross section measurement is negligible and
the efficiency inserted into Eq. 9.1 to Eq. 9.3 is sel = 1. As the track multiplicity in data
is 5% higher than in simulation, the event selection efficiency is determined with a looser
(6) and a tighter (12) cut on the number of tracks in the primary vertex. The deviation
between both efficiencies is calculated and was found to be smaller than ∆sel   0.0005.
This systematic uncertainty is neglected due to its small impact.
For completeness the jet reconstruction efficiency has been determined in other studies [101]
and reveals that jets with at least 30 GeV transverse momentum are reconstructed with
approximately 100% efficiency. The jet cleaning efficiency is determined on data using bb̄
dijet events. The b-tagging selection cuts remove all jets arising from background sources
and calorimeter noise. The bb̄ dijet mass distribution is reconstructed with and without
the jet cleaning cuts. The resulting efficiency is presented in Fig. 9.1(b). The selected
event samples are completely identical to each other and in the bb̄ dijet cross section
measurement no b-jet is rejected due to the jet cleaning cuts. The resulting efficiency is
clean = 1. Consequently, the measurements using the other variables ∆φ and χ are also
not affected. Because the b-jet selection is not affected by the cleaning cuts no systematic
uncertainty has to be evaluated.
131
9 The cross section measurement
0.001
1.04
0.0009
Pythia 1.02 Data: periods A to I
0.0008 Inclusive jets 1
0.0007
0.98
0.0006
0.96
0.0005
0.94
0.0004
0.92
0.0003
0.9
0.0002
0.88
0.0001
0.86
0
0 200 400 600 800 1000 0 200 400 600 800 1000
dijet mass [GeV] bb dijet mass [GeV]
(a) Event selection inefficiency (b) Jet cleaning efficiency
Figure 9.1: (a) Event selection inefficiency p1 selq as a function of inclusive dijet mass, (b)
Jet cleaning efficiency clean as a function of bb̄ dijet mass for data periods A to I.
9.2.2 Trigger selection
Two sources of systematic uncertainties on the trigger efficiency are evaluated. First
systematics arising from the choice of the reference sample and of the method are studied.
Then effects on the trigger efficiency caused by differences between inclusive jets and
b-tagged jets are discussed.
Uncertainties on the measurement: The orthogonal trigger method using L1 MBTS
is the baseline for the determination of the trigger efficiency in data periods A to F. Events
selected by the minimum bias trigger L1 MBTS are assumed to be unbiased. The trigger
requires a single hit in one of the Minimum Bias Trigger Scintillators covering the end-cap
calorimeter region at both sides of the detector. This trigger efficiency is compared to
the trigger efficiency, which is obtained with respect to the L1 ZDC trigger, as shown
in Fig. 9.2(a). This trigger uses the Zero-Degree Calorimeter placed in the very forward
region just after the LHC beam pipe splits in two. The comparisons between both trigger
efficiencies are shown for the trigger with the lowest threshold and the unprescaled trigger
with the lowest threshold. The assumption that the minimum bias trigger is unbiased
and orthogonal with respect to jets is proven to be correct for the jets in the plateau
regions. The plateaus are reached in the same pT bin and therefore the efficiencies are in
agreement to less than the one per cent level because a plateau is defined above the 99%
trigger efficiency. In case of the L1 J55 trigger the comparison to the trigger efficiency
measured with the bootstrap method with the help of L1 J30 is presented in Fig. 9.2(b).
The bootstrap method yields the more precise measurement in terms of statistical error.
The trigger efficiencies in the data periods G to I were obtained using the bootstrap method
which can determine the efficiency at event level. The L2 j15 trigger is an exception and
has to be measured with the tag-and-probe method. The unbiased triggers are highly
prescaled in this data period and the available statistics are very low. A systematic
check on L2 j15 with the help of the L1 MBTS trigger shows that they are in agreement
within their statistical errors. The trigger efficiencies of the triggers with higher thresholds
obtained from the bootstrap method are tested with the help of the tag-and-probe method.
Both trigger efficiencies are presented in Fig. 9.3 for the triggers L2 j30 and L1 J95. The
beginning of the plateaus regions are in agreement of the order of less than 1%. The
deviations between both methods arise from the fact that the tag-and-probe method
132
∈sel
∈clean
9.2 Correction factors and systematic uncertainties
1 1
0.8 0.8
0.6 0.6
0.4 L1_J5: 0.4 L1_J55:
L1_MBTS
L1_MBTS
L1_ZDC
0.2 L1_ZDC 0.2 L1_J30
0 0
0 20 40 60 80 100 0 50 100 150 200 250
p  [GeV] p  [GeV]
T T
(a) Trigger L1 J5 (b) Trigger L1 J55
Figure 9.2: (a) Systematic check of the trigger efficiency of L1 J5 calculated from L1 MBTS
with the help of the orthogonal trigger L1 ZDC in data periods A to F, (b) Systematic check
of the trigger efficiency of L1 J55 calculated from L1 MBTS and L1 ZDC with the help of the
bootstrap method using L1 J30 in data periods A to F. The vertical lines indicate the trigger
plateaus.
determines per jet trigger efficiencies. In summary, the trigger efficiencies are tested to be
in agreement at the one per cent level or better.
Systematic effects due to the b-tagging selection: The subset of b-tagged jets may
1 1
0.8 0.8
0.6 0.6
0.4 L2_j30: 0.4 L1_J95:
Bootstrap Bootstrap
0.2 Tag-probe 0.2 Tag-probe
0 0
0 20 40 60 80 100 0 50 100 150 200 250 300
p  [GeV] p  [GeV]
T T
(a) Trigger L2 j30 (b) L1 J95
Figure 9.3: (a) Systematic check of the trigger efficiency of L2 j30, which has been calculated
with the bootstrap method, with the help of the tag-and-probe method in data periods G to I, (b)
Systematic check of the trigger efficiency of L1 J95, which has been calculated with the bootstrap
method, with the help of the tag-and-probe method in data periods G to I. The vertical lines
indicate the trigger plateaus.
have a slightly different trigger efficiency than inclusive jets due to their production
mechanism and different fragmentation. Due to the different production mechanism for
b-jets the rapidity correlation between the leading jets is different with respect to inclusive
jets. As the trigger efficiency depends on the jet rapidity as presented in Ref. [112]
(Fig. 2), the integrated trigger efficiency for jets within |y|   2.1 may be affected by this.
To conservatively estimate the uncertainty, the extreme case is considered in which all
133
∈trig ∈trig
∈trig ∈trig
9 The cross section measurement
b-tagged jets are assumed to be reconstructed in the region with highest inefficiencies. The
maximum difference between the trigger efficiencies for jets |y|   1.2 and 1.2   |y|   2.1 is
assigned as a systematic uncertainty and added in quadrature to the previously discussed
uncertainty. In periods A to I the difference |y| 1.2  1.2 |y| 2.1 is identical to zero for
all triggers except L1 J5 or respectively L2 j15. An asymmetric uncertainty of 1.2% is
assigned in the pT region of 40 to 60 GeV for periods A to F and an uncertainty of
1% in periods G to I. Furthermore, it is checked if the identification of RoIs is biased
by the b-tagging selection. The trigger efficiency was separately determined from the
sample of b-tagged jets and compared to the full data set of periods A to F. The necessary
information on b-tagging for data periods G to I is not accessible in the available trigger
sample. The resulting trigger efficiencies for the available data set and the b-tagging
selection are presented in Fig. 9.4 for the triggers L1 J5 and L1 J55. The effect of a
different fragmentation for L1 J5 is visible in the segment of the curve with very high
slope. The efficiency measured with the b-tagging selection is significantly higher than
the efficiency in the inclusive sample. This may come from the harder fragmentation and
the requirement of high pT tracks in the b-tagging track selection, so that jets with this
signature in the calorimeter may more easily be identified as a local energy maximum. But
this effect has almost vanished in case of the L1 J55 trigger. More importantly when both
trigger curves approach the plateau region, the difference in the efficiency measurement
vanishes and both efficiencies are in agreement within the statistical errors. Because the
cross section measurement does not rely on the trigger efficiency below the plateau region,
the relevant trigger efficiencies of the full data set and the b-tagging selection are found to
be identical. The trigger selection is not biased with respect to the data sample used in
the analysis. There are no restrictions to translate this directly onto the data periods G
to I. This will be proven explicitly in Section 9.2.7.
In summary, an additional uncertainty of 1.2% and 1% for |y|   1.2 and 1.2   |y|   2.1
respectively is assigned to the jet pT region of 40 to 60 GeV to cover possible biases in the
rapidity distribution between inclusive and b-tagged jets.
1 1
0.8 0.8
0.6 0.6
0.4 L1_J5 0.4 L1_J55
Data Data
0.2 Data: b-tagged jets 0.2 Data: b-tagged jets
0 0
0 20 40 60 80 100 0 50 100 150 200 250 300
p  [GeV] p  [GeV]
T T
(a) Trigger L1 J5 (b) Trigger L1 J55
Figure 9.4: Systematic check of the trigger efficiencies between the inclusive jet sample and a
b-tagged jet sample using the bootstrap method for L1 J55 and the L1 MBTS trigger for L1 J5
in periods A to F: (a) for trigger L1 J5, (b) for trigger L1 J55. For technical reasons, periods G
to I are not accessible for this systematic check. The vertical lines indicate the trigger plateaus.
134
∈trig
∈trig
9.2 Correction factors and systematic uncertainties
9.2.3 b-tagging efficiency
To obtain the b-tagging efficiency bb̄ the b-tagging calibration which was presented in
Section 8.2 is applied to simulation. For each b-jet which is b-tagged in simulation and
selected by the analysis cuts, the scale factor κbppTq depending on jet pT is extracted and
applied as a weight. Consequently, a dijet event has an b-tagging efficiency weight which
is the product of each individual scale factor . The determination of the jet flavour is
described in Section 3.1. For each desired variable the b-tagging efficiency is evaluated
by using Eq. 6.1. The efficiency is determined from the fraction of b-jets which are also
b-tagged as a function of dijet mass, ∆φ and χ. To evaluate the systematic uncertainty
arising from the calibration itself the weights which are applied to each jet are varied
according to their total uncertainty. The variations are conservatively taken as fully
correlated including the statistical uncertainty. For each variation the shifted efficiency
is evaluated and the maximum deviation from the nominal efficiency is calculated. The
maximum deviation is symmetrised in order to be less sensitive to statistical fluctuations
and assigned as systematic uncertainty.
The resulting efficiencies and systematic uncertainties are presented in Figs. 9.5 and 9.6.
1.2 1.2
Pythia M > 110 GeV Pythia
1 Fit result 1
Syst. error Syst. error
0.8 0.8
0.6 0.6
0.4 0.4
0.2 0.2
0 0
0 200 400 600 800 1000 0 0.5 1 1.5 2 2.5 3
bb dijet mass [GeV] ∆φ [rad]
(a) (b)
Figure 9.5: The b-tagging efficiency bb̄ as a function of (a) dijet mass and (b) ∆φ. The
efficiency as function of the dijet mass is fitted with the function: a  xb   c with 0   b   1. The
error bands (hatched area) on the fit result describe the 95% confidence-level on each bin centre.
The efficiency as a function of dijet mass in Fig. 9.5(a) exhibits a positive slope over the
full dijet mass range. As discussed in Section 6.5 the efficiency increases with pT at low
pT until a plateau is reached. The working point which is used yields a 50% b-tagging
efficiency integrated over jet pT. Naively, the bb̄ efficiency should be 50%50%=25%. This
assumption is proven to describe the efficiency well and shows that the efficiencies for both
jets are largely uncorrelated. The efficiency as a function of dijet mass ranges from 20% to
30%. In order to be less sensitive to statistical fluctuations the efficiency as a function of
dijet mass is fitted by the function a  xb  c with 0   b   1.1 In case of the other variables
∆φ and χ the expected behaviour of the efficiency is not well known and these are not
fitted. The statistical uncertainty which drives the fit result as a function of dijet mass
is calculated under the assumption of uncorrelated variables. The remaining b-tagging
efficiencies are calculated according to the following calculation assuming that the true
1The resulting parameters are a  5.0 2.2, b  1.2  102  3.8  102 and c  5.1 2.2.
135
∈
bb
∈
bb
9 The cross section measurement
1.2 1.2
110 GeV < M < 370 GeV Pythia 370 GeV < M < 850 GeV Pythia
1 1
Syst. error Syst. error
0.8 0.8
0.6 0.6
0.4 0.4
0.2 0.2
0 0
5 10 15 20 25 30 5 10 15 20 25 30
χ χ
(a) (b)
Figure 9.6: The b-tagging efficiency bb̄ as a function of angular variable χ in mass regions (a)
110 GeV   M   370 GeV and (b) 370 GeV   M   850 GeV.
efficiency is estimated from the measured efficiency:d
 Npass Ñ NpassNnotpassbb̄ δN  N bb̄  , (9.6)pass notpass N3total
where Ntotal  Npass   Nnotpass, and where Nnotpass and Npass are assumed to be inde-
pendently Poisson distributed.
In addition to the systematic uncertainty arising from the b-tagging calibration and in
case of the efficiency as a function of dijet mass, the 95% confidence-level on the fit result
in each bin is assigned as the systematic uncertainty on the fit. At low dijet mass the
uncertainty on the fit result dominates the total systematic uncertainty. The maximum of
the uncertainty from the fitting results is approximately 0.05. The systematic uncertainty
due to the b-tagging calibration dominates for dijet masses above 150 GeV. This systematic
uncertainty increases with dijet mass because the uncertainty is increasing with pT. The
highest total uncertainty on the scale factor is about 20% for jets with pT ¡ 140 GeV
(cf. Section 8.2.2). In case of dijet events in which both transverse momenta of the jets are
above 140 GeV the maximum expected uncertainty is 40%. This maximum is reached at
M  1 TeV as can be read off Fig. 9.5(a). Table 9.1 gives an overview of the systematic
uncertainties on the efficiency measurement, where the efficiency as a function of dijet
mass is chosen as representative:
The b-tagging efficiencies as function of the angular variable χ and of the azimuthal angle
between the leading jets are nearly constant because the full spectrum of jet pT values
contributes to each bin. These efficiencies are summarised in Table I.1 and Table I.2. They
range approximately between 20% and 30%. The efficiency as a function of ∆φ decreases
slightly when approaching the back-to-back configuration. The systematic uncertainty
on the efficiency as a function of ∆φ is also nearly constant. The fractional systematic
uncertainty is about 20% for the efficiency measurement in ∆φ. The efficiencies as a
function of the angular variable χ in Fig. 9.6 tend to slightly decrease with higher χ values.
The mass region 110 GeV   M   370 GeV is dominated by jets with lower pT. Therefore
the systematic uncertainty is smaller than for the mass region 370 GeV   M   850 GeV.
For the lower mass region the uncertainty varies between 10% and 20%, for the higher
136
∈
bb
∈
bb
9.2 Correction factors and systematic uncertainties
Dijet mass bin [GeV] b-tagging Systematic Syst. fractional
efficiency uncertainty uncertainty [%]
110-160 0.20 0.04 20
160-210 0.22 0.05 22
210-260 0.24 0.06 25
260-310 0.25 0.07 28
310-370 0.26 0.08 31
370-440 0.28 0.09 32
440-510 0.29 0.10 34
510-590 0.30 0.10 33
590-670 0.30 0.11 36
670-760 0.31 0.12 39
760-850 0.32 0.12 38
850-950 0.33 0.13 39
950-1060 0.34 0.14 41
Table 9.1: b-tagging efficiency as a function of dijet mass.
mass region between 25% and 40%.
9.2.4 b-tagging purity
The b-tagging purity which is explained in Eq. 6.4 is determined from the ratio between
the number of events with two b-jets which pass the b-tagging requirement and the number
of events with two b-tagged jets. The sample of b-tagged jets also includes mistagged
c-jets, light-quark and gluon-initiated jets and their contribution needs to be estimated.
This purity is extracted from template fits with data, fitting the distribution of the sum of
the secondary vertex masses of the two b-tagged jets. The discriminating power of this
sum and the different contributions to it are illustrated in Fig. 9.7 integrated over all dijet
masses. The events are categorised in three samples with the help of the identification of
the jet flavour in simulation: true bb̄ events, events with only one true b or b̄ and anything
else (bpb̄qX) and events with no true b-jet (XY ). The purities of both jets are correlated.
If a b-tagged jet in an event has been found already, the probability that a second b-tagged
jet corresponds to a real jet with bottom-flavoured content is 90%. The purity in bb̄ events
is therefore only deducible from an event variable describing this correlation directly (two
dimensional) or indirectly by a combination of variables. The sum of the SV0 masses of
both jets is a good discriminator describing the correlation indirectly, although due to the
presence of neutral particles and energy losses from detector effects the b-hadron invariant
mass cannot be fully reconstructed. The core area of the distribution of bpb̄qX events lies
between the other two, since one component of each event contains a secondary vertex
with an invariant mass spectrum of a bottom-flavoured jet. Because of the bb̄ fraction is of
major interest, denoted as b-contribution, and because of the statistical fluctuations in the
137
9 The cross section measurement
other two samples which contain mistagged events, the bpb̄qX and the XY contributions
are merged into a single non-b contribution. The binning of the SV0 mass distribution is
optimised to reduce statistical fluctuations in simulation and to ensure that every SV0
mass sum distribution in data contains at least few bins with 15 events minimum. With
both contributions a linear combination c1  bb̄  c2  pXY   bpb̄qXq where c1  1 c2 can
be found to describe the full SV0 mass sum distribution.
The template fit finds the best suited linear combination to describe data with the help
of a binned maximum likelihood method, the so-called TFractionFitter [113]. The b-
contribution describes the signal template were both jets are matched to a b-hadron at
particle level and the other component describing the background is formed by the non-b
contribution. To be able to perform these template fits enough data events in each analysis
bin are required to ensure the stability of the template fit. It was found that mass bins
with a half width of twice the detector mass resolution are sufficient. But the template
fit stability limits the cross section measurement as a function of dijet mass to 760 GeV.
The templates for higher mass regions have lost their discriminating power due to the
increasing mistag rate. Due to the mistag rate the contribution bpb̄qX with one b-jet shifts
the core area of the template for the non-b contributions towards the b-templates. This
causes a large overlap and the instability of the template fit due to the similarities in the
template shapes. In the following the measurement of the cross section as a function of
dijet mass is limited to 760 GeV. Furthermore, this requirement sets the bin widths of the
cross section measurements as a function of ∆φ and χ and limits the ∆φ measurement
to the region above π{2 due to a lack of statistics. The chosen bin widths in the ∆φ
measurement are also required to be twice as large as the ∆φ resolution [114]. Because
the SV0 tagging algorithm possesses a large mistag rate, it is not possible to measure the
bb̄ dijet cross section without requiring a second b-tag. Without this second b-tag, the
statistics could be increased to a large amount but the discriminating power of the SV0
mass vanishes because the non-b contribution becomes overwhelming. The advantage of
this data-based approach could not be preserved.
In the following the construction of both templates is described and the final results on the
bb events
0.06
b(b)X events
0.05 XY events
0.04
0.03
0.02
0.01
0
0 2 4 6 8 10 12 14
SV0 mass sum [GeV]
Figure 9.7: The distribution of the sum of the SV0 masses for all selected b-tagged dijet events
with jets pT ¡ 40 GeV. Events are separated into three categories: true bb̄ events, events with
only one true b or b̄ and anything else (bpb̄qX events) and events with no true b-jet denoted as
XY events. The single contributions are drawn stacked on top of each other.
b-tagging purity are presented. This is followed by the discussion and presentation of the
138
11//NN  ddNN//dd((SSVV00  mmaassss  ssuumm))  [[GGeeVV--11]]
9.2 Correction factors and systematic uncertainties
systematic uncertainties. Finally, additional cross checks on the systematic uncertainties,
the fitting method and implementation are presented.
To reduce the deficiencies of the simulated samples and their technical combination, high
statistics b- and non-b templates are constructed from the simulated distributions by fitting
them. Signal and background templates are needed for every bin in the cross section
measurements. The fit used to extract the shape of a template uses either a Gaussian
or a Landau distribution with mean µ and sigma σ. Both shapes are well motivated.
Templates, which have no impurities and are only subject to resolution effects, should
be well described by a Gaussian shape. Templates like the non-b templates have a core
region, which is defined by the dominant fraction of light-jets, and a tail from the events
with a c- and/or b-contribution.
As the shapes may vary with phase space range the optimal fitting function is determined
automatically for each template by fitting the sum of both possible functions with a
fraction factor f : f Gaussian  p1 fq  Landau. The fraction factor then determines the
optimal fitting function with which the template is then re-fitted. For a Gaussian shape
is decided if f ¡ 0.5 and otherwise for a Landau distribution. This selection is justified
because the shapes of the templates clearly favour one fit function and the values of f are
always either close to zero or close to one. The distributions are fitted with a Gaussian
distribution in 85% of all cases. Two examples of fits on the b- and non-b contributions
are given in Fig. 9.8 for the mass range 160 GeV   M   210 GeV. Appendix I contains all
fits on b- and non-b contributions. The lack of statistics in the templates is clearly visible.
With the help of the fitting procedure the contributions below 1 GeV and above 5 GeV
are determined because this phase space is insufficiently filled. An additional advantage of
this method is that it can constrain a bin content with the help of the neighbouring bins
more than the statistical error would allow. The outcome of the fits is used to generate
high statistics templates so that the statistical error on the likelihood fit is completely
dominated by the available data statistics.
The systematic uncertainty on the fitting procedure is evaluated with the help of the
25000
50000 b-template Fit: non-b template Fit:
160 GeV < M < 210 GeV Mean: 3.969 ± 0.003 20000 160 GeV < M < 210 GeV Mean: 2.600 ± 0.004
40000 Sigma: 1.283 ± 0.002 Sigma: 0.935 ± 0.003
Pythia 15000 Pythia
30000
20000 10000
10000 5000
0
0 2 4 6 8 10 0 2 4 6 8 10
SV0 mass sum [GeV] SV0 mass sum [GeV]
(a) (b)
Figure 9.8: Examples of construction of templates for (a) b and (b) non-b contribution in the
SV0 mass sum distribution from simulation for the measurement of the dijet cross section as
a function of dijet mass. Shown are the raw templates and the fit result for the mass range
160 GeV   M   210 GeV.
error parameters from the fit. Because both fitting functions are well motivated and in
139
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EEvveennttss  //  ((00..66  GGeeVV))
9 The cross section measurement
each case the optimal shape is used, no additional uncertainty on the choice of fitting
function is obtained. The covariance matrix is used to generate the error ellipses of the
fit parameters mean µ and sigma σ. Two examples of the error ellipses are illustrated
in Fig. 9.9. The results of the fitting procedures represent the centre of the ellipses. In
case of Fig. 9.9(a) the correlation between the fit parameters is small and the ellipse is
almost circular, the correlation in Fig. 9.9(b) is negative and large. Pseudo-experiments
are performed according to the error ellipse returning the pair (µ,σ) to evaluate the 68%
confidence-level of the fit result in each bin. Consequently, variations of the fit prediction
are obtained and serve as basis for variations in the template construction. Two examples
of variations are presented in Fig. 9.10 for a b- and a non-b template in the ∆φ range
2.8 rad to 2.9 rad and in the χ range 3 to 5, respectively. The dashed lines indicate the
variations in the template construction and the continuous black line is the nominal fit
prediction.
Using the constructed templates the template fits are performed on data in bins of dijet
1.5 105 1.3
510 GeV < M < 590 GeV 510 GeV < M < 590 GeV
1.25 3
1.4 Fit of b-template 104 Fit of non-b template
10
1.2
1.3 1.15
Pythia 103 1.1 Pythia 102
1.2 1.05
102 1
1.1 0.95 10
10
1 0.9
0.85
3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 1 2.3 2.4 2.5 2.6 2.7 2.8 1
Mean Mean
(a) (b)
Figure 9.9: Generated error ellipsis for an example of templates (a) b-template and (b) non-b
template for the dijet mass range 510 GeV   M   590 GeV.
mass, ∆φ and χ. Examples of these fits are collected in Fig. 9.11: (top) in bins of dijet
mass, (middle) ∆φ and (bottom) χ. The non-b and b-template are drawn stacked on top
of each other. The template fits not shown here are included in Appendix I. The statistical
uncertainty on the purities reflect the available statistics in data because the constructed
templates contribute a negligible statistical uncertainty. The statistical uncertainties
are re-calculated from the covariance matrix [115]. With decreasing data statistics the
statistical uncertainty on the likelihood results grows for example with increasing dijet
mass. The lower parts of the plots show the ratio between the data distribution and
the summed simulation templates with applied fractions from the likelihood fit. The
overall agreement between data and simulation and the fit quality gives high confidence
in the fitting procedure. The systematic uncertainty arising from the fitting procedure is
determined by re-doing the template fit on data with the varied templates introduced in
Fig. 9.10. The effects of the variations are added in quadrature to the statistical uncertainty
of the likelihood fit.
The bin widths for the SV0 mass sum distribution may cover shifts in the SV0 mass
distributions between data and simulation. The variations on the templates from the
68% confidence-level on the fitting parameters do not cover possible shifts in the scale of
140
Sigma
Arbitrary units
Sigma
Arbitrary units
9.2 Correction factors and systematic uncertainties
Pythia Pythia
Fit Fit
104 Variation 1 102 Variation 1
Variation 2 Variation 2
103
10
102 non-b template
1
b-template 510 GeV < M < 590 GeV
10 3 < χ < 5
10-10 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14
SV0 mass sum [GeV] SV0 mass sum [GeV]
(a) (b)
Figure 9.10: Shown are the raw templates from Pythia simulation and the constructed templates
from the fitting procedure with the overlaid variations (dashed lines). The variations reflect the
68% confidence-level for the constructed templates.
the invariant mass of the secondary vertex. Therefore the template fits are re-done with
templates shifted by half a bin width. The resulting deviations are added in quadrature to
the systematic uncertainty obtained.
The total uncertainty on the b-tagging purity consists of the variations on the shape and
the scale of the templates and the statistical uncertainty on the template fits themselves.
The total uncertainty is symmetrised. In cases where the systematic uncertainties would
shift the b-tagging purity outside the definition interval r0, 1s, the uncertainty is not
symmetrised. The resulting purities and systematic uncertainties for the dijet mass and
∆φ bins are presented for the measured phase space in Fig. 9.12 and detailed information
on the purities and the systematic uncertainties are summarised in Table 9.2 for the
measurement as a function of dijet mass. Further details on the remaining variables are
given in Table I.3 and Table I.4. The purities measured in dijet mass bins range from
50% in the high mass region to 90% in the low mass region. The maximum fractional
systematic uncertainty is 30%. The purity decreases with increasing dijet mass, reaches a
plateau at around 60% and increases in the two last bins. The systematic uncertainties
are driven by the lack of statistics in the simulation. Only in the last four dijet mass
bins, the statistical uncertainty competes with the systematic uncertainty and at last
dominating at 670 GeV to 750 GeV. At low dijet mass the mistag rate is very small
and the construction of the non-b templates suffers from the small fraction of inclusive
jets which enter into these distributions. Consequently, the non-b templates suffer from
large systematic uncertainties due to the fit variations. Since the variations in the non-b
template cause the largest effect on the b-tagging purity, the uncertainty at the low mass
region becomes very large. Variations affecting the tails of the non-b templates, which
pollute the core region of the b-templates, have a very large effect on the b-tagging purity.
The systematic uncertainty then decrease with increasing dijet mass. On the other side of
the phase space the b-tagging efficiency decreases and the b-templates suffer from small
statistics. Therefore the systematic uncertainties tend to grow slightly again with dijet
mass due to the fit uncertainties on the b-templates. The purities in the ∆φ bins range
from 55% to 70%, and when approaching the back-to-back configuration the purities are
decreasing. The systematic uncertainty is about 20% to 30%. The statistical uncertainties
141
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EEvveennttss  //  ((00..66  GGeeVV))
9 The cross section measurement
are negligible compared to the systematic uncertainty. In Fig. 9.13 the purities in bins of
the angular variable χ are presented for both mass regions. The purities vary between 50%
and 70% for 110 GeV   M   370 GeV and 30% and 40% for 370 GeV   M   850 GeV.
The second lowest bin in both mass regions is suffering from large systematic uncertainties
due to the badly distributed simulation events and the systematic uncertainty reaches up
to 50% in the lower mass region and up to 90% in the higher mass region. Except for
those bins the fractional systematic uncertainty is about 30% for the lower mass region
and 50% in the higher mass region.
Systematic checks of the method:
Dijet mass bin [GeV] b-tagging Total Fractional
purity uncertainty uncertainty
[%]
110-160 0.90 +0.07 +8-0.27 -30
160-210 0.72 0.17 24
210-260 0.59 0.20 33
260-310 0.59 0.13 21
310-370 0.65 0.15 24
370-440 0.69 0.17 25
440-510 0.53 0.13 25
510-590 0.49 0.12 24
590-670 0.64 0.19 30
670-760 0.81 0.16 19
Table 9.2: b-tagging purity as a function of dijet mass.
Systematic uncertainties based on physical arguments like the dependency of the non-b
template on the correct modelling of the c- and light-jet contribution can hardly be
estimated because their effects are hidden below large statistical uncertainties in the
simulated contributions. Nevertheless, the systematic shifts in the templates are evaluated
due to the uncertainty on the amount of light- and c-jet contributions. Both contributions
are multiplied separately by a factor of 3 and 0.33. From these distributions new templates
are constructed and used in the template fit on data. The resulting deviations between the
nominal and the shifted purities is plotted in Fig. 9.14 on top of the systematic uncertainty
assigned by the uncertainty on the fitting procedure. This nominal systematic uncertainty
covers the deviations from the templates with weighted contributions. Therefore the
physics motivated systematic uncertainties are well estimated by the assigned systematic
variations. The uncertainty from the fitting procedure partly covers the systematic from
the modelling of the non-b contributions but has the advantage of being well defined. The
variations in the templates from the fitting procedure mainly influence the tails. Most
importantly the rising edge at low SV0 mass sum dominated by the non-b template and
the falling edge of the non-b template reaching into the core area of the b-template as well
as the falling edge of the b-template describing the very high SV0 mass sum distribution
are influenced. These are the critical parts in the template fit. These parts are also mainly
142
9.2 Correction factors and systematic uncertainties
70
80 210 GeV < M < 260 GeV 60 440 GeV < M < 510 GeV70
60 χ2/DoF: 25.2/23 50 χ2/DoF: 22.2/23
50 P : 0.60±0.06 P : 0.54±0.07bb 40 bb
40 Data 30 Data
30 b-template b-template
20 non-b template 20 non-b template
10 10
00 2 4 6 8 10 12 14 00 2 4 6 8 10 12 14
3 3
2 SV0 mass sum [GeV] 2 SV0 mass sum [GeV]
1 1
0 0
0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14
SV0 mass sum [GeV] SV0 mass sum [GeV]
70 2.8 rad < ∆φ < 2.9 rad
60
χ2/DoF: 15.6/23
50 P : 0.60±0.05
bb
40
30 Datab-template
20 non-b template
10
0
0 2 4 6 8 10 12 14
3
2 SV0 mass sum [GeV]
1
0
0 2 4 6 8 10 12 14
SV0 mass sum [GeV]
90
80 3.0 < χ < 5.0 60 3.0 < χ < 5.0
70 110 GeV < M < 370 GeV 50 370 GeV < M < 850 GeVχ2/DoF: 35.4/23 χ2/DoF: 29.4/23
60 P : 0.50±0.08 40 P : 0.35±0.09
50 bb bb
40 Data 30 Data
30 b-template 20 b-template
20 non-b template non-b template
10 10
0 0
0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14
3 3
2 SV0 mass sum [GeV] 2 SV0 mass sum [GeV]
1 1
0 0
0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14
SV0 mass sum [GeV] SV0 mass sum [GeV]
Figure 9.11: Examples of the final template fits on data using a binned maximum likelihood fit
(TFractionFitter): template fits in a bin of dijet mass (top) for a low mass bin (top left) and a
high mass bin (top right), a template fit in a bin of ∆φ (middle) and a template fit in a bin of χ
(bottom) for the lower mass range (bottom left) and the upper mass range (bottom right). The
uncertainty on Pbb̄ denotes the statistical uncertainty from the likelihood fit. DoF stands for the
number of degrees of freedom. The single contributions are drawn stacked on top of each other.
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Data / MC EEEEnnnnttttrrrriiiieeeessss    ////    ((((0000....6666    GGGGeeeeVVVV))))
Data / MC EEEEnnnnttttrrrriiiieeeessss    ////    ((((0000....6666    GGGGeeeeVVVV)))) Data / MC EEEEnnnnttttrrrriiiieeeessss    ////    ((((0000....6666    GGGGeeeeVVVV))))
9 The cross section measurement
1.4 Data 1.4 Data
Stat.+ Sys. error M > 110 GeV Stat.+ Sys. error
1.2 1.2
Stat. error Stat. error
1 1
0.8 0.8
0.6 0.6
0.4 0.4
0.2 0.2
0 0
0 100 200 300 400 500 600 700 1.6 1.8 2 2.2 2.4 2.6 2.8 3
bb dijet mass [GeV] ∆φ [rad]
(a) (b)
Figure 9.12: The b-tagging purity Pbb̄ as a function of (a) dijet mass and (b) the azimuthal
difference ∆φ extracted from the template fits. The statistical error are extracted from the
likelihood fit. The systematic uncertainty contribution to the error band are extracted with the
help of variations of the templates within the 68% confidence-level.
the focus in the physics motivated systematics but are not sufficiently constrained by the
simulated distributions. The templates with weighted contributions can only represent the
limited phase space filled by the simulation. In this sense the uncertainty from the fitting
procedure is well-defined because it is independent from such uncontrollable effects.
The quark multiplicity inside a jet modifies the b-tagging performance. A jet including
two b-quarks is more likely to be b-tagged because the jet contains on average more tracks
and has a higher probability that a secondary vertex is reconstructed. The uncertainty on
the modelling and the frequency of the multiplicity of b-quarks is included in the b-tagging
calibration. The effect on a measurement which requires two b-tagged jets is therefore
overestimated because the sensitivity to such jets are largely reduced. This may also affect
the modelling of the SV0 mass. A higher number of tracks attached to the secondary
vertex can change the shape of the SV0 mass distribution. This effect is studied with the
help of the SV0 mass distributions in bins of track multiplicity in the secondary vertex.
Also here it is expected that the effect on a dijet measurement is small compared to an
inclusive b-jet measurement. These distributions studied are included in Appendix I as
Fig. I.11 and show no deviation between the track multiplicity and the shape of the SV0
mass distribution in data and simulation.
To validate the chosen templates the purities obtained by the nominal templates are
compared to the purities in simulation. As the purities in simulation suffer from the lack of
Monte-Carlo statistics, it is expected that the purities agree within their uncertainties. In
Fig. 9.15(top left) it is shown how both purities agree with each other. In the lower part of
the plot it is visible that the purities agree within their uncertainties and that the overall
characteristics are reproduced by simulation. Furthermore, the results obtained with the
nominal templates are compared to the results of template fits with a simplified version of
the templates. The templates integrated over the dijet mass region used in the analysis are
the basis for two generic templates of each type: b-template and non-b template. The SV0
mass distribution for b-jets is a Gaussian distribution with mean at around 2 GeV and for
background jets the shape follows mainly a Landau distribution with a mean around 1 GeV.
From this a simplified, generic template for each sort of events can be generated by adding
144
P
bb
P
bb
9.2 Correction factors and systematic uncertainties
1.4
1.4 Data Data
110 GeV < M < 370 GeV Stat.+ Sys. error 1.2 370 GeV < M < 850 GeV Stat.+ Sys. error
1.2
Stat. error Stat. error
1
1
0.8
0.8
0.6 0.6
0.4 0.4
0.2 0.2
0 0
5 10 15 20 25 30 0 5 10 15 20 25 30
χ χ
(a) (b)
Figure 9.13: The b-tagging purity Pbb̄ as a function of the angular variable χ for (a)
110 GeV   M   370 GeV and (b) 370 GeV   M   850 GeV extracted from the template
fits. The statistical error are extracted from the likelihood fit. The systematic uncertainty contri-
bution to the error band are extracted with the help of variations of the templates within the 68%
confidence-level.
two Gaussian distributions for the b-template and two Landau distributions for the non-b
template. They are simplified in the sense that they do not account for any change in the
non-b template concerning the relative contributions from c- and light-jets nor between
the XY and bpb̄qX contributions. The mistag rates accordingly develop independent from
each other with dijet mass. The template fits on data are evaluated with these generic
template and the outcome is presented in Fig. 9.15(top right). Also here the relations
between purities and dijet mass range is reproduced and the purities agree well within
their uncertainties.
At last the implementation of the likelihood fit in the TFractionFitter is compared to the
RooFit package [116]. This comparison is shown in Fig. 9.15(bottom). The results deviate
from each other within only a small fraction of the statistical uncertainties. Even more in
both methods the statistical uncertainties agree in size and the available statistics set in
each bin is sufficient to ensure the stability of the template fits. In all discussed cases the
conclusions hold also in terms of variables ∆φ and χ.
9.2.5 Jet energy scale
Besides the b-tagging related systematic uncertainties the jet energy scale is the dominant
experimental uncertainty in jet measurements. In Section 8.3.3 the jet energy scale
uncertainty for b-jets has been presented and Table 8.3 summarised the uncertainty as a
function of jet pT and rapidity. The jet energy scale uncertainty includes contributions
from inclusive jets and b-jet specific ones estimated with the help of tracking information.
The minimum jet energy scale uncertainty on b-jets is 3.2% and the maximum amounts to
4.9%. To evaluate the effect on the cross section measurement with the help of simulation,
the energies of all jets at the beginning of the event selection are re-scaled. The variation
is fully correlated in each jet pT bin. The shifts between the measured cross section
with nominal scale and the cross sections with varied scales are determined. It is found
that the variations in the sample of b-tagged jets are largely influenced by statistical
145
P
bb
P
bb
9 The cross section measurement
1
Sys. uncertainty
0.8 c-jets × 3 Light-jets × 3
0.6 c-jets × 0.33 Light-jets × 0.33
0.4
0.2
0
-0.2
-0.4
200 300 400 500 600 700
bb dijet mass [GeV]
Figure 9.14: Difference between the purities obtained by templates with an varied c- and light-jet
contribution and the nominal purities presented in Table 9.2. The differences are compared to
the nominal systematic uncertainty obtained from the uncertainty on the fitting procedure.
fluctuations. Therefore the effect of the jet energy scale on the cross section measurement
of b-jets is calculated with the help of the inclusive jet sample. It has been verified that
the uncertainty on bb̄ events is of the same order and can be estimated by inclusive jets.
The variation which increases (decreases) the energy scale of jets causes that events with
two jets near the selection cut of 40 GeV are selected (discarded) because the transverse
momenta of both jets are increased (decreased). On the other side events with two jets
with a dijet mass near 760 GeV migrate out of (into) the valid phase space. In case of the
dijet cross section as a function of dijet mass the steeply falling cross section amplifies the
effect of such migrations. In case of the variation which increases (decreases) the energy
scale the cross section in each mass bin is increased (decreased). The fractional variation
in the cross section as a function of dijet mass is presented in Fig. 9.16 and summarised in
Table 9.3. The resulting systematic uncertainties due to the jet energy scale are between
10% to 20%. The systematic uncertainty decreases slowly with increasing dijet mass
because the jet energy scale uncertainty decreases with increasing transverse momentum.
The region with rising uncertainty above 500 GeV is hardly touched in this measurement.
As a reminder Fig. 7.5 illustrates the composition of each dijet mass bin in terms of the
transverse momentum of the leading jet. The effect of the jet energy scale uncertainty is
higher when the energy scale is increased because of the steeply falling spectrum in which
the migration is larger from the right edge of each bin. The detailed numbers for the jet
energy scale uncertainty on the cross section measurements as a function of ∆φ and χ are
given in Tables 9.4 and 9.5. The systematic uncertainties of the cross section measurement
as a function of ∆φ are between 12% and 19%. The uncertainties decrease slightly for
back-to-back configuations. The systematic uncertainties of the cross section measurement
as a function of χ are between 10% and 20%. In the lower mass region the uncertainty
is larger due to the larger fraction of jets with pT between 40 GeV and 100 GeV which
contribute the largest jet energy scale uncertainty. The higher mass region exhibits almost
a constant systematic uncertainty due to the jet energy scale between 10% to 13%.
9.2.6 Unfolding correction
In order to compare to higher-order QCD calculations, the measured cross section measure-
ment has to be corrected for detector effects after which the measurement is independent
146
P  (var) - P  (nominal)
bb bb
9.2 Correction factors and systematic uncertainties
1.4 Data P +sys. error 1.4 Data:
bb
1.2 1.2 Nominal templates (+sys. error)Pythia P +stat. error
bb Generic templates (+stat. error)
1 1
0.8 0.8
0.6 0.6
0.4 0.4
1.40 100 200 300 400 500 600 700 1.50 100 200 300 400 500 600 700
1.2
1
0.8 bb dijet mass [GeV]
1 bb dijet mass [GeV]
0.6 0.5
0 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700
bb dijet mass [GeV] bb dijet mass [GeV]
1.3
Data: (only stat. errors)
1.2
TFractionFitter (TF)
1.1
1 Roofit (Rf)
0.9
0.8
0.7
0.6
0.5
0.4
1.20 100 200 300 400 500 600 700 800 900
1
0.8
0 100 200 300 400 500 600 700 800 900
bb dijet mass [GeV]
Figure 9.15: The outcome of the nominal template fits are compared to: (top left) the purities
in simulation, (top right) the purities in data with different templates and (bottom) the purities
in data obtained with a different fitting programme (RooFit [116]).
from the detector used. The jet energy calibration restores the jet to the hadronic scale
on calorimeter level but does not account for smearing effects or jet migration between
bins in a measurement as a consequence of the finite energy resolution of the calorimeter
and the jet energy calibration. To restore the measured cross section to particle level a
correction is necessary which is referred to as unfolding correction. A bin-by-bin unfolding
based on the Pythia simulation is used to correct for all detector effects in a single
step. The correction factors are calculated from b-jets reconstructed from calorimeter
clusters and b-jets at particle level reconstructed from final-state particles including non-
interacting particles, namely neutrinos and muons. The jet flavour is determined as
discussed in Section 3.1 from an angular matching to b-hadrons. The unfolding correction
0.5
0.4 Pythia:
0.3 Fractional JES uncertainty
0.2
0.1
0
-0.1
-0.2
-0.3
200 300 400 500 600 700
bb dijet mass [GeV]
Figure 9.16: The fractional jet energy scale uncertainty on the bb̄ dijet cross section as a
function of dijet mass determined on simulated events.
147
data pythia data pythiaP  / P P  / P
bb bb bb bb
FFrraaccttiioonnaall  JJEESS  uunncceerrttaaiinnttyy
PTF / PRf PPP
bb bb bbbbbb
gen gen
Pnom / P Pnom / P
bb bb bb bb
9 The cross section measurement
Dijet mass bin [GeV] Fractional JES uncertainty [%]
110-160 +17- 15
160-210 +17- 16
210-260 +18- 15
260-310 +18- 16
310-370 +20- 16
370-440 +18- 16
440-510 +17- 16
510-590 +19- 16
590-670 +21- 17
670-760 +18- 17
Table 9.3: Jet energy scale uncertainty as a function of dijet mass.
∆φ bin [rad] Fractional JES uncertainty [%]
1.6-2.5 +21- 18
2.5-2.8 +20- 16
2.8-2.9 +19- 16
2.9-3.0 +17- 15
3.0-3.1 +15- 14
Table 9.4: Jet energy scale uncertainty as a function of the difference in azimuthal angle ∆φ.
is determined from the bin-by-bin ratio of the calorimeter jet and particle jet cross sections:
p q  d
nσ{pdX1...dXnq(particle b-jets)  Nbb̄pXq(particle b-jets)Cunf X
dnσ{pdX1...dXnq (calorimeter b-jets) Nbb̄p q
, (9.7)
X (calorimeter b-jets)
where X stands for dijet mass M , ∆φ or χpMq and N for the number of events in each
bin at calorimeter or particle level. The correction factors are applied to each measured
cross section to obtain the particle-level measurement. The correction includes effects from
acceptance cuts and from the jet energy resolution, as well as the underestimation of the
b-hadron energy due to lost neutrinos and muons. In Section 9.2.8 these contributions are
disentangled with the help of the inclusive jet cross section.
The most important systematic uncertainty arises from the discrepancies between the cross
section shape in data and simulation. Pythia simulation as discussed in Section 8.1.1 is
not able to describe the inclusive jet pT and dijet mass distribution. So the underlying
particle-level prediction of Pythia underestimates the distribution at high pT and conse-
quently overestimates the number of jets in the low pT range. On the basis of Fig. 8.1(a)
an event weight is computed to cover the deviations between data and Pythia simulation.
The event weight is calculated as a function of leading jet transverse momentum at particle
level ptruthT with the help of the following function:
148
9.2 Correction factors and systematic uncertainties
110 GeV   M   370 GeV 370 GeV   M   850 GeV
χ bin
Fractional JES uncertainty [%]
1-3 +15 +17- 14 -15
3-5 +17 +17- 15 -15
5-10 +18 +17- 16 -15
10-30 +20 +18- 18 -16
Table 9.5: Jet energy scale uncertainty as a function of angular variable χ for both mass ranges.
 

ptruth    T {
q
GeV  17
event weight 1 p , (9.8)
1103
with parameters p  1,0.5 and q  0.33, 1, 3. The event weights are illustrated in
Fig. 9.17(a). These event weights change the number of jets in each pT bin as a function of
leading jet pT at particle level. In case of the dijet cross section as a function of dijet mass
the resulting effect of the event weights is presented in Fig. 9.17(b) and the differences in
the cross section cover the deviations in Fig. 8.1(b). The tendency of the discrepancy in
Fig. 8.1(a) is also visible in comparison to other parton shower generators. In the appendix
the comparison is shown for the Herwig++ generator in Fig. I.12(a). Therefore the
discrepancy is dominated by missing next-to-leading order contributions. Consequently,
this systematic error cannot be estimated with the help of other parton shower generators
but with the help of data. Furthermore, involving different generators into the estimation
of the systematic uncertainty introduces a duplication in the systematic uncertainty due
to the jet energy scale. Deviations in the unfolding correction between different generators
are partly due to different, simulated jet energy scales.
Besides this systematic error on the modelling of the cross section shape, the uncertainty
on the modelling of the detector resolution needs to be accounted for. The size of the
unfolding correction is directly linked to the finite detector resolution which is simulated.
In addition to the energy resolution and uncertainty presented in Section 8.3.2 also the
angular resolutions are important for the cross section measurements. According to Eq. 5.1
the resolutions of the azimuthal angle and the rapidity are determined with the help of the
simulation in which jets at generator level are matched in angular space to reconstructed
jets. The resolutions are presented in Fig. 9.18 as a function of jet pT. The resolutions
are determined through fits in bins of pT with a Gaussian distribution on the difference
between the generated and reconstructed value normalised to the generated value.
In the following the contributions to the systematic uncertainty are discussed in detail
and presented separately for the different cross sections.
Systematic contributions to the unfolding correction factors as a function of
dijet mass:
 The unfolding factors for the dijet mass are fitted by an exponential function
a  ebM{ GeV to limit the effect of missing statistics.2 The statistical error is calculated
assuming uncorrelated quantities. An exponential function is chosen as it is flexible
2The resulting parameters are a  1.5  101  3.1  102 and b  6.2  105  4.5  105.
149
9 The cross section measurement
3
p = 1, q=0.33 p = -0.5, q=0.33 2.2 Pythia: inclusive jets
p:1, q: 0.33 p:-0.5, q: 0.33
2.5 p = 1, q=1.00 p = -0.5, q=1.00 2 p:1, q: 1.00 p:-0.5, q: 1.00
p = 1, q=3.00 p = -0.5, q=3.00 1.8 p:1, q: 3.00 p:-0.5, q: 3.00
2 1.6
1.4
1.5
1.2
1
1
0.8
0.5 0.6
0 200 400 600 800 1000 0 200 400 600 800 1000
leading jet ptruth [GeV] dijet mass [GeV]
T
(a) (b)
Figure 9.17: The discrepancies between data and simulation are the basis for the event weights
with are parametrised with the function Eq. 9.8. (a) shows the chosen parametrisations as a
function of leading jet ptruthT at particle level. The resulting effect on the dijet cross section as a
function of dijet mass is presented in (b).
enough to fit the unfolding correction of the dijet cross section as well as the
unfolding corrections from the b-jet cross section as a function of pT [117, 118] and
the unfolding corrections from the inclusive analysis [119]. There is no theoretical
prediction for the functional form of the unfolding correction factors. The uncertainty
on the fit prediction is estimated from the 95% confidence-level on the fit result
and contributes about 4% to the systematic uncertainty. The resulting unfolding
correction is presented in Fig. 9.20(top left).
 The resulting effect of the cross section shape variations by the function in Eq. 9.8
on the unfolding correction factors for the dijet mass are around 2% and included in
Appendix I in Fig. I.13. Due to the limited statistics the varied unfolding corrections
are fitted by the exponential function a  ebM{ GeV and the resulting deviation from
the nominal unfolding correction is calculated. The deviations are symmetrised
and the maximum deviation observed is added in quadrature to the systematic
uncertainty.
 The energy resolution in data is about 10% worse than simulated in Pythia (cf.
Section 8.3.2). In pseudo-experiments a randomised energy amount that corresponds
to a resolution smearing of 10% is added to each reconstructed jet at calorimeter
level . Due to the limited statistics this systematic uncertainty is evaluated using
inclusive jets. The deviation in the unfolding correction for the energy resolution
smearing is presented in Fig. 9.19 for three different smearing factors: 5, 10 and 15%.
The assigned systematic uncertainty which is added in quadrature is based on the
10% resolution smearing and contributes at most 1% to the systematic uncertainty.
 Uncertainties on the unfolding correction for the cross section measurement as a
function of dijet mass from the angular resolutions on azimuthal angle and rapidity
are negligible.
150
event weight
weight
N nomdijets /Ndijets
9.2 Correction factors and systematic uncertainties
9
0.1 10 0.1 10
9
Pythia: inclusive jets 108 Pythia: inclusive jets 108
0.08 7 0.08
Fitted resolution 10 Fitted resolution 107
0.06 106 0.06 106
105 50.04 0.04 10
104 104
0.02 3 0.0210 103
0 102 0 102
-0.02 10 -0.02 10
1 1
-0.04 -1 -0.0410 10-1
-0.06 10-2 -0.06 10-2
10-3 10-3-0.08 -0.08
0 100 200 300 400 500 600 700 800 900 1000 10
-4 -4
0 100 200 300 400 500 600 700 800 900 1000 10
p  [GeV] p  [GeV]
T T
(a) (b)
Figure 9.18: The resolutions of the azimuthal angle and the rapidity determined with the help
of the simulation. The resolutions are identical to the Gaussian width of the distribution of
the difference between generated and reconstructed value normalised to the generated one. The
coloured density distribution in each figure shows the fractional resolution as a function of leading
jet ptruthT .
The methods and description of the evaluation of the systematic uncertainties in case
of the cross section as a function of dijet mass are equivalent for the variables ∆φ and
χ. For those two cases the unfolding correction factors are not fitted and no systematic
uncertainty due to the fit needs to be assigned. The statistical errors on the unfolding cor-
rection is calculated by separating the number of events in each bin into three statistically
uncorrelated numbers:
 Nptruth&recoq  Nptruth&!recoqCunf (bin i)
Nptruth&recoq   p , (9.9)N !truth&recoq
where Nptruth&recoq is the number of events in which both reconstructed dijet masses
lie in the same bin, and Nptruth&!recoq and Np!truth&recoq are the number of events in
which the reconstructed dijet mass at calorimeter level and the dijet mass at particle level
do not correspond to either other. Either the reconstructed event has migrated out of this
bin (Nptruth&!recoq) or a reconstructed event from a different bin has migrated into this
bin (Np!truth&recoq). With the help of this separation error propagation for uncorrelated
variables is applicable.
The remaining contributions are the shape variation and the resolution uncertainty which
are both added in quadrature. The resolution uncertainty on the angular variables is
estimated with the help of different sources. In preliminary studies with early data the
deviation between the resolution in data and simulation was estimated to be 10% by
matching topological clusters (cf. Section 5.1.2) to tracks [114]. In between improvements
in simulation have increased the agreement [120]. For this analysis and phase space, the
uncertainty is estimated to be 5%. The contributions are described in more detail in the
following.
Systematic contributions to the unfolding correction factors as a function of
∆φ:
 The effects of the cross section shape variations on the unfolding correction factors
as a function ∆φ are within 1.5%.
151
(φ-φ )/φ
truth truth
Arbritary units
(y-y )/y
truth truth
Arbritary units
9 The cross section measurement
0.1
Pythia: inclusive jets
0.08 resolution +5%
resolution +10%
0.06 resolution +15%
0.04
0.02
0
-0.02
-0.04
0 100 200 300 400 500 600 700
dijet mass [GeV]
Figure 9.19: Effect of the resolution smearing on reconstructed jets at calorimeter level on the
unfolding correction as a function of dijet mass. The systematic uncertainty on the bb̄ unfolding
correction is evaluated using inclusive jets.
 The resolution of the azimuthal angle φ is determined from simulation. The resolution
is smeared by 5%. In pseudo-experiments a randomised smearing term is added to
each reconstructed jet at calorimeter level and the cross section as a function of ∆φ
is re-evaluated. The effect is of the order of 1% to 5%.
Systematic contributions to the unfolding correction factors as a function of
χ:
 The effects of the cross section shape variations on the unfolding correction factors
as a function χ are within 1.5%.
 The resolution of the angular variable χ is determined from simulation. The resolution
is smeared by 5%. In pseudo-experiments a randomised smearing term is added to
each reconstructed jet at calorimeter level and the cross section as a function of χ is
re-evaluated. The effect is of the order of 1% to 2%.
The individual contributions to the systematic uncertainties are symmetrised and finally
summed in quadrature. The unfolding correction factors and the resulting systematic error
bands are collected in Fig. 9.20. The corrections range from 20% to about 55% at most.
The corrections predominately account for the energy lost due the semi-leptonic b-hadron
decays. The size of these corrections are in agreement with the unfolding corrections
determined from Herwig++ simulation which can be found in Fig. I.12(b) with uses a
different model for fragmentation and decays. Previous studies discussing the transverse
momenta of muons and the jet energy scale with respect to the total transverse momentum
in tracks have shown that the missing energy is described appropriately (cf. Sections 8.1.3
and 8.3.3) in Pythia simulation. The final systematic uncertainties on the unfolding
correction as a function of dijet mass is of the order of 5% independent of the dijet mass
and dominated by the uncertainty assigned to the fit prediction. This is reasonable because
the unfolding correction is not well constrained due to the lack of statistics. The systematic
uncertainties on the unfolding correction as a function of ∆φ range between 1% and 7%.
The maximum uncertainty is reached in the last four bins of the measurement. The
systematic uncertainty on the unfolding correction as a function of χ is nearly 1% in the
lower mass region 110 GeV   M   370 GeV and between 1% and 2% in the higher mass
region 370 GeV   M   850 GeV.
152
Cnomunf -C
res
unf
9.2 Correction factors and systematic uncertainties
1.6
2.4
Pythia: b-jets Pythia: 
2.2 χ2/DoF: 1.7 1.5 Fit
2 Fit + sys. uncertainty Syst. error
1.8 1.4
1.6
1.3
1.4
1.2 1.2
1
0.8 1.1
0.6
0 100 200 300 400 500 600 700 10 100 200 300 400 500 600 700
bb dijet mass [GeV] bb dijet mass [GeV]
2
Pythia: 
1.9
M > 110 GeV Stat. error
1.8 Syst. error
1.7
1.6
1.5
1.4
1.3
1.2
1.11.6 1.8 2 2.2 2.4 2.6 2.8 3
∆φ [rad]
2 2
1.9 Pythia: 1.9 Pythia: 
110 GeV < M < 370 GeV Stat. error 370 GeV < M < 850 GeV1.8 1.8 Stat. error
Syst. error Syst. error
1.7 1.7
1.6 1.6
1.5 1.5
1.4 1.4
1.3 1.3
1.2 1.2
1.1 1.1
1 1
1 10 1 10
χ χ
Figure 9.20: The unfolding correction factors Cunf necessary to correct the measured bb̄ cross
sections to particle level with the corresponding systematic uncertainties: (top left) the fit of the
unfolding correction as a function of dijet mass with a systematic uncertainty from the 95%
confidence-level, (top right) the resulting unfolding correction as a function of dijet mass with the
total systematic uncertainty, (middle) the unfolding correction as a function of ∆φ, (bottom)
the unfolding correction as a function of χ for the lower mass region 110 GeV   M   370 GeV
(left) and the higher mass region 370 GeV   M   850 GeV(right).
153
CCuunnff Cunf
CCuunnff
CCuunnff CCuunnff
9 The cross section measurement
9.2.7 Systematics from pile-up and b-tagging algorithm
The data set in use for this cross section measurement consists of mainly three different
run blocks. With start of the data taking, each beam crossing contained on average 0.15
interactions until the number of protons per bunches increased and the size of the bunches
decreased. With periods E and F, the average number of interactions increased to 1.5.
At the end of the data taking (periods G to I) the instantaneous luminosity increased to
2.07  1032 cm2 s1 and the number of interactions per beam crossing was on average
3. In Section 5.1.3 it was discussed how the bias in the jet reconstruction due to pile-up
is treated and corrected. The jet energy scale uncertainty accounts for differences and
uncertainties in the pile-up correction. So the jet energy measurement was adapted to
cope with the pile-up conditions at the LHC and the nominal simulation samples are
without pile-up. Further studies on the inclusive jet cross sections in [119] have shown that
the cross section does not depend on the number of reconstructed vertices in the events
which is a direct measure of the additional interactions. This section discusses possible
biases from pile-up on the b-tagging identification and secondary vertex properties which
are used to deduce the b-tagging purity. Finally, the independence of the measured cross
section from the choice of the b-tagging algorithm is shown.
The identification of b-jets in the spatial algorithms is based directly on the reconstruction
of tracks and consequently depend on primary vertices. With additional interactions a
larger number of particles are emerging simultaneously from the beam crossing and a
higher density of tracks and jets is created in the detector. In consequence, the distances
between objects are reduced and in the extreme case the objects overlap and affect the
reconstruction of each other. Therefore tracks of nearby objects may influence and even
facilitate the reconstruction of secondary vertices which are important for the b-tagging
algorithm used. This could have an effect directly on the b-tagging efficiency and mistag
rate. Indirectly the track multiplicities in the secondary vertex could additionally change
the invariant mass distribution of the secondary vertices. Both issues are studied by
investigating their behaviour as a function of instantaneous luminosity in data and by
comparing simulation samples with two different pile-up scenarios: the default Pythia
sample and a pile-up sample with the configuration of data periods G to I (cf. Section 4.4).
It can be seen in Fig. 9.21(a) that within the statistical uncertainties the b-tagging efficiency
determined in the pile-up and in the nominal Pythia sample are identical. The presence
of additional jets reconstructed in the event does not alter the identification power of the
b-tagging algorithm in the pile-up scenario in ATLAS 2010 data. This assumption is verified
by Fig. 9.21(b) measured from data. The average number of b-tagged jets with respect
to the total number of reconstructed jets is determined as a function of instantaneous
luminosity. It is distinguished between data periods A to D with instantaneous luminosities
below 1031 cm2s1 and data periods E to I with instantaneous luminosities between
1031 cm2s1 and 1033 cm2s1. The latter distribution is shifted by 0.2 on the vertical
scale. The average number xny as a function of instantaneous luminosity is fitted by a
constant function. The matching fit results confirm that the average number of b-tagged
jets with respect to the total number of reconstructed jets does not depend on the amount
of pile-up in the data period.
With the help of Fig. 9.22 two properties of the reconstructed secondary vertex in
data as a function of instantaneous luminosity are studied. The shapes of the invariant
mass of the charged particles associated to the secondary vertex in Fig. 9.22(a) for
any dijet mass are compared in the data periods A to D (L   1030 cm2s1), E to F
154
9.2 Correction factors and systematic uncertainties
1
0.9 0 50 100 150 200 250 300 350 400 450 500Nominal 0.8
0.8
0.7 Pile-up 0.7
Periods A to D
Const. func.: 0.07±0.000
0.6 0.6 Periods E to I (+0.2)Const. func.: 0.07±0.000
0.5
0.4 0.5
0.3 0.4
0.2
0.3
0.1
1.50 200 400 600 800 1000
0.2
1 0.1
0.5 0
0 200 400 600 800 1000 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
inst. luminosity L [1030cm-2s-1]
bb dijet mass [GeV]
(a) (b)
Figure 9.21: (a) The b-tagging efficiency bb̄ deduced from different simulation samples using
different pile-up scenarios. (b) The fraction of b-tagged jets with respect to all jets in data as a
function of instantaneous luminosity from periods A to I. The data points for periods E to I have
an offset of 0.2 for visibility.
(1030 cm2s1   L   1031 cm2s1) and G to I (1031 cm2s1   L   1033 cm2s1)
with different instantaneous luminosities. The overlaid ratio with respect to the data
period without pile-up shows that the shape is unchanged with respect to the amount
of simultaneous interactions. Within the reconstruction step of the secondary vertex
two-track vertices are built. Under the influence of nearby and overlapping tracks the
number of two-track vertices could change depending on the amount of pile-up interactions.
In Fig. 9.22(b) the average number of two-track vertices is determined as a function of
instantaneous luminosities and fitted by a constant function. The average number of
two-track vertices increases slightly from periods A to D to periods E to I which are shifted
by 0.2 on the vertical scale. The increase is not significant because the deviation of 0.01
between the fit results is covered by fit systematics due to the choice of the binning. In
summary, within the amount of pile-up in data 2010 the b-tagging identification is not
significantly biased.
The independence of the cross section measurement from the pile-up can also be seen in the
comparison between the cross section measurement [117] using 3 pb1 and the measurement
presented in this analysis. The ratio between these cross section measurements presented
in Fig. 9.23(a) shows the agreement between them within the systematic uncertainties. The
simulation samples with MC09 contain several deficiencies in the description of data [95].
The deficiencies were correctly treated and the observed discrepancies between the cross
section measurements are partly due to the underlying tune and detector description used.
Finally, the cross section as a function of dijet mass deduced with the SV0 b-tagging
algorithm is compared to the measurement with the JetProb algorithm. The main event
selection steps are identical except the b-tagging selection cut. The b-tagging efficiency and
purity are deduced solely on simulated events. A b-tagged jet from the JetProb algorithm
does not necessarily contain a reconstructed secondary vertex. The assigned SV0 mass to
such jets is zero. Therefore the SV0 mass distribution of b-tagged jets from the JetProb
algorithm is strongly influenced by tracking efficiencies, vertex reconstruction efficiencies
and systematic uncertainties from the tracking selection cuts. It is not possible to use a
data-driven method based on the invariant mass of the secondary vertex. Nevertheless the
155
∈ /∈PU ∈∈∈
bb bb bbbbbb
<<nn>>  ooff  bb--ttaaggggeedd  jjeettss  ww..rr..tt..  aallll  jjeettss
9 The cross section measurement
0 50 100 150 200 250 300 350 400 450 500
1.8 1
1.6 Data: L < 1030 cm-2s-1 0.9 Periods A to D
Const. func.: 0.18±0.002
1.4 0.8Data: 1030 < L < 1031 cm-2s-1 Periods E to I (+0.2)
0.7 Const. func.: 0.17±0.001
1.2 Data: 1031 < L < 1033 cm-2s-1
3 0.61 Ratios w.r.t. luminosity
L < 1030
0.5
0.8  cm-2s-12 0.4
0.6
1 0.3
0.4 0.2
0.2 00 2 4 0.1
0 0
0 2 4 6 8 10 12 14 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
SV0 mass for b-tagged jets [GeV] inst. luminosity L [1030cm-2s-1]
(a) (b)
Figure 9.22: (a) The SV0 mass distribution for any dijet mass separately measured in 3 different
data periods with small (periods A to D), medium (periods E and F) and high (periods G to I)
instantaneous luminosity. The ratio of the SV0 mass distribution, which is presented in the inlay,
is calculated with respect to (w.r.t) the instantaneous luminosities below 1031 cm2s1. (b) The
average number of reconstructed two-track vertices as a function of instantaneous luminosity
from periods A to I. The data points for periods E to I have an offset of 0.2 for visibility.
sample of b-tagged jets between both b-tagging selections are strongly correlated (more
than 50%). To calculate a representative statistical error the dijet events selected each are
taken to be 50% correlated. The unfolding correction is identical in both measurements.
The resulting comparison between both measurements is presented in Fig. 9.23(b). Within
the systematic uncertainty of the SV0 based measurement both cross sections agree.
According to this the choice of the b-tagging algorithm does not affect the measured cross
section.
3 3
Data Data
2.5 Sys. uncertainty (34 pb-1) 2.5
Sys. uncertainty (3 pb-1) Sys. uncertainty (SV0)
2 2
1.5 1.5
1 1
0.5 0.5
0 0
0 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700
bb dijet mass [GeV] bb dijet mass [GeV]
(a) (b)
Figure 9.23: (a) The comparison between the cross section measurement as a function of dijet
mass with 3 pb1 (data periods A to F) [117] and the full 34 pb1 ATLAS data from 2010.
156
ddσσ  ((LL  ==  33  ppbb--11))  //  ddσσ  ((LL  ==  3344  ppbb--11  ))
1/N dN/d(SV0 mass) [GeV-1]
Ratio
ddσσ  ((JJeettPPrroobb))  //  ddσσ  ((SSVV00))
<<nn>>  ooff  ttwwoo--ttrraacckk  vveerrttiicceess
9.2 Correction factors and systematic uncertainties
9.2.8 The cross section ratio measurement
This section describes the measurement of the inclusive cross section briefly as the most
important aspects and approaches have been discussed in case of the bb̄ cross section and
are completely analogous. The systematic uncertainties on the inclusive cross section and
the determination of the systematic uncertainties on the ratio measurement are presented.
The trigger strategy, event selection and luminosity used are identical. Hence their system-
atic uncertainties cancel out in the cross section ratio. The jet cleaning for the inclusive
cross section is based on the medium selection (cf. Section 7.2) in contrast to the loose
selection used in case of b-jets. The medium selection makes it necessary to correct for
the inefficiency of the selection because the inefficiency is larger than 1%. The cleaning
efficiency as a function of jet pT and η has to be measured using data because some
cleaning variables are not reproduced in simulation. The efficiency for identifying real
jets is measured with a tag-and-probe method [121]. With the help of well-balanced,
back-to-back dijet events similar to the ones used in Section 8.3.2 in which the tag jet is
within |η|   2.0 and fulfils the jet quality criteria, the fraction of probe jets being rejected
by the jet quality cuts is measured. A dijet event is well-balanced if pp avgT,1pT,2q{pT   0.4.
The event selection ensures to select signal events without jets from background sources
or noise bursts. The systematic uncertainty on this efficiency is obtained by varying
the selection criteria on the tag jet. The jet selection inefficiency is below 4% for jets
considered in the measurement and decreases with pT at smaller than 1% for pT ¡ 100 GeV
in all rapidity regions. This inefficiency as a function of jet pT is applied to simulated
events. For each jet entering the dijet mass measurement a random numbers between 0
and 1 is generated. If the random number in an event exceeds the corresponding efficiency,
the event is discarded and the fraction of events removed is measured. In Fig. 9.24 the
cleaning efficiency and its systematic uncertainty as a function of dijet mass for inclusive
jets is presented. In Table I.8 details of this efficiency are given. The inefficiency in the
dijet cross section measurement is at most 4% at low dijet mass and decreases to less than
1% at 300 GeV. The systematic uncertainty is no more than 1% for all dijet mass bins.
The dijet cross sections are corrected for these inefficiencies according to Eq. 9.4 and the
systematic uncertainty on the efficiency is taken as a systematic uncertainty on the cross
section.
The unfolding factors are calculated in analogy bin-by-bin from Pythia simulation and
the same systematic uncertainties are evaluated as mentioned in Section 9.2.6 except for
the fit systematics. The unfolding correction factors for inclusive jets are not fitted. The
resulting unfolding correction with its systematic uncertainty can be seen in Fig. 9.25.
The unfolding correction for inclusive dijets differs from the one on bb̄ dijets by more than
20%. Apart from the correction due to the finite detector resolution the energy losses
from neutrinos and muons seem to account for the additional and dominant 20% of the
correction. The unfolding factors for inclusive jets are in agreement with unity for the dijet
mass range measured. The corrections and the systematic uncertainties are summarised in
detail in Table I.9. The systematic uncertainty ranges from 1.8% to 2.3%. The dominant
contribution to the uncertainty is the uncertainty on the cross section shape and adds
about 2% whereas the resolution uncertainty accounts for approximately 1%.
The uncertainty arising from the jet energy scale is determined in analogy to the approach
discussed in Section 9.2.5. The applied uncertainties are presented coarsely in Table 8.2.
It is expected that the uncertainty on the inclusive measurement compared to the bb̄ one is
slightly smaller because the contribution to account for the b-jet modelling is unnecessary.
157
9 The cross section measurement
1.15
Pythia: inclusive jets
1.1 Syst. error
1.05
1
0.95
0.9
0 100 200 300 400 500 600 700
dijet mass [GeV]
Figure 9.24: The efficiency for jet identification as a function of dijet mass for inclusive jets
and the medium cleaning selection. The black circles indicate the efficiency measured using the
tag-and-probe method. The systematic uncertainty on the efficiency is obtained by varying the
tag jet selection.
1.2
Pythia: inclusive jets
1.15
Stat. error
1.1 Syst. error
1.05
1
0.95
0.9
0.85
0.8
0 100 200 300 400 500 600 700 800
dijet mass [GeV]
Figure 9.25: The unfolding correction factors necessary to correct the measured dijet cross
section as a function of dijet mass to particle level with the corresponding systematic uncertainty
arising from the uncertainty on the jet energy resolution and cross section shape.
The resulting systematic uncertainties on the inclusive dijet cross section measurement as
a function of dijet mass are given in Table 9.6. The systematic uncertainties range from
about 11.5% to 14% in the dijet mass range measured.
At this point all the necessary correction factors to measure the inclusive dijet cross
section as a function of dijet mass have been presented. The cross section measurement is
done according to Eq. 9.4. The systematic uncertainties discussed are added in quadrature
and arise from the luminosity, the jet energy scale, the unfolding and the jet cleaning.
The cross section ratio in Eq. 9.5 can be simplified by neglecting corrections which were
found to be identical between both measurements or identical to unity. The cross section
ratio is then given by:

dσbb̄{dM P  Cbb̄ incl  bb̄ unf  clean  Nbb̄pMq , (9.10)
dσ inclincl{dM Cunf  bb̄  NinclpMqM
158
UUnnffoollddiinngg  ccoorrrreeccttiioonn  CC ∈∈iinncclluunnff cclleeaann
9.2 Correction factors and systematic uncertainties
Dijet mass bin [GeV] Fractional uncertainty [%]
110-160 +14- 12
160-210 +14- 13
210-260 +14- 13
260-310 +14- 13
310-370 +16- 13
370-440 +13- 13
440-510 +13- 12
510-590 +14- 12
590-670 +14- 13
670-760 +13- 12
Table 9.6: Jet energy scale systematic uncertainty as a function of dijet mass for inclusive jets.
The calculation of the systematic uncertainty on the cross section ratio follows these
assumptions:
 The systematic uncertainty arising from the jet cleaning on inclusive jets and from
the b-tagging efficiency and purity on the bb̄ measurement are uncorrelated. These
are handled by the error propagation of uncorrelated uncertainties and added in
quadrature.
 To first order the systematic uncertainties on the unfolding correction from the cross
section shape and resolution smearing are fully correlated with the exception of the
fitting procedure for the bb̄ dijets. This part of the systematic error is uncorrelated
and considered by the error propagation of uncorrelated uncertainties and added in
quadrature to the other systematic uncertainties. The uncertainty from the fitting
procedure contributes about 4%.
 The systematic uncertainties from the jet energy scale (JES) are correlated. The
uncertainty on the cross section ratio is evaluated by pseudo-experiments. The jet
energy scale uncertainty for b-jets is the quadratic sum of the JES uncertainty on
inclusive jets and the heavy flavor component. So the contribution based on inclusive
jets is fully correlated and the other is uncorrelated. Two Gaussian distributions
are generated with the width of the jet energy scale uncertainties: the relative
inclusive jet energy scale uncertainty and the relative b-jet energy scale uncertainty
of 2.5%. Each pseudo-experiment generates a Gaussian distributed random number
w1 which describes the inclusive cross section jet energy scale variation and another
Gaussian distributed random number w2 which describes the variation due to the
2.5% additional contribution for b-jets. The ratio measurement symbolised by A is
B
then varied by Ap1 pw1 w2qqp   q . Several million pseudo-experiments are generated. AnB 1 w1
example of the variations of the central value by the pseudo-experiments is presented
in Fig. 9.26 for the asymmetric jet energy scale uncertainties. The outcome of
159
9 The cross section measurement
the pseudo-experiments are finally fitted by a Gaussian distribution and the 68%
confidence-level is assigned as the jet energy scale uncertainty on the cross section
ratio. The jet energy scale uncertainty on the ratio is of the order of 10% to 15%
and recorded in detail in Table 9.7.
25000
dσ/dM + σJESup
370 GeV < M < 440 GeV
20000 dσ/dM + σJESdown
15000
10000
5000
0
-0.006 -0.004 -0.002 0 0.002 0.004 0.006
Variation from pseudo-experiments
Figure 9.26: Pseudo-Experiment variations of the jet energy scale according to two Gaussian
distributions in the dijet mass bin 370 GeV   M   440 GeV.
Dijet mass bin [GeV] Fractional uncertainty [%]
110-160 +10- 9
160-210 +10- 10
210-260 +10- 10
260-310 +11- 11
310-370 +13- 11
370-440 +11- 11
440-510 +12- 11
510-590 +13- 11
590-670 +14- 13
670-760 +13- 12
Table 9.7: Jet energy scale systematic uncertainty as a function of dijet mass for the ration
measurement between inclusive jets and b-jets.
9.3 Results of the cross section measurements
The cross section measurements using the ATLAS detector and recorded data from 2010
which correspond to a total integrated luminosity of 34 pb1 are presented. The previous
sections supply the necessary correction factors and have discussed the systematic uncer-
tainties arising in the measurements:
160
nnuummbbeerr  ooff  eexxppeerriimmeennttss
9.3 Results of the cross section measurements
s=7TeV, ∫ Ldt=34 pb-1 1.5
103 Data + stat. error Total systematic b-tagging efficiency
Luminosity Template fits
102 Sys. uncertainty
1 Jet energy scale Unfolding + Trigger
10 0.5
1 0
Anti-k t R=0.4 EM+JES
|y|<2.1, p >40GeV
10-1 T
-0.5
0 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700
bb dijet mass [GeV] bb dijet mass [GeV]
(a) (b)
Figure 9.27: Differential cross section measurement of bb̄ dijets as a function of dijet mass (a)
with the ATLAS detector and data corresponding to an integrated luminosity of 34 pb1. The
fractional systematic uncertainty is presented as a function of dijet mass (b). The shaded area
shows the combined uncertainty and the magnitude of the individual components are presented by
the markers.
 The uncertainty on the luminosity.
 The uncertainty on the trigger selection.
 The uncertainty on the jet energy scale.
 The uncertainty on the b-tagging efficiency.
 The uncertainty on the unfolding correction.
Among those corrections the unfolding procedure has been presented which corrects all
cross sections to hadron level. The cross sections are measured with jets with transverse
momenta above 40 GeV and within the rapidity |y|   2.1. The cross section is measured
only above a minimum dijet mass not biased by residual kinematic effects. The systematic
uncertainties presented in Section 9.2 are all added in quadrature.
For the statistical error calculation on the unfolded cross sections the statistical error from
the trigger efficiency and from the event selection efficiency are neglected due to their
small contribution. For all cross section measurements on b-jets the statistical uncertainty
on the b-tagging purity and calibration are incorporated into the systematic uncertainty.
A jet cleaning in the bb̄ measurement is unnecessary therefore no statistical error needs
to be accounted for. Furthermore for the bb̄ cross section measurement as a function
of dijet mass the statistical uncertainties are treated differently compared to the other
measurements as discussed in the previous section. The statistical uncertainty on the
b-tagging efficiency as well as on the unfolding correction as functions of dijet mass are
transferred into the systematic uncertainty by the fitting procedure. For the measurement
as a function of ∆φ and χ the statistical uncertainties on the b-tagging efficiency and
161
ddσσ//ddMM  [[ppbb  GGeeVV--11]]
FFrraaccttiioonnaall  ssyysstteemmaattiicc  uunncceerrttaaiinnttyy
9 The cross section measurement
unfolding correction are calculated using error propagation and the correlations between
the number of events. The contributions from the statistical uncertainties are propagated
to the cross section measurement:
 
 fgfe 
2  
2  
2dσbb̄  dσbb̄  δN   δCbb̄δ unf   δbb̄ , (9.11)
d∆φ or dχ d∆φ or dχ N Cbb̄ unf bb̄
where δN{N is the fractional error on the number of events, δCbb̄unf{Cbb̄unf is the fractional
error on the unfolding corrections and δbb̄{bb̄ the one on the b-tagging efficiency.
For the inclusive cross section measurement as a function of dijet mass the statistical
contributions are as follows:
 
 d 
2  
2  

dσ incl incl
2
incl  dσincl  δN   δCδ unf   δclean , (9.12)
dM dM N C incl inclunf clean
where δN{N is as defined above, δC incl inclunf {Cunf is the fractional error on the unfolding
corrections and δinclclean{inclclean the one on the jet identification efficiency.
For the ratio measurement the statistical uncertainty consists on the one hand of the terms
from the error propagation from the statistical error on the unfolding corrections and on
the jet identification efficiency for inclusive jets and on the other hand from the statistical
error on the number of events from the bb̄ measurement. As the bb̄ dijets are a real subset
of the inclusive jets entering in the cross section measurement the event samples are partly
correlated. But from the raw event numbers the correlation is determined to be of the
order of per mill and has a negligible effect on the statistical error. Therefore the statistical
error from the counting statistics is calculated for uncorrelated events overestimating the
uncertainty but beyond the precision of the measurement.
The measurements as a function of ∆φ and χ are normalised by the cross section, inte-
grated over the same phase space. This minimises experimental uncertainties. Therefore
the uncertainty arising from the luminosity cancels out in these measurements and the
normalisation reduces the uncertainties due to the jet energy scale, unfolding correction
and jet cleaning uncertainty, but the measurement stays sensitive to differences in the
shapes of the cross sections.
Cross section as a function of dijet mass: The cross section measurement as a func-
tion dijet mass is presented in Fig. 9.27 together with the fractional systematic uncertainty
on the cross section. The cross sections spans over almost four orders of magnitude and is
measured up to a dijet mass of 760 GeV. The cross section as a function of dijet mass is
a steeply falling function as expected from QCD. The cross section measured at around
400 GeV seems to stand out. This exceptional behaviour is already present in the raw
data spectra for each trigger. In Chapter 12 this disagreement is studied and quantified.
With only 34 pb1 of integrated luminosity this measurement extends the dijet mass cross
section from Tevatron with an integrated luminosity of 260 pb1 by more than 300 GeV (cf.
Section 3.2). The inclusive cross section of b-jets as a function of transverse momentum
has been measured and is presented along with the dijet cross section in [118]. The total
systematic uncertainty ranges from 30% to 60%. On average the largest contributions
are the b-tagging related systematics. The b-tagging calibration driving the b-tagging effi-
ciency uncertainty causes the dominant contribution above 250 GeV. Because the b-tagging
calibration has to be extended to measure the cross section of b-jets in this kinematic
162
9.3 Results of the cross section measurements
1.5
s=7TeV, ∫ Ldt=34 pb-1
Data + stat. error Total systematic b-tagging efficiency
1 Luminosity Template fits
Sys. uncertainty
Jet energy scale Unfolding + Trigger
1
0.5
Anti-k t R=0.4 EM+JES
|y|<2.1, p >40GeV
T
10-1 M > 110 GeV 0
-0.5
1.6 1.8 2 2.2 2.4 2.6 2.8 3 1.6 1.8 2 2.2 2.4 2.6 2.8 3
∆φ [rad] ∆φ [rad]
(a) (b)
Figure 9.28: Differential cross section measurement of bb̄ dijets as a function of dijet azimuthal
angle (a) with the ATLAS detector and data corresponding to an integrated luminosity of 34 pb1.
The fractional systematic uncertainty is presented as a function of ∆φ(b). The shaded area shows
the combined uncertainty and the magnitude of the individual components are presented by the
markers.
region the uncertainty was conservatively estimated. The statistical uncertainties on the
cross section measurement as a function of dijet mass range from about 2% to 8%. The
details on the cross section measurement are written down in Table J.1.
Cross section as a function of ∆φ: The cross section as a function of ∆φ  |φ1  φ2|
normalised to the total cross section measured in this phase space is presented in Fig. 9.28
along with the fractional systematic uncertainty. By normalising the cross section un-
certainties are reduced and only the shape of the cross section is determined. The cross
section falls rapidly over two orders of magnitude with decreasing angular separation
∆φ.The fractional systematic uncertainty as a function of ∆φ shows a homogeneous picture
as almost all uncertainties are approximately constant over the measured phase space.
Due to the mixing of different jet pT values in each ∆φ bin the systematic uncertainties
represent an average. Especially, the b-tagging efficiency uncertainty is constant and adds
only 20% uncertainty. The systematic uncertainty on the measurement amounts to 40%
over the measured phase space. The dominant uncertainty in this measurement is the
uncertainty on the b-tagging purity from the template fits.
The details on the cross section measurement are written down in Table J.2. The statistical
uncertainties on the cross section measurement range from about 16% to 25%. The increase
of the statistical error in contrast to the measurement as a function of dijet mass is due to
the fact that neither the b-tagging efficiency nor the unfolding correction are fitted. In
case of the dijet cross section as a function of dijet mass, the statistical uncertainties are
taken into account by the fitting uncertainties and inserted into the systematics.
Cross section as a function of χ: The cross sections as a function of the angular
variable χ  exp |y1 y2| normalised to the corresponding total cross section are presented
in Fig. 9.29 and Fig. 9.30. The cross sections are plotted until χ   30 and in this region
163
11//σσ  ddσσ//dd∆∆φφ  [[rraadd--11]]
FFrraaccttiioonnaall  ssyysstteemmaattiicc  uunncceerrttaaiinnttyy
9 The cross section measurement
10-2 1.5
s=7TeV, ∫ Ldt=34 pb-1
110 GeV < M < 370 GeV Data + stat. error Total systematic b-tagging efficiency
1 Luminosity Template fits
Sys. uncertainty
10-3 Jet energy scale Unfolding + Trigger
0.5
Anti-k t R=0.4 EM+JES
|y|<2.1, p >40GeV
10-4 T 0
-0.5
10-5 5 10 15 20 25 30 5 10 15 20 25 30
χ χ
(a) (b)
Figure 9.29: Double differential cross section measurement of bb̄ dijets as a function of angular
variable χ in the mass region 110 GeV   M   370 GeV (a) with the ATLAS detector and data
corresponding to an integrated luminosity of 34 pb1. The fractional systematic uncertainty is
presented as a function of chi (b). The shaded area shows the combined uncertainty and the
magnitude of the individual components are presented by the markers.
the cross sections decrease with increasing χ. A side effect of the chosen binning in χ
which increases exponentially with increasing χ from the point of statistics in the purity
templates is that migration effects are a minor issue. The magnitude of the systematic
uncertainty depends on the mass region in which the cross section as a function of χ is
measured. In the mass region 110 GeV   M   370 GeV the uncertainties tend to be
smaller. They range from 30% to 60%. In the second χ bin the non-b template suffers
from statistical problems. In the higher mass region the b-tagging calibration uncertainty
and the template fit uncertainties dominate and add up to effects of more than 100% in
the asymmetric systematic uncertainty. The systematic uncertainty in the higher mass
region goes down to a minimum of 40%. The details on the cross section measurement are
written down in Table J.3 and Table J.4. The statistical uncertainties on the cross section
measurement as a function of angular variable χ range from about 10% to 25%. Also here
the statistical uncertainties from the simulation on the b-tagging efficiency and unfolding
correction are accounted for in the statistical error on the measurement.
Inclusive cross section and ratio measurement as a function of dijet mass: Fi-
nally, the inclusive cross section measurement followed by the ratio measurement are
presented. The measurement of the inclusive cross section as a function of dijet mass is
presented in Fig. 9.31. The measurement is preformed in the same phase space region
110 GeV   M   760 GeV which is used in the bb̄ measurement. The inclusive cross
section falls also almost four orders of magnitude. In this measurement the jet energy
scale uncertainty is the dominating uncertainty and contributes about 12% to 15%. The
next significant uncertainty is the uncertainty on the luminosity determination. The
remaining uncertainties add about 2% to the total uncertainty. The statistical error on the
measurement is maximum about 2% at around 700 GeV and below per mill level at low
164
11 ddσσ22 --11
σσ  χχ  [[GGeeVV ]]ddMMdd
FFFrrraaaccctttiiiooonnnaaalll   sssyyysssttteeemmmaaatttiiiccc   uuunnnccceeerrrtttaaaiiinnntttyyy
9.3 Results of the cross section measurements
10-2 2
s=7TeV, ∫ Ldt=34 pb-1
370 GeV < M < 850 GeV Data + stat. error Total systematic b-tagging efficiency1.5
Luminosity Template fits
Anti-k t R=0.4 EM+JES Sys. uncertainty
10-3 1 Jet energy scale Unfolding + Trigger
|y|<2.1, p >40GeV
T
0.5
10-4 0
-0.5
10-5 -15 10 15 20 25 30 5 10 15 20 25 30
χ χ
(a) (b)
Figure 9.30: Double differential cross section measurement of bb̄ dijets as a function of angular
variable χ in the mass region 370 GeV   M   850 GeV (a) with the ATLAS detector and data
corresponding to an integrated luminosity of 34 pb1. The fractional systematic uncertainty
is presented as a function of χ (b). The shaded area shows the combined uncertainty and the
magnitude of the individual components are presented by the markers.
dijet masses. The details on the cross section measurement are written down in Table J.5.
The inclusive cross section measurement is used to determine the ratio to the bb̄ dijet cross
section. The ratio measurement is presented in Fig. 9.32 as a function of dijet mass. The
fraction of bb̄ dijets decreases slightly from about 1% to 0.3% with increasing dijet mass.
Also here, the ratio measured at around 400 GeV stands out in the ratio caused by the
bb̄ dijet measurement. The statistical uncertainty ranges from about 2% at lower dijet
mass to about 9%. The total systematic uncertainty on the ratio measurement is about
30% to 60%. The systematic uncertainties not related to b-tagging are smaller than 13%.
The jet energy scale uncertainty is reduced by the correlation between both jet measure-
ments. The remaining part of the uncertainty is contributed by the b-tagging efficiency and
purity. At high dijet masses the b-tagging efficiency is the dominant systematic uncertainty.
The magnitudes of the systematic uncertainties in the measurements are summarised in
Table 9.8
The dominating systematic uncertainties are related to the b-tagging performance. With
the magnitude of data recorded in 2011 by the ATLAS detector, the b-tagging calibration
can be improved with the help of the sample of tt̄ events. There are three methods to the
measure the b-tagging efficiency in a sample of tt̄ events. Compared to the calibration
in events with a semi-leptonic decay into a muon, these methods do not break down at
transverse momenta of 200 GeV and inherently include the hadronic decays of the b-hadrons.
The extension of the calibration from the semi-leptonic decay to all possible b-hadron
decay modes contributes a large fraction to the systematic uncertainty. Additionally, the
methods based on tt̄ events have the advantages of a high-purity sample solely based
on kinematic selections and the possibility to cross-check the calibration with the total
165
11 22
σσ  
ddσσ
χχ  [[GGeeVV
--11]]
ddMMdd
FFrraaccttiioonnaall  ssyysstteemmaattiicc  uunncceerrttaaiinnttyy
9 The cross section measurement
105 0.5
s=7TeV, ∫ Ldt=34 pb-1
Data + stat. error
0.4 Total systematic
Jet cleaning
4 Sys. uncertainty Luminosity10
0.3 Unfolding+Trigger
Jet energy scale
0.2
103
0.1
0
102
Anti-k t R=0.4 EM+JES
-0.1
|y|<2.1, p >40GeV
T
-0.2
0 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700
inclusive dijet mass [GeV] inclusive dijet mass [GeV]
(a) (b)
Figure 9.31: Differential cross section measurement of inclusive dijets as a function of dijet
mass (a) with the ATLAS detector and data corresponding to an integrated luminosity of 34 pb1.
The fractional systematic uncertainty is presented as a function of dijet mass (b). The shaded area
shows the combined uncertainty and the magnitude of the individual components are presented by
the markers.
measured cross section of top pairs in ATLAS.
The usage of more advanced algorithms to identify b-jets is another step towards a
precision measurement of b-jets. These algorithms in general make use of two-dimensional
distributions and heavy-flavour properties. With equally good b-tagging efficiency an
increase in light jet rejection of a factor of 3 can be achieved. These high-performance
taggers will allow for searches of new phenomena with low production cross sections.
Uncertainties in relation to the purity determination can be reduced by improving the
theoretical uncertainties on c-quark production and modelling as well as on bottom
fragmentation. With the help of dedicated studies the b-tagging properties of charm-
flavoured hadrons can be understood and better constrained in measurements.
The uncertainty determination on the luminosity in this early data taking period has been
experimentally very challenging and the luminosity uncertainty has been measured as
precisely as by accelerators which are operating for years.
The jet energy scale uncertainty on the cross section measurement contributes about 15%
to 20%. This precision has been established using various techniques in the first year of
proton-proton collisions. It is a long time project to reduce the jet energy scale significantly
by the use of more sophisticated methods. With increasing integrated luminosity the
calibrations of jets using data-driven methods like the transverse momentum balance in
γ jet and Z+jet events become the focus of the jet energy scale uncertainty determination.
For the cross section ratio measurement it is also of use if the b-tagging related contributions
in the systematic uncertainty decrease to take advantage of the correlation of experimental
and theoretical systematic uncertainties in the measurement.
166
ddσσiinnccll//ddMM  [[ppbb  GGeeVV
--11]]
FFrraaccttiioonnaall  ssyysstteemmaattiicc  uunncceerrttaaiinnttyy
9.3 Results of the cross section measurements
0.1
s=7TeV, ∫ Ldt=34 pb-1
Data + stat. error
1.5 Total systematic Template fits
Anti-k t R=0.4 EM+JES Sys. uncertainty Jet energy scale Jet cleaning
|y|<2.1, p >40GeV
T b-tagging efficiency Unfolding+Trigger1
0.02
0.01 0.5
0
0.002
-0.5
0 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700
bb dijet mass [GeV] dijet mass [GeV]
(a) (b)
Figure 9.32: Differential cross section ratio measurement between bb̄ and inclusive dijets as
a function of dijet mass (a) with the ATLAS detector and data corresponding to an integrated
luminosity of 34 pb1. The fractional systematic uncertainty is presented as a function of dijet
mass (b). The shaded area shows the combined uncertainty and the magnitude of the individual
components are presented by the markers.
Contribution to cross section
Systematic uncertainty
Dijet mass Ratio ∆φ χ
Jet energy scale 15-20% 9-14% 10-20% 20%
b-tagging efficiency 30-60% 30-60% 20% 20-80%
b-tagging purity 20-30% 20-30% 20-30% 30-70%
Luminosity 3.4% 3.4% 3.4% 3.4%
Unfolding and Trigger   5%   5%   10%   5%
Jet cleaning - 1% - -
Table 9.8: Summary of the important systematic uncertainties on the dijet cross section of
b-jets using the SV0 b-tagging algorithm and of inclusive dijets.
167
ddσσ //ddMM  //  ddσσiinnccll  //ddMMbbbb  
FFrraaccttiioonnaall  ssyysstteemmaattiicc  uunncceerrttaaiinnttyy

10 Next-to-leading order calculations
This chapter discusses briefly the methods used to perform NLO calculations and presents
the NLO predictions which are compared to the measured cross sections presented in the
previous chapter. Three different NLO generators are used for this purpose and explained
in the following. Finally, the generators and their predictive power is compared and
summarised.
10.1 Introduction
The leading-order predictions of parton shower generators like Pythia and Herwig
can in general describe the main features of partonic processes and give a first estimate
of their cross sections. Divergences in QCD calculations are absorbed by introducing
unphysical renormalisation and factorisation scales as discussed in Section 2.1.3. The
inherent uncertainty in a lowest-order calculations due to the scale dependence is large. In
contrast, calculations at higher orders show reduced uncertainties and in addition give
control over the uncertainties due to the scale choice (cf. Eq. 3.6). A calculation to all
orders, if possible, would be independent from the choice of these scales. The extension to
next-to-leading order (if available) is the logical step. In addition, as shown in case of bb̄
production (cf. Section 3.1.1), new partonic processes may contribute at NLO emphasising
the need for higher order calculations.
The next-to-leading order dijet cross section can be written as:
σ  σLO   σNLO, (10.1)
where the LO term contains the Born approximation for 2 partons in the final state. In
Section 2.1.4 the NLO contributions have been discussed and in correspondence the NLO
term in Eq. 10.1 is given by»: » »
σNLO  dσNLO  dσR   dσV, (10.2)
2+1 partons 2 partons
where dσR denotes the real corrections from the 3-parton final states and dσV denotes the
virtual corrections to the 2-parton final states. The renormalisation procedure has been
carried out on the virtual correction to remove ultraviolet divergences. On their own both
integrals are divergent (in four dimensions) due to low-momentum and small-angle regions,
although their sum is finite. Among different schemes, which deal with these divergences
to calculate next-to-leading order jet cross section, the subtraction scheme [122] is widely
used and is implemented into the core of all three NLO generators used. The general
idea behind the subtraction method is to add and subtract counterterms dσA which are a
proper approximation of the real emission amplitude dσR. The NLO contributions are
rewritten as follows:
dσNLO  rdσR  dσAs   dσA   dσV. (10.3)
169
10 Next-to-leading order calculations
The counterterms need to have the same behaviour in each phase-space point as dσR to
act as a local counterterm. The first term in Eq. 10.3 is integrable in four dimensions and
the remaining singularities are associated with the last two.1 If the analytical integration
of dσA over the one-parton subspace leads to the same poles as in the integration of dσV,
the counterterm can cancel the divergences of the virtual corrections. The final structure
of the calculation is t»hen given by:
2
»  » 
σNLO  rdσR  dσAs   dσV   dσA . (10.4)
2+1 partons 2 partons 1 parton
The final challenging task is to obtain the actual form of the counterterm. The so-called
dipole factors deliver a general construction prescription outlined in detail in Ref. [123].
In case of initial-state hadrons additional soft and collinear singularities in the final state
are absorbed in the PDFs and give rise to extra counterterms.
This procedure is guaranteed to be valid for cross sections of hadronic observables as long
as they are collinear and infrared safe which is obeyed by the anti-kt jet algorithm.
10.2 The NLO generators and predictions
This section presents the configurations and generators which are used to obtain the NLO
predictions. The generators themselves are described briefly. The resulting NLO cross
sections are prepared in context of the measurements using the same event selection criteria
from the previous chapters.
The NLO predictions which are compared to the measurement are obtained by these three
generators: MCFM [124, 125], MC@NLO [56] and Powheg [126, 127]. The MCFM
generator is a NLO fixed-order generator which calculates the cross section at parton level.
In addition to the MCFM prediction corrections are necessary, so-called non-perturbative
corrections (non-perp.), to include the effects of multiple interactions, parton shower and
hadronisation. The other two NLO generators MC@NLO and Powheg combine the
precision of NLO matrix element calculations with the treatment of higher orders, soft
and collinear configurations via the parton shower approximation. The predictions of both
generators are interfaced to a parton shower program which then finally produces the
prediction at hadron level. On either the parton level from MCFM or the hadron-level
from MC@NLO and Powheg the anti-kt jet algorithm reconstructs jets with the radius
parameter R  0.4. On these events the same phase space selection cuts are applied as on
data: pT ¡ 40 GeV and |y|   2.1. On both levels the b-jets are identified by the angular
matching ∆R   0.3 to either b-quarks or b-hadrons (p bT ¡ 5 GeV). The basis for the NLO
calculation is the MSTW 2008 NLO PDF [12].3 This PDF set contains the uncertainties
on the PDFs evaluated at the 68% confidence-level. To evaluate the impact of the choice
of a different PDF the CTEQ66 [129] PDF is used. The parton shower generator used to
obtain the corrections for the parton-level prediction from MCFM and to generate the
parton shower for the predictions from Powheg is Pythia with the AMBT1 tune (cf.
Section 2.3.1). MC@NLO connects to Herwig to obtain the hadron-level prediction.
The b-quark mass is set to mb  4.95 GeV for all computations. In these calculations
the requirement of pT ¡ 40 GeV diminishes the dependence of the theoretical result on
1With dimensional regularisation in d  4 2 dimensions the singularities turn into poles in .
2In the limit of Ñ 0 in context of dimensional regularisation.
3The PDF sets are provided via the LHAPDF interface [128].
170
10.2 The NLO generators and predictions
the inserted b-quark mass. Furthermore, given the large mass of the b-quark and the
phase space probed, effects from intrinsic transverse momenta of the partons in the hadron
should be negligible.
The theoretical uncertainties on the NLO calculations arise from the experimental uncer-
tainties on the measurements on which the PDFs are extracted from, from the uncertainties
on αs in the NLO calculation and in the PDF fits, from the factorisation and renormal-
isation scales and from the choice of the parton shower generator and tune to generate
hadron-level predictions. These four uncertainties are in general added in quadrature, if
not it is stated otherwise. The uncertainties on the total cross sections from each NLO
generator are mostly below 0.5% and neglected.
The error propagation of experimental uncertainties to the PDF uncertainties is done
using the Hessian method [12], which is based on linear error propagation from a set of
eigenvectors. The MSTW 2008 PDF set includes 20 eigenvectors. These are evaluated in
positive and negative direction around the central value. The uncertainty on the cross
section is the quadratic sum of each variation in the positive and negative direction.
The renormalisation and factorisation scales are set to be equal, and are denoted by µ0.
The scale uncertainties are evaluated by varying the renormalisation or the factorisation
scale µ0 by a factor of 2 ( 2µ0 and 1µ0). The systematic uncertainty arising from the2
scale variation are estimated by the maximum deviation of each cross section from the
renormalisation or factorisation scale variations.
The uncertainty on the cross section from the uncertainty on αs can be evaluated either
directly with the help of PDF fits obtained with a varied αs [130] value or in case of the
MSTW PDFs in combination with the PDF uncertainties [131]. In the direct case the
PDF uncertainty on the cross section is added in quadrature to the uncertainty from
αs. In case of MSTW the PDF+αs uncertainty is extracted taking the correlations into
account from the envelop of five PDF predictions of PDF sets and their eigenvector sets in
which αs is displaced by t1σ,σ{2, 0, σ{2, 1σu.
The uncertainty on the parton shower model and on the tune is evaluated by comparing
the cross section predictions from different tunes and parton shower generators. The
envelop of these predictions is taken as systematic uncertainty on the cross section.
The calculation of NLO predictions is CPU-intensive. Therefore the number of calculated
NLO predictions are a compromise between CPU power and necessity. Theoretical uncer-
tainties are rated proportional to the importance of their contribution to the prediction.
The significant scale dependence of the NLO calculations for bottom production is due
to large contributions from higher orders. In the high energy limit large corrections can
occur in diagrams where the gluon exchanged in the t-channel becomes soft. At high
transverse momentum of the produced b-quark the quark mass is negligible and the quark
behaves like a massless particle. This introduces significant contributions of radiation
processes of gluons. The processes FEX and GSP which appear at NLO are calculated
without considering higher orders. The inclusion of such higher orders can reduce the scale
dependence. In comparison to the scale uncertainties the PDF uncertainty on the bb̄ cross
section is marginal although the gluon parton density carries large uncertainties at large
momentum fractions x. In light of the importance of the αs uncertainties and the amount
of CPU time needed it is considered to be impracticable to evaluate this uncertainty.
The uncertainty induced by αs is therefore neglected. The evaluation of the uncertainty
from the non-perturbative corrections is performed in detail for the MCFM prediction.
With the help of observations from the non-perturbative corrections for MCFM, this
uncertainty on the other generators is estimated due to the limitation in computing power.
171
10 Next-to-leading order calculations
The following subsections go into details on the NLO generators used.
10.2.1 The MCFM Generator
MCFM (Monte Carlo for FeMtobarn processes) is a parton-level program providing NLO
predictions for a range of processes. The final state for an NLO calculation at the matrix
element level contains at most three partons. The anti-kt algorithm (R  0.4) forms jets
from these partons. For the calculation of the bb̄ cross sections the scale µ0 is set to the
scalar sum of the pT’s of all the partons in the event. The number of integrations necessary
for sufficient statistics is about 10 million. To illustrate the effect of the inclusion of higher
orders the MCFM program calculates the cross section at LO with a LO PDF and at
NLO with a NLO PDF. The comparison between LO and NLO is presented as functions of
dijet mass and χ in Fig. 10.1. Higher orders, generally speaking, reduces the cross section
at small dijet masses and increases it at the high dijet mass. The overall effect of the
higher orders on the cross section as a function of dijet mass is comparable to the ratio
between the leading-order Pythia prediction and data in Fig. 8.1(b). Because of the use
of LO* PDFs which incorporates some of the properties of NLO PDFs in Pythia the
differences seen in Fig. 10.1 are larger. The higher orders seem to reshuffle the events as a
function of χ to lower values of rapidity difference.
The parton-level predictions have to be complemented by the non-perturbative corrections
MCFM MCFM
102 10
NLO (MSTWNLO 2008) NLO (MSTWNLO 2008)
LO (MSTWLO 2008) LO (MSTWLO 2008)
10
1
1
10-1
110 GeV < M < 370 GeV
100 200 300 400 500 600 700 5 10 15 20 25 30
2.5
1
2
1.5 0.8
1 0.6
100 200 300 400 500 600 700 5 10 15 20 25 30
bb dijet mass [GeV] χ
(a) (b)
Figure 10.1: The dijet cross section of b-jets at parton level calculated with MCFM at leading
and next-to-leading order with the corresponding PDF set from MSTW 2008 (a) as a function of
dijet mass and (b) as a function of the angular variable χ for 110 GeV   M   370 GeV. The
ratio of both predictions is illustrated in the lower part of the plot.
which include multiple interactions, parton shower and hadronisation.
10.2.1.1 Non-perturbative corrections
The non-perturbative corrections are obtained by a parton shower generator using the pre-
dictions at different levels of the simulation. The corrections are obtained by the ratio PNP :
172
NLO/LO ddσσ//ddMM  [[ppbb  GGeeVV--11]]
ddσσ22 --11
NLO/LO χχ  [[ppbb  GGeeVV ]]ddMMdd
10.2 The NLO generators and predictions

dnσpX1,...,Xnq 
 dX1...dX

n
P shower+had.+UENP . (10.5)
dnσpX1,...,Xnq 
dX1...dX

n shower
The b-jets before hadronisation (had.) are identified by the angular matching (∆R  
0.3) to b-quarks, after hadronisation the b-jets are identified with respect to b-hadrons.
This procedure includes effects in which the b-quarks in the process of hadronisation may
be disconnected from the jet. The predictions after the parton shower is set equivalent
to the NLO prediction at parton level. The effects of multiple interactions (UE) add
activity to the event and can add energy to the jet and increase the measured cross section.
On the other hand the effects from hadronisation in which hadrons are formed from the
unphysical partons may decrease the cross section. To simulate the bb̄ cross section in
Pythia correctly, it is required to generate inclusive jets and to filter out the desired
events. This makes the calculations computing time intensive, in order to achieve a smooth
phase space coverage of bb̄ events. For each necessary cross section prediction more than
600 million events are generated. In this sense it is reasonable to restrict the number of
tunes and other parton shower generators studied to obtain the systematic uncertainties
on the corrections. As mentioned before the default choice is Pythia and the AMBT1
tune. With the help of Pythia the effects on the non-perturbative corrections from differ-
ent tunes and b-fragmentation functions are examined. The following variations are studied:
 The Perugia tunes (cf. Section 8.3.1 and [107, 108]) are used to obtain LHC
independent corrections which are tuned to LEP and Tevatron data. Distinguished are
two tunes: the Perugia hard tune has a higher amount of activity from perturbative
physics and counter-balances this with reduced production of particles from non-
perturbative sources, the Perugia soft tune behaves the opposite way.
 The b-fragmentation function used in Pythia is the Lund-Bowler function presented
in Section 3.1.3 Eq. 3.8. Two variations of this function’s parameters are studied.
The chosen parameters are: a  0.3, b  0.58 GeV2 and rQ  1 denoted as Bowler
(high) and a  0.3, b  0.58 GeV2 and rQ  0.5 denoted as Bowler (low) in the
following. In addition the non-perturbative corrections are calculated using the
Peterson fragmentation function Eq. 3.7 with the parameter   0.005. Only the
fragmentation parameters are changed, the remaining parameters for Pythia are
taken from the AMBT1 tune.
 The corrections are also obtained using the Herwig++ generator with the LHC-
UE7-2 tune.4
The envelop of these six non-perturbative corrections around the default Pythia correction
is used as systematic uncertainty. The different corrections are shown in Figs. 10.2 and 10.3.
The non-perturbative correction not shown here are included in Appendix Fig. K.1. In
case of the dijet mass the corrections despite the large statistics generated are suffering
from large fluctuations (see Fig. 10.2(a)). In case of the angular cross sections this effect
is smaller due to the smaller number of bins and the composition of different kinematic
4Due to problems in Herwig++ version 2.5.0 and LHC-UE7-1 which are used in the MC10 simulation
samples, for this standalone calculation the version 2.5.1 and LHC-UE7-2 are used.
173
10 Next-to-leading order calculations
regions. To smoothen the correction as a function of dijet mass, the correction is fitted
and the resulting correction is presented in Fig. 10.2(b). The non-perturbative corrections
are close to unity with at most 10% deviation. Therefore both effects influencing the
corrections with opposite behaviour seem to balance each other mostly.
The lower uncertainty on the correction is based on the prediction of Herwig++. This
prediction consistently yields the largest effect onto the parton-level prediction from
MCFM. Because both tunes AMBT1 and LHC-UE7-2 have been adjusted to LHC data,
it is probable that the large deviation is mostly due to the different hadronisation concepts.
This assumption is supported by the differences seen in jet fragmentation studies in [132].
The variations based on Pythia seem to stay very close to the default correction. The
five variations in Pythia have bigger correction factors in the lower mass region and vice
versa in the higher mass region above about 400 GeV at which point the correction factors
intersect.
Using the non-perturbative corrections, the resulting MCFM predictions are presented in
1.2 1.2
Simulation: Bowler (high) Simulation: Bowler (high)
1.15 Pythia (default) Bowler (low) 1.15 Pythia (default) Bowler (low)
Perugia (soft) Peterson Perugia (soft) Peterson
1.1 Perugia (hard) Herwig++ 1.1 Perugia (hard) Herwig++
1.05 1.05
1 1
0.95 0.95
0.9 0.9
0.85 0.85 Systematic uncertainty
0.8 0.8
200 300 400 500 600 700 800 900 1000 0 200 400 600 800 1000
bb dijet mass [GeV] bb dijet mass [GeV]
(a) (b)
Figure 10.2: The non-perturbative corrections as a function of dijet mass for the measurement
of the dijet cross section of b-jets: (a) the original corrections and (b) the fitted corrections with
resulting uncertainty envelop around the default Pythia correction.
Figs. 10.4 and 10.5. The PDF uncertainty on the MCFM prediction is calculated directly
by MCFM with the central prediction. The statistical uncertainties are negligible. In case
of the cross section as a function of the azimuthal angle between the leading jets the results
from pQCD from MCFM at large ∆φ 3 are excluded because fixed-order perturbation
theory fails to describe the data in this region due to the dominating contribution of soft
processes.
The theoretical uncertainties range between 5% and 25%. Clearly visible is the dominating
effect of the scale uncertainties in all cross sections. The scale uncertainty is at most 20%.
On average the scale uncertainty contributes between 5% and 20% to the total uncertainty.
The contribution of the PDF uncertainty increases with the transverse momenta and
ranges between 2% and 6% in all cross sections. The contribution from the non-perp.
corrections ranges between 2% and 20% in rare cases.
174
PNP
PNP
10.2 The NLO generators and predictions
1.2 1.2
Simulation: Bowler (high) Simulation: Bowler (high)
Pythia (default) Bowler (low) 1.15 Pythia (default) Bowler (low)1.15
Perugia (soft) Peterson Perugia (soft) Peterson
Perugia (hard) Herwig++ 1.1 Perugia (hard) Herwig++
1.1
M > 110 GeV 1.05
1.05
1
1
0.95
370 GeV < M < 850 GeV
0.95
Systematic uncertainty 0.9 Systematic uncertainty
0.9 0.85
1.6 1.8 2 2.2 2.4 2.6 2.8 3 5 10 15 20 25 30
∆φ [rad] χ
(a) (b)
Figure 10.3: The non-perturbative corrections as a function of (a) azimuthal difference and (b)
the angular variable χ in the mass range 370 GeV   M   850 GeV with resulting uncertainty
envelop around the default Pythia correction.
10.2.2 The MC@NLO generator
MC@NLO can generate exclusive events. The calculation is done with the NLO matrix
element and the soft and collinear emissions are handled by a parton shower. The im-
plementation of MC@NLO allows to insert the NLO calculations to the parton shower
generators Herwig and Herwig++ in general. In case of bb̄ production only the Her-
wig simulation is usable. To overcome the problem of double counting configurations
which can occur in the matrix element calculation or in the parton shower process, the
NLO calculation is modified. MC@NLO can deliver events with negative weights. It
should be noted that these negative-weight events have a different origin than the negative
contributions that appear in NLO computations. In case of the bb̄ production the number
of negative events is sizable about 20%. To balance this effect more statistics is necessary.
All calculations of MC@NLO contain at least 900 million events which needs a large
computing effort. The scale used to compute the predictions is set toathe transverse mass of
the heavy quark in the rest frame of the two-parton system: m  m2T   p2T. The core of
the NLO generator uses a modified version of the subtraction method to take into account
the terms that are generated by the parton shower. For more details see [56]. The pure
NLO calculation with the matrix element is modified to avoid the double counting using
the Sudakov form factor from Herwig. The system can undergo an arbitrary number
of emissions with probability controlled by the Sudakov form factor and the amount of
emissions which occur twice is estimated and subtracted from the NLO calculation before
inserting them into the parton shower program.
The implementation of bottom flavour production has to take into account that it is
included in the evolution of initial-state and final-state showers in the parton shower
programs, consistent with the FEX and GSP processes. Switching off these parts in the
parton shower responsible for bottom flavour would lead to inconsistencies. Therefore the
implementation of MC@NLO is based on FCR processes only at orders α2s and α
3
2. The
prescription of the production formulae is given in [133]. However, all contributions from
GSP and FEX cannot be included, like GSP diagrams in which the gluon emits another
gluon before splitting. Nevertheless, besides the advantages of predictions of exclusive
final states as measured in a detector and the inclusion of soft and collinear contributions,
175
PPNNPP
PPNNPP
10 Next-to-leading order calculations
103 10
MCFM MCFM s=7TeV, Anti-k t R=0.4
102 MSTW 2008 MSTW 2008 |y|<2.1, p >40GeVT
1
Total sys. uncertainty Total sys. uncertainty
10
s=7TeV
1 10
-1
Anti-k t R=0.4
|y|<2.1, p >40GeV
10-1 T M > 110 GeV
-2
0 100 200 300 400 500 600 700 10 1.6 1.8 2 2.2 2.4 2.6 2.8 3
Scale variation Scale variation
1.2 PDF uncertainty bb dijet mass [GeV] PDF uncertainty ∆φ [rad]
Non-perp. corr. unc. 1.2 Non-perp. corr. unc.
1.1
1
1
0.9
0.8 0.8
0 100 200 300 400 500 600 700 1.6 1.8 2 2.2 2.4 2.6 2.8 3
bb dijet mass [GeV] ∆φ [rad]
(a) (b)
Figure 10.4: Dijet cross sections calculated at NLO with the help of MCFM as a function
of (a) dijet mass and (b) azimuthal difference ∆φ with the total theoretical uncertainty. The
contributions of individual uncertainties are presented by the shaded ares in the lower part of the
plots. The markers on the central prediction included the statistical uncertainty.
GSP contributions are taken into account fully efficient in contrast to the implementation
in standard parton shower predictions.
The PDF uncertainty on the MC@NLO prediction is obtained with the procedure ex-
plained above. The predictions according to the different eigenvectors i are calculated
using a re-weighting technique. This calculation is different to the MCFM calculation.
With the information of the parton’s identity (id), their momentum fraction x and the
scale Q2 of the hard process a reweighting factor W for each eigenvector i and event upon
the available central prediction with PDF S0 can be calculated by [134]:
fidpx1, Q, Siqfidpx2, Q, Siq
reweighting factor W i  p q p q , (10.6)fid x1, Q, S0 fid x2, Q, S0
where W 0 is identical to unity, Si denotes the i-th eigenvector and f represents the
probability to find the partons 1 and 2 with momentum fraction x in the proton. This
method is theoretically correct in the limit of a full phase space coverage with high statistics.
Because each event is simulated only once, the kinematics are unchanged and there is
no residual statistical variation in uncertainty. However, it should be taken care when
applying this method because the re-weighted events do not correctly modify the Sudakov
form factors used to avoid double counting. The re-weighting can only affect the hard
process. However, the impact of this was shown to be negligible (two orders of magnitude
below the PDF uncertainty) [135].
The resulting MC@NLO prediction with the total systematic uncertainty obtained only
via the PDF uncertainty are presented in Figs. 10.6 and 10.7. The PDF uncertainties
obtained for the MSTW 2008 PDFs are comparable to the PDF uncertainty from MCFM.
This supports the validity of the PDF re-weighting approach. For the cross section as
a function of dijet mass the PDF uncertainty increases with dijet mass and is at most
176
FFrraacc..  ssyyss..  uunncceerrttaaiinnttyy ddσσ//ddMM  [[ppbb  GGeeVV--11]]
FFrraacc..  ssyyss..  uunncceerrttaaiinnttyy 11//σσ  ddσσ//dd∆∆φφ  [[rraadd--11]]
10.2 The NLO generators and predictions
10-3 MCFM 10
-3
s=7TeV, Anti-k t R=0.4 MCFM
MSTW 2008 |y|<2.1, p >40GeVT MSTW 2008
Total sys. uncertainty Total sys. uncertainty
10-4 10-4
s=7TeV
Anti-k t R=0.4
10-5 |y|<2.1, p >40GeV -5T 110 GeV < M < 370 GeV 10 370 GeV < M < 850 GeV
5 10 15 20 25 30 1.31.4 5 10 15 20 25 30Scale variation Scale variation
PDF uncertainty χ 1.2 PDF uncertainty χ
1.2 Non-perp. corr. unc. Non-perp. corr. unc.
1.1
1 1
0.8 0.9
5 10 15 20 25 30 5 10 15 20 25 30
χ χ
(a) (b)
Figure 10.5: Dijet cross sections calculated at NLO with the help of MCFM as a function of χ
in the mass region (a) 110 GeV   M   370 GeV and (b) 370 GeV   M   850 GeV with the
total theoretical uncertainty. The contributions of individual uncertainties are presented by the
shaded ares in the lower part of the plots. The markers on the central prediction included the
statistical uncertainty.
about 6%. For the cross sections as functions of angular variables the PDF uncertainty
is in general reduced and at minimum about 1.5%. In contrast to MCFM, MC@NLO
is capable of predicting the region around π due to the parton shower approach from
Herwig. As expected the cross section as a function of ∆φ peaks at π. Due to negative
events the statistical precision of this prediction is a bit worse than compared to the others.
10.2.3 The POWHEG method
The method used in Powheg [136, 137, 138] (POsitive Weight Hard Event Generator)
to calculate the NLO prediction is the most recent development. This generator is used
to calculated not only the dijet cross sections of b-jets but also the prediction for the
inclusive dijet cross section and furthermore the ratio between b-jets and inclusive jets.
The approach taken by the Powheg generator is similar to the method in MC@NLO
but is meant to overcome its deficiencies.
Powheg takes advantage of the leading-log approximation in parton shower generators
but improves the NLO accuracy of the hard emission to combine the best features of
both methods. The drawbacks from MC@NLO are that the NLO generator approach
is specific to a particular parton shower generator and may generate negative weighted
events. Powheg overcomes this by the implementation of its own Sudakov form factor.
The strategy to achieve this is correcting NLO by the hardest emission and this has
to be generated first. Details on the treatment of pT-ordered and angular order parton
showers are given in [127]. It can be interfaced to Herwig and Pythia. But it has to
be mentioned that the approach in Powheg requires minor modification to the parton
shower generators which are currently not implemented. However, the effects of these
177
FFrraacc..  ssyyss..  uunncceerrttaaiinnttyy 11  ddσσ
22
σσ χχ  [[GGeeVV
--11]]
ddMMdd
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10 Next-to-leading order calculations
103 10
MC@NLO MC@NLO s=7TeV, Anti-k t R=0.4
102 MSTW 2008 MSTW 2008 |y|<2.1, p >40GeVT
1
Total sys. uncertainty Total sys. uncertainty
10
s=7TeV
1 10
-1
Anti-k t R=0.4
|y|<2.1, p >40GeV
10-1 T M > 110 GeV
-2
0 P10D0F unce2r0t0
10
ainty 300 400 500 600 700 1.6 P1D.F8 uncer2tainty 2.2 2.4 2.6 2.8 3
1.05 bb dijet mass [GeV] ∆φ [rad]
1.05
1
1
0.95
0.95
0 100 200 300 400 500 600 700 1.6 1.8 2 2.2 2.4 2.6 2.8 3
bb dijet mass [GeV] ∆φ [rad]
(a) (b)
Figure 10.6: Dijet cross sections calculated at NLO with the help of MC@NLO as a function
of (a) dijet mass and (b) azimuthal difference ∆φ with the total theoretical uncertainty. The
total theoretical uncertainty consists only of the contribution from the PDF uncertainty and
is presented by the area in the lower part of the plots. The markers on the central prediction
included the statistical uncertainty.
adjustments are expected to be small [139]. a
The scale used in Powheg is identical to choice made in MC@NLO (m  m2   p2T T).
For this NLO prediction the scale variations are calculated and give rise to a contribution
to the theoretical uncertainty as described above. The uncertainty on non-perturbative
corrections are dominated by the difference of Pythia to Herwig++ and this difference
may serve as a reasonable estimate for this uncertainty. Due to the necessary statistics of
more than 700 million events, the uncertainty from the non-perturbative corrections are
therefore estimated only from Herwig.
The resulting NLO predictions for the cross sections of b-jets are given in Figs. 10.8
and 10.9. In these predictions the PDF uncertainties are missing. It was found that the
PDF re-weighting procedure applied to Powheg does not give consistent results. This
may be due to the fact that the real contributions are evaluated with different structure
functions and different x’s than in the hard process. It was concluded that it was better to
not follow the procedure. Consequently, only the comparison to a different PDF (CTEQ66)
was studied, another solution did not seem manageable in terms of computing time. In
Fig. 10.11(a) lower part the deviations to CTEQ66 are at most 10%. The total uncertainty
on the cross section as a function of dijet mass Fig. 10.8(a) are at most 25% of which
the scale uncertainty is dominating. The total uncertainty on the measurement with ∆φ
are overall smaller than 6% and both uncertainties are equivalent. The cross sections as
function of χ have total uncertainties in the range between 10% and 25%. Also here the
scale uncertainties are dominant.
In the last two years the dijet production has been implemented into Powheg, about four
years after the implementation of bb̄ pair production. In the implementation each event
is built by first producing the underlying Born configuration, 2 Ñ 2 scattering. From
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10.2 The NLO generators and predictions
10-3 MC@NLO 10
-3
s=7TeV, Anti-k t R=0.4 MC@NLO
MSTW 2008 |y|<2.1, p >40GeVT MSTW 2008
Total sys. uncertainty Total sys. uncertainty
10-4 10-4
s=7TeV
Anti-k t R=0.4
10-5 |y|<2.1, p >40GeV -5T 110 GeV < M < 370 GeV 10 370 GeV < M < 850 GeV
PD5F uncerta1in0ty 15 20 25 30 PD5F uncerta1in0ty 15 20 25 30
χ χ
1.05 1.05
1 1
0.95 0.95
5 10 15 20 25 30 5 10 15 20 25 30
χ χ
(a) (b)
Figure 10.7: Dijet cross sections calculated at NLO with the help of MC@NLO as a function
of χ in the mass region (a) 110 GeV   M   370 GeV and (b) 370 GeV   M   850 GeV with
the total theoretical uncertainty. The total theoretical uncertainty consists only of the contribution
from the PDF uncertainty and is presented by the area in the lower part of the plots. The markers
on the central prediction included the statistical uncertainty.
this Born configuration the pT of the system is used as factorisation and renormalisation
scale. To control the divergences in the inclusive cross section a generation cut of 1 GeV
is applied. In addition, the Powheg event generation is capable of weighting events to
populate the high-pT regions of phase space with less statistics. When this weighting
procedure is activated, events are distributed according to the differential cross section
multiplied by  3
2
SpkTq  kT  , (10.7)k2 k2T T,supp
where kT is the transverse momentum of the final-state partons. In case of the inclusive
dijet production the suppression factor was set to kT,supp  250 GeV. This weighting
procedure is unfortunately not tested and bears problems in case of bb̄ production and
was abandoned in this case. The necessary statistics is reduced to about 50 million events.
Evaluated are the scale uncertainty and with the help Herwig the uncertainty from the
non-perturbative corrections.
The resulting inclusive dijet cross section as a function of dijet mass is presented in
Fig. 10.10. The total uncertainty ranges between 4% and 20%. The scale uncertainty
contributes at most 10% at medium and high dijet mass. The non-perturbative corrections
contribute at most 20% in negative direction in general.
For the ratio measurement Powheg is used exclusively. This ensures complete correlation
between the scale uncertainties in both predictions and allows to propagate the scale
uncertainty directly onto the ratio measurement. To illustrate the effects of the change in
the parton shower model and the effects of a different PDF onto the ratio measurement
Fig. 10.11 is given. The Powheg calculations are repeated in case of the bb̄ measurement
179
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22
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ddσσ   [[GGeeVV--11]]
ddMMddχχ
10 Next-to-leading order calculations
103 10
POWHEG POWHEG: s=7TeV, Anti-k t R=0.4
102 MSTW 2008 MSTW 2008 |y|<2.1, p >40GeVT
1
Total sys. uncertainty Total sys. uncertainty
10
s=7TeV
1 10
-1
Anti-k t R=0.4
|y|<2.1, p >40GeV
10-1 T M > 110 GeV
-2
1.40 100 200 300 400 500 600 700 110.21.6 1.8 2 2.2 2.4 2.6 2.8 3
Scale variation Scale variation
1.2 Non-perp. corr. unc. bb dijet mass [GeV] Non-perp. corr. unc. ∆φ [rad]
1.1
1
1
0.8
0.6 0.9
0 100 200 300 400 500 600 700 1.6 1.8 2 2.2 2.4 2.6 2.8 3
bb dijet mass [GeV] ∆φ [rad]
(a) (b)
Figure 10.8: Dijet cross sections calculated at NLO with the help of Powheg as a function
of (a) dijet mass and (b) azimuthal difference ∆φ with the total theoretical uncertainty. The
total theoretical uncertainty consists only of the contributions from the scale uncertainty and
the uncertainty on the non-perturbative corrections. The shaded areas present the individual
contributions in the lower part of the plots. The markers on the central prediction included the
statistical uncertainty.
as well as the inclusive cross section with the CTEQ66 PDF because to some extend the
PDF uncertainties from the eigenvectors from MSTW 2008 cancel in the ratio measurement.
Due to the limitation in computing time, the PDF uncertainty on the ratio measurement
is estimated using the PDF CTEQ66. Both plots in Fig. 10.11 indicate the same Herwig
behaviour with respect to the non-perturbative corrections in Fig. 10.2(b). Both Herwig
predictions are about at most 20% below the corresponding Pythia prediction. In case of
the Powheg calculation with CTEQ66 the prediction is also up to 10% below the MWST
2008 prediction. This effect seems to be larger in the cross sections of b-jets.
The resulting ratio measurement of dijets between b-jets and inclusive jets is presented
in Fig. 10.12. The total uncertainty on the measurement is at most 20% but in general
reduced by the correlations between the uncertainties on the individual cross sections.
The similar tendencies in the predictions with CTEQ66 reduce the PDF uncertainty
to about 5%. The remaining scale uncertainties are caused by opposite effects of the
scale uncertainties in the individual cross sections. The scale uncertainty ranges from a
minimum of 8% to 20% in the last bin of the measurement. Also the strong correlations
in the ratios of the prediction with Pythia parton shower to the prediction with Herwig
parton shower reduce the uncertainty on the non-perturbative correction. Except for five
bins, this uncertainty is negligible, these bins show a different behaviour with respect to
the default prediction. Besides the advantage of reducing experimental uncertainties also
the theoretical uncertainties are positively influenced.
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10.3 Summary
10-3 -3POWHEG 10 s=7TeV, Anti-k t R=0.4 POWHEG
MSTW 2008 |y|<2.1, p >40GeVT MSTW 2008
Total sys. uncertainty Total sys. uncertainty
10-4 10-4
s=7TeV
Anti-k t R=0.4
10-5 |y|<2.1, p >40GeV -5T 110 GeV < M < 370 GeV 10 370 GeV < M < 850 GeV
5 10 15 20 25 30 5 10 15 20 25 30
1.2 Scale variation
1.4 Scale variation
Non-perp. corr. unc. χ Non-perp. corr. unc. χ
1.2
1.1
1
1
0.8
0.9
5 10 15 20 25 30 5 10 15 20 25 30
χ χ
(a) (b)
Figure 10.9: Dijet cross sections calculated at NLO with the help of Powheg as a function of
χ in the mass region (a) 110 GeV   M   370 GeV and (b) 370 GeV   M   850 GeV with the
total theoretical uncertainty. The total theoretical uncertainty consists only of the contributions
from the scale uncertainty and the uncertainty on the non-perturbative corrections. The shaded
areas present the individual contributions in the lower part of the plots. The markers on the
central prediction included the statistical uncertainty.
10.3 Summary
The performed NLO calculations and uncertainty assessments represent a compromise
between their importance and the estimated computing power needed. The PDF uncertain-
ties approximately amount to 6% fractional uncertainty at most. The uncertainty arising
from the choice of a parton shower model is about 10% for MCFM or 20% for Powheg
at most depending on the models which are compared. The dominating uncertainty is the
scale variation which contributes in general 15% to 20% fractional uncertainty.
In terms of computing power the fixed order NLO calculation from MCFM have some
advantages. The PDF uncertainties are calculated directly without consuming additional
computing power and the scale variations are also not time consuming. But in addition the
non-perturbative corrections are necessary. The limitations of the fixed-order prediction
are the inability to produce predictions in regions in which soft processes are important
and the necessity of non-perturbative corrections in which the NLO accuracy is exchanged
with the prediction from the leading-order parton shower generator.
The procedure of PDF re-weighting is proven to be problematic on Powheg. But the
similarities between MC@NLO and Powheg allow at least an estimation of them for the
Powheg prediction. So it can be roughly assumed that the PDF uncertainties calculated
for MC@NLO also hold for the Powheg calculations. They are not explicitly added to
the calculation but it is kept in mind that they ought to contribute as well.
With the ability to produce inclusive dijet as well as bb̄ predictions, the focus for the NLO
calculations has been relying on Powheg. Therefore the scale uncertainties have been
calculated for Powheg (about 4.5 billion events).
181
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--11]]
ddMMdd
22
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--11]]
ddMMdd
10 Next-to-leading order calculations
105
POWHEG
104 MSTW 2008
Total sys. uncertainty
103
s=7TeV
102 Anti-k t R=0.4
|y|<2.1, p >40GeV
T
0 100 200 300 400 500 600 700
1.2 Scale variation
Non-perp. corr. unc.
1.1
1
0.9
0.8
0 100 200 300 400 500 600 700
dijet mass [GeV]
Figure 10.10: Inclusive dijet cross sections calculated at NLO with the help of Powheg as a
function of dijet mass with the total theoretical uncertainty. The total theoretical uncertainty
consists only of the contributions from the scale uncertainty and the uncertainty on the non-
perturbative corrections. The shaded areas present the individual contributions in the lower part
of the plots. The markers on the central prediction included the statistical uncertainty.
The dominating effect of Herwig++ in the non-perturbative corrections has given the
possibility to estimate these uncertainties with reasonable computing effort on Powheg.
The effects on the MC@NLO calculation from a change in the Herwig tune have been
neglected.
Differences between MC@NLO and Powheg are due to the treatment of higher or-
ders [140]. They are tracked down to the role of how the radiation of the matrix element is
generated, sub-leading terms in the parton shower may differ in the two approaches, due to
reshuffling of the splitting process in the parton shower and to different scaling choices in
both generators. But both still are proven to be at NLO accuracy. New implementations
and improvements are on their way.
From the fact, that the difference seen in the non-perturbative corrections between Pythia
and Herwig++ for MCFM are consistently smaller than the ones evaluated with the
help of Powheg predictions using Herwig’s and Pythia’s parton showers, may be
concluded that the minor modifications needed in the parton shower generators lead to
opposite effects in Pythia and Herwig parton showers. This was reported to the authors
of the generator and is under investigation.
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10.3 Summary
2 2
Pythia/Herwig Pythia/Herwig
1.5 1.5
1 1
0.5 0.5
POWHEG POWHEG
0 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700
MSTW 2008/CTEQ66 MSTW 2008/CTEQ66
1.5 1.5
1 1
0.5 0.5
POWHEG POWHEG
0 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700
bb dijet mass [GeV] dijet mass [GeV]
(a) (b)
Figure 10.11: Ratio of the default Powheg prediction using Pythia with MSTW 2008 PDF
to (upper plot) the Herwig prediction using the same PDF and (lower plot) to the prediction
using Pythia but the CTEQ66 PDF: (a) dijet cross section of b-jets as a function of dijet mass
and (b) dijet cross section of inclusive jets as a function of dijet mass. The statistical errors are
calculated uncorrelated.
10-1
s=7TeV POWHEG
Anti-k t R=0.4 MSTW 2008
|y|<2.1, p >40GeV
T Total sys. uncertainty
10-2
10-30 100 200 300 400 500 600 700
Scale variation
1.4 PDF uncertainty bb dijet mass [GeV]
Non-perp. corr. unc.
1.2
1
0.8
0 100 200 300 400 500 600 700
bb dijet mass [GeV]
Figure 10.12: Ratio of the dijet cross sections of b-jets and inclusive jets calculated at NLO
with the help of Powheg as a function of dijet mass with the total theoretical uncertainty. The
total theoretical uncertainty consists of the contributions from the scale uncertainty, the PDF
uncertainty evaluated with CTEQ66 and the uncertainty on the non-perturbative corrections. The
shaded areas present the individual contributions in the lower part of the plots. The markers on
the central prediction included the statistical uncertainty.
183
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RRaattiioo RRaattiioo

11 Results of the cross section
measurements
The previous chapters have gone into detail on the object reconstruction and understanding
of jets and b-jets. The trigger menu used to record the data, the event and object selection
cuts have been presented. These cuts are amongst other things determined by the triggers
and the trigger efficiencies to make optimal use of the trigger plateau regions and to
minimise systematic uncertainties on the trigger selection. The event and jet selection cuts
are influenced by b-tagging requirements to stay as conform as possible to the b-tagging
calibration. At last the detector layout dictates immutable conditions for the reconstruction.
Furthermore, migration effects are minimised if possible by the choice of the binning.
The most important systematic uncertainties on these cross section measurements arise
from the jet reconstruction and b-jet identification. Major parts of the jet and b-jet energy
scale uncertainty determination have been discussed. The extension of the b-tagging
calibration which is the basis for this measurement has been verified with the aid of
data. Additional small uncertainties are coming from the luminosity and event and
trigger selection. The measurement has been corrected for detector effects to make the
measurement experiment independent and the correction has been proven to be mostly
unbiased from the simulation model used. It has been validated that the small amount of
pile-up interactions in the data have a negligible effect on the measurement.
The measurement is compared to the calculations at next-to-leading order presented in
the previous chapter and the Pythia prediction. For all NLO predictions the theoretical
uncertainties have been estimated. For the measurements as a function of azimuthal
difference and angular variable χ the cross sections are normalised to the measured cross
section which reduces the experimental as well as the theoretical uncertainties. The
theoretical uncertainty is dominated mostly by the choice of the scales and the effect is
found to be approximately 20% for all kinematic regions whereas the PDF uncertainty is
at most 10%.
The measurement of the one-particle inclusive b-jet cross section has been performed which
serve as a strong test of pQCD [118]. However, several important features of the production
mechanisms of b-jet pairs can only be probed with the help of the correlation between
the quark and antiquark. Measurements at hadron colliders are in addition sensitive to
fragmentation effects and can deliver valuable insights in non-perturbation processes.
This measurement includes the bb̄ pairs produced via tt̄ production. The inclusive tt̄ cross
section measured in ATLAS is about 170 pb1 [141]. Assuming that the major part of the
b-jets are produced with a transverse momentum between 60 and 80 GeV the contribution
to the inclusive b-jet cross section ( 120 nb) is at most per mill level. Furthermore, as the
measurement select jets with pT ¡ 40 GeV and measures the invariant mass M ¡ 110 GeV,
the major fraction of events from Z Ñ bb̄ ( 5 nb) decays are cut away. Besides these
known contributions, the large QCD background and the prescaling of QCD events in
the trigger selection diminishes the sensitivity of this measurement to the Higgs decay
mode into bb̄although the branching ratio into bb̄ for a Higgs boson at low masses around
185
11 Results of the cross section measurements
50 GeV to 150 GeV is large. The discovery potential in the other possible decay modes
into vector boson pairs or photon pairs is enhanced due to the cleanness of the signals.
11.1 Dijet cross sections of b-jets
The measurement of bb̄ dijets studies to a large extend the kinematic properties of the
quarks arising in flavour creation (FCR) processes. Since the measurement refers to leading
and sub-leading jets, the event selection enhances this contribution. In addition the major
part of bb̄-quark pairs from gluon splitting are merged into one jet and thus are not resolved
into a dijet event topology.
The b-tagging templates and the purity determination dictates the maximal phase space
studied in this measurement. Furthermore, they also define for the most part the available
bin sizes. But it has been shown that as much as the b-jet identification influences choices
made in the measurement the choice of the b-tagging algorithm does not alter the final
cross section.
The following sections present in detail the resulting comparisons between data and MC
predictions. In case of the NLO predictions the MSTW 2008 PDF is used and in order to
obtain the particle-level prediction the hadronisation and shower model from Pythia is
used from the MC10 tune. The Pythia prediction itself uses the MRSTLO* PDFs. In all
cases b-jets are defined at particle level with an angular matching to a b-hadron within
∆R   0.3. The cross section in ATLAS data is compared to four QCD predictions, one
from Pythia at leading order and the other three from MCFM, Powheg and MC@NLO
at next-to-leading order. From these predictions the central values are overlaid on top of
the measurement without any statistical uncertainties.
11.1.1 Cross section as a function of dijet mass
The dijet cross section of b-jets as a function of dijet mass is presented in Fig. 11.1 for
jets with pT ¡ 40 GeV and |y|   2.1. The cross section is steeply falling over almost four
orders of magnitude which is well reflected by all MC predictions. Independent from the
order at which the calculation was done all four MC predictions seem to describe the
general features of the cross section. However, the Pythia prediction is not expected to
reproduce the correct normalisation. Therefore, leading-order prediction of Pythia is
scaled to the measured integrated cross section in data. The scaling factor needed is 0.83.
The right hand side in Fig. 11.1 presents the ratios of data to each MC prediction. The
statistical uncertainty from the measurement and from the MC predictions are propa-
gated into the ratio assuming uncorrelated errors. The systematic uncertainty on the
measurement ranges from 40% to 60%. From Fig. 3.11(b) it was deduced that the NLO
contributions from gluon splitting (GSP) and flavour excitation (FEX) contribute at most
10% to the measured dijet cross section due to the emphasis on 2 Ñ 2 configurations. In
consideration of the systematic uncertainty and the portion of GSP/FEX processes, it
can be concluded that it is probable that even without those contributions from GSP and
FEX an agreement between data and MC is achievable. But it should be another time
stressed that categorising the events is strictly speaking incorrect.
The dijet cross section from MCFM at leading order with a leading-order PDF which
has been presented in Fig. 10.1 would not be in agreement with data. Therefore, NLO
corrections are essential to obtain consistency between the measured cross section and
186
11.1 Dijet cross sections of b-jets
2
Data + stat. error Stat. error Data sys. unc.
1.28
103 Sys. uncertainty
POWHEG 1.61
MC@NLO 20 100 200 300 400 500 600 700
1.4 Shaded areas: sys. theo. unc.
102 MCFM 1.5
Pythia (x 0.83) 1.21
0.5
2.51
10 0 100 200 300 400 500 600 700
2
0.8
1.5
0.61
1 s=7TeV, ∫ Ldt=34 pb-1 0.5
2.50 100 200 300 400 500 600 700
Anti-k  R=0.4 EM+JES 0.4 only statistical errort 2
|y|<2.1, p >40GeV 01T .
.52
10-1 1
0.05
0 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700
bb dijet mass [GeV] bb dijet mass [GeV]
Figure 11.1: The bb̄ dijet cross section as a function of dijet mass for b-jets with pT ¡ 40 GeV
and |y|   2.1 is presented on the left hand side. The data are compared to MC predictions
from Powheg, MC@NLO, MCFM and Pythia. Only the central values of the theoretical
predictions are drawn. The leading-order Pythia prediction is scaled to the measured to the
measured integrated cross section. On the right hand side the corresponding ratios between data
and the MC simulations are presented. The shaded areas around the MC prediction indicate the
systematic theoretical uncertainty (except for Pythia). The statistical error is calculated from
the uncorrelated statistical errors from MC and data.
QCD. However, Pythia would be in agreement even without the scaling factor, this can
be concluded from Fig. 11.1 (right bottom). This agreement is achieved by the parton
shower approach and the usage of a PDF which mimics NLO properties. All four MC
predictions are in agreement with data within the systematic uncertainties from data and
the systematic theoretical uncertainties from the scale choice. The different size of the
theoretical uncertainties has been explained in the previous chapter.
11.1.2 Cross section as a function of ∆φ
The dijet cross section of b-jets normalised to the total measured cross section as a function
of azimuthal difference ∆φ is presented in Fig. 11.2 for jets with pT ¡ 40 GeV and |y|   2.1.
The cross section shows that the majority of events exhibit a pronounced back-to-back
configuration in the transverse plane which is generally well reproduced by the QCD
calculations. The cross section decreases rapidly with diminishing azimuthal separation.
The predictions from the fixed-order calculation of MCFM are excluded for the region near
π. Due to the dominating soft processes in this region and contributions from logarithmic
terms, the fixed-order prediction is divergent. The systematic uncertainty on data is about
40% all kinematic regions.
With the help of the studies on heavy-flavour production, the relative contributions to
this cross section are understood. In Fig. 3.9(a) the distribution of the azimuthal distance
from different production mechanisms between the b-hadrons is illustrated. The leading-
order production via the flavour creation (FCR) requires back-to-back configurations and
187
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DDaattaa// DDaattaa// DDaattaa// DDaattaa//
Pythia MCFM MC@NLO POWHEG
11 Results of the cross section measurements
dominates the region around ∆φ  π. The NLO contributions to FCR (real and virtual
emission) shift the angular separation to smaller values. Until a angular separation of
∆φ  2 the FCR contributions dictate the shape of the cross section. Below this region
the NLO production mechanisms FEX and GSP which are approximately flat for the
entire phase space 0  ∆φ   π are responsible for the cross section shape and value. The
measurement is only understandable with the contributions from FEX and GSP.
The cross section for small azimuthal angle differences is affected by the separation in η-φ
space of the b-hadrons. This determines the possibility of the reconstruction algorithms to
resolve them into different physical objects, namely here jets. The cross section therefore
depends heavily on the resolution parameter of the jet reconstruction.
The normalisation of the cross sections reduces experimental and theoretical uncertainties
and allows only a shape comparison between data and MC. Consequently, there is no need
to extract a Pythia scaling factor. In the region above ∆φ ¥ 2.5 all four MC predictions
show an agreement with data as can be seen in the ratios on the right side of Fig. 11.2. The
statistical uncertainty from the measurement and from the MC predictions are propagated
into the ratio assuming uncorrelated errors. Among those four Powheg, MC@NLO and
Pythia show excellent agreement, even if only the statistical uncertainty is considered. In
the region below ∆φ   2.5 MCFM is still in agreement but underestimates the relative
cross section by a factor of almost 2. Whereas the other predictions show a deviation to
data of maximal twice the uncertainty. The smallest deviation is between data and the
Powheg prediction. The cause of this deviation may be enlightened with the help of two
measurements.
The angular correlations between the BB̄-hadrons with pBT ¡ 15 GeV and |ηB|   2.0 have
been measured of the CMS collaboration [142]. This measurement uses displaced secondary
vertices to identify the BB̄-hadrons. The measurement is performed with a total integrated
luminosity of 3.1 pb1. For three leading jet pT regions, the differential BB̄ production
cross section as a function of ∆R and ∆φ is measured and compared to predictions of
Pythia and MC@NLO. The CMS measurement exhibits a substantial enhancement of
the cross section with respect to MC predictions at small angular separation (∆φ   1) and
a small deficiency in the intermediate region around ∆φ  2. In these regions the Pythia
prediction is even closer to data than the prediction of MC@NLO. The overshoot seen in
the lowest bin of the cross section as a function of ∆φ in this analysis may be qualitatively
explained by the CMS measurement. When approaching the region below ∆φ   2, the
processes FEX and GSP become important. The CMS measurement predicts a stronger
negative slope in the cross section as a function of ∆φ which decreases the number of
events in the intermediate region around ∆φ  2 and reduces the measurable dijet cross
section. This would lead to exactly the same effect as seen in this analysis.
Besides this, also the inclusive b-jet measurement [118] in ATLAS have seen a remarkable
difference in the track multiplicities and secondary vertex mass. With an increasing
number of tracks in the secondary vertex, the secondary vertex mass measured in data and
reconstructed in the simulation begin to disagree. The secondary vertex mass measured in
data is shifted to larger values. It seems reasonable to assume that jets containing two
b-hadrons likely have a large numbers of tracks measured in the secondary vertex and this
fraction of jets seems to be underestimated in the simulation as it can be concluded from
the CMS measurement.
However, it cannot be confirmed that the deviation seen in this analysis can be completely
attributed to these two observations nor quantitatively explained by them. These observa-
tions can only serve as a guidance.
188
11.1 Dijet cross sections of b-jets
1.5 Stat. error Data sys. unc.
Data + stat. error
Sys. uncertainty 12.5
POWHEG 0.5
MC@NLO
MCFM 1.6 1.8 2 2.2 2.4 2.6 2.8 31.5 Shaded areas: sys. theo. unc.
Pythia 2
1 1
0.5
s=7TeV,∫ Ldt=34 pb-1 1.5
1.6 1.8 2 2.2 2.4 2.6 2.8 3
Anti-k t R=0.4 EM+JES 2
|y|<2.1, p >40GeV 1.5
T
11
10-1 0.5
1.6 1.8 2 2.2 2.4 2.6 2.8 3
1.5 statistical error only
0.5
1
M > 110 GeV 0.5
0
1.6 1.8 2 2.2 2.4 2.6 2.8 3 1.6 1.8 2 2.2 2.4 2.6 2.8 3
∆φ [rad] ∆φ [rad]
Figure 11.2: The bb̄ dijet cross section as a function of ∆φ for b-jets with pT ¡ 40 GeV and
|y|   2.1 is presented on the left hand side. The data are compared to MC predictions from
Powheg, MC@NLO, MCFM and Pythia. Only the central values of the theoretical predictions
are drawn. On the right hand side the corresponding ratios between data and the MC simulations
are presented. The shaded areas around the MC prediction indicate the systematic theoretical
uncertainty (except for Pythia). The statistical error is calculated from the uncorrelated statistical
errors from MC and data.
11.1.3 Cross section as a function of angular variable χ
The dijet cross section of b-jets normalised to the total measured cross section as a function
of angular variable χ is presented in Figs. 11.3 and 11.4 in two different mass regions for
jets with pT ¡ 40 GeV and |y|   2.1. The maximum allowed range due to the rapidity
selection cut would be e4.2  67. The measurement restricts the allowed rapidity separation
to |y1  y2|   3.4. The separation in different mass regions increases the sensitivity to the
behaviour of the partonic cross section. For fixed ŝ the partonic cross section dσ̂{dχ is
approximately constant. Deviations from QCD in context of new resonances are more
likely to give rise to events peaking at low χ. The correspondence between ŝ and dijet
mass M makes it preferable to separate a measurement into different dijet mass bins.
Due to statistical restrictions, this measurement makes use of only two dijet mass regions:
110 GeV   M   370 GeV and 370 GeV   M   850 GeV.
In hadron-hadron interactions the PDFs need to be considered and are convoluted with the
partonic cross section. The momentum fractions x of the cross section are equivalent to
parameters dependent from the rapidities. The cross section dσ{dχ measured in a specific
mass region belongs to a nearly constant partonic cross section. But each χ bin samples
events in which only the rapidities vary according to the PDF convolution. To control
this contribution and to ensure the conformity of all χ bins in terms of PDF weighting
factors, the acceptance cut 1 |y1   y2|   1.1 enforces the same py1   y2q range in all bins.2
This cut rejects part of the events in the χ range between 1 and 10. This in addition
also controls the PDF uncertainties due to the rejection of events in which both jets are
189
11//σσ  ddσσ//dd∆∆φφ  [[rraadd--11]]
DDaattaa// DDaattaa// DDaattaa// DDaattaa//
Pythia MCFM MC@NLO POWHEG
11 Results of the cross section measurements
10-2 0.1
110 GeV < M < 370 GeV 2 Stat. error Data sys. unc.
Data + stat. error 0.09
s=7TeV,∫ Ldt=34 pb-1 1.5Sys. uncertainty
1
Anti-k  R=0.4 EM+JES POWHEG 0.08t
MC@NLO 0.5
|y|<2.1, p >40GeV MCFM 5 10 15 20 25 30T 0.027 Shaded areas: sys. theo. unc.
10-3 Pythia
1.5
0.06
1
0.5
0.025 5 10 15 20 25 30
1.5
0.04
1
10-4
0.00.35
2 5 10 15 20 25 30
0.02 statistical error only
1.5
0.011
-5 0.510 5 10 15 20 25 30 5 10 15 20 25 30
χ χ
Figure 11.3: The bb̄ dijet cross section as a function of χ in the mass region
110 GeV   M   370 GeV for b-jets with pT ¡ 40 GeV and |y|   2.1 is presented on the
left hand side. The data are compared to MC predictions from Powheg, MC@NLO, MCFM
and Pythia. Only the central values of the theoretical predictions are drawn. On the right
hand side the corresponding ratios between data and the MC simulations are presented. The
shaded areas around the MC prediction indicate the systematic theoretical uncertainty (except for
Pythia). The statistical error is calculated from the uncorrelated statistical errors from MC and
data.
boosted strongly in the same direction.
On the left side of Figs. 11.3 and 11.4 the measurements are overlaid with the cor-
responding MC predictions. The cross sections as a function of χ are decreasing with
increasing rapidity separation. In the lower mass region the cross section falls more than
one order of magnitude. In the higher mass region this slope is relaxed and the cross
section descents only a factor of about 2. On first sight the MC predictions are all in
agreement with data. The systematic uncertainty on data is about 40% to 55% in the
lower mass region and 50% to 100% in the higher mass region.
At leading order the χ distributions consist of two contributions: from light-quark annihi-
lation (cf. Eq. 3.4) and gluon fusion (cf. Eq. 3.5). The characteristic properties in terms
of rapidity correlation of these two contributions are discussed in Section 3.1.1. The cross
section for light-quark annihilation is a rapidly decreasing function of ∆y (cf. Fig. 3.4(b))
due to the fact that this subprocess proceeds entirely through an s-channel propagator
exchange. On the other hand the partonic cross section of the gluon-fusion subprocess
dominated by t- and u-channel exchange diagrams is a broad distribution as a function of
rapidity difference with a maximum at |∆y|  1 (cf. Fig. 3.3(b)). The first contribution
via the s-channel exchange peaks strongly at χ  1 and decreases rapidly with increasing
χ. The second contribution describes a much slower decrease with increasing χ and is
much more flat than the first contribution. The next factor which needs to be considered
is the product of the parton momentum densities which is in general not a function of
∆y. The χ cross section in the lower mass region falls almost two orders of magnitude
until χ  30, in the higher mass region the decrease of the cross section is damped. Here
190
11 22
σσ  
ddσσ
χχ  [[GGeeVV
--11]]
ddMMdd
DDaattaa// DDaattaa// DDaattaa// DDaattaa//
Pythia MCFM MC@NLO POWHEG
11.1 Dijet cross sections of b-jets
10-2
370 GeV < M < 850 GeV 3 Stat. error Data sys. unc.
-1 Data + stat. errors=7TeV,∫ 2Ldt=34 pb  Sys. uncertainty 2
Anti-k t R=0.4 EM+JES
POWHEG 1
MC@NLO
|y|<2.1, p >40GeV MCFM 5 10 15 20 25 30T 3 Shaded areas: sys. theo. unc.
10-3 Pythia
1.25
1
5 10 15 20 25 30
3
21
10-4 1
statistica5l error only10 15 20 25 30
2
0.5
1
10-5 5 10 15 20 25 30 5 10 15 20 25 30
χ χ
Figure 11.4: The bb̄ dijet cross section as a function of χ in the mass region
370 GeV   M   850 GeV for b-jets with pT ¡ 40 GeV and |y|   2.1 is presented on the
left hand side. The data are compared to MC predictions from Powheg, MC@NLO, MCFM
and Pythia. Only the central values of the theoretical predictions are drawn. On the right
hand side the corresponding ratios between data and the MC simulations are presented. The
shaded areas around the MC prediction indicate the systematic theoretical uncertainty (except for
Pythia). The statistical error is calculated from the uncorrelated statistical errors from MC and
data.
two effects from the parton density functions play a role. It is useful to parametrise the
PDFs with the following function: xfpx,Q2q  cxαp1 xqβ with 0   α  1 [12, 34]. The
parameters c, α and β are unique to each parton at a given scale Q2, at high x gluons can
be described by β  5 and quarks with β  3 assuming Q2  5 GeV2.
At small x1 and x2 the behaviour of the product of the parton momentum densities
x 21x2f1px1, Q qf2px ,Q22 q supports the positive correlation peaked at ∆y  0 of the outgo-
ing partons (p1 xqβ  1) using the Eq. 2.16:
px1x qα2 9p1  coshp∆yqqα (11.1)
The product p1 x1qβ1p1 x qβ22 itself cannot be expressed in terms of ∆y. The damping
effect of the product p1 x1qβ1p1 x β22q cannot be neglected if x grows. With increasing
invariant dijet masses the momentum fractions of the partons rise, the factors p1 x qβ11
and p1 x β22q cannot be neglected and produce an anti-correlation between the outgoing
partons forcing ∆y away from zero. The structure function and the cross section at
Born level favour opposite configurations. The rapidity correlation in the gluon-fusion
process counteracts the influence of the gluon structure functions and the favoured harder
momenta spectra of valence quarks counteract the strong and narrow correlation of the
light-quark annihilation process. In the lower mass region the structure functions do not
counteract strongly against the rapidity correlations from the cross sections. In the higher
mass region the parton momenta are larger and both effects influence the shape of the χ
cross sections shifting the χ values away from one and flattening the cross section shape.
The higher orders leading to configurations with three emerging partons, in which the bb̄
pair is not back-to-back or a heavy quark at large angle to the beam direction and the
191
11 ddσσ22 --11
σσ    [[GGeeVV ]]ddMMddχχ
DDaattaa// DDaattaa// DDaattaa// DDaattaa//
Pythia MCFM MC@NLO POWHEG
11 Results of the cross section measurements
other close to the incident proton, are likely to broaden the rapidity correlation whereas
the gluon splitting contribution tends to accentuate a peak at small rapidity differences.
In Fig. 3.12 the expected subprocess contributions are illustrated and it is shown that the
pure NLO subprocesses are a small fraction.
On the right side of Figs. 11.3 and 11.4 the ratios of the corresponding cross sections
to the MC predictions are shown. The statistical uncertainty from the measurement
and from the MC predictions are propagated assuming uncorrelated errors into the ra-
tio. The agreement of the MC predictions with data is very good. In most of the
cases the agreement is achieved even at the level of the statistical uncertainties. It can
be concluded as QCD powerfully describes the data in the kinematic region measured,
that there seems to be not much space left for new phenomena. The agreement in the
angular and rapidity related cross sections indicate that the slight bump registered in
the dijet mass cross section at around 400 GeV is completely caused by experimental effects.
11.1.4 Summary
In all measured cross sections an agreement between data and MC predictions is observed.
In some cases the agreement is at a few per cent level and covered by the statistical
uncertainty on data.
The NLO corrections are essential to understand the measured cross sections. This is
especially true in case of the cross sections as a function of azimuthal angle between
the leading jets and of the correlation in polar angle. However, it has been observed
that the predictions from Pythia give reliable distributions. The Pythia prediction
cannot reproduce the normalisation but delivers a good description for shape comparisons.
Therefore the widely spread use of Pythia to obtain all relevant corrections seems to be
justified.
MC@NLO which uses Herwig for the modelling of the parton shower shows good
agreement with data. But the predictions of Powheg using Herwig reveal large difference
compared to predictions in which the parton shower was modelled with Pythia. So far
no explanation for this has been found.
At a unprecedented center-of-mass energy of 7 TeV higher order processes become more
important and measurements may indicate deficiencies in the theoretical calculations and
simulation. The measurement on BB̄-hadrons from CMS and the deviations seen in the
lowest bin of ∆φ indicate such deficiencies.
The measured dijet mass spectrum of bb̄ dijets extends to around 1.5 TeV (cf. Fig. 3.5). The
presented cross sections which make use of the SV0 b-tagging algorithm only cover partly
this available statistics. Solely the ∆φ cross section contains all these events. However
from the agreement found between NLO calculations and data, it can be concluded that
no evidence for new phenomena has been found. This will be quantified more precisely in
Chapter 12.
11.2 Ratio measurement between bb̄ dijets and
inclusive dijets
This section presents the inclusive dijet cross section and the ratio measurement between
bb̄ and inclusive dijets. Both measurements as a function of dijet mass are presented
192
11.2 Ratio measurement between bb̄ dijets and inclusive dijets
in Fig. 11.5. The top plots in this figure on both sides show the measurement overlaid
with predictions from Powheg and Pythia. The plots in the lower part on both sides
present the ratio between data and the corresponding MC prediction. The statistical
uncertainty from the measurement in data and from the MC predictions are propagated
assuming uncorrelated errors. The Pythia prediction for the inclusive cross section has
small statistical errors, too small to visualise them on the ratio plot. The prediction from
Pythia is scaled by 0.65 to the integrated cross section in data for the inclusive cross
section on the left side.
The inclusive dijet cross section is a steeply falling function of the dijet mass. The cross
section spans over almost four orders of magnitude. The measurement is restricted to
the phase space region explored in the bb̄ measurement. The dijet mass spectrum in data
extends to more than 2 TeV. The jet energy scale uncertainty dominates the systematic
uncertainty on the measurement. This uncertainty accounts to 15% on average. The
prediction from Powheg overestimates the cross section in the lower and medium dijet
mass region by 20%. Within the systematic theoretical uncertainty the Powheg prediction
and data are in agreement. The scaling factor of Pythia is even further away from unity
than in the case of the bb̄ cross section. It is eye-catching from the comparison of Fig. 11.1
(right bottom) and Fig. 11.5 (right bottom), that the Pythia prediction of the bb̄ cross
section is better than the prediction of the cross section of inclusive jets. Contribution
to this fact is, that for bb̄ production in most of the parton shower generators the flavour
excitation matrix element is included in the hard process. So part of the additional
processes contributing at NLO can be accounted for in Pythia. The deviation in Pythia
for inclusive jets ranges from a deficit of 5% to an overshoot of 30% at high dijet masses.
The ratio measurement on the right side of Fig. 11.5 shows a fraction of bb̄ dijets of about
0.3% to 1% decreasing with increasing dijet mass. The systematic uncertainty on the
measurement is dominated by b-tagging related uncertainties and amounts to 40% to
60%. The prediction from Pythia is not scaled. In the measured phase space the major
contribution to the inclusive dijet cross section comes from gg, gq initial states which
dominate until far above 1 TeV whereas the bb̄ production is dominated by the gluon-fusion
process. With increasing dijet mass the fraction of light-quark annihilation (qq̄) processes
leading to bb̄ final states increases by three (cf. Fig. 3.11(b)). Simultaneously the fraction
of general quark initial states (qq̄, qq, q̄q̄) in which all possible channels contribute becomes
more important in the inclusive case. Therefore the drop of the fraction of bb̄ pairs is
explained by the influence of the parton densities.
The ratios between data and MC predictions for the fraction of bb̄ dijets show that both
MC simulations underestimate this fraction. The Powheg prediction is on average 50%
below data in the lower and medium dijet mass region. Above 450 GeV the prediction
and data seem to converge. The deviation at around 400 GeV seen before in the bb̄ cross
section has a strong influence in the ratio measurement. It causes a deviation between
once and twice the uncertainty in both MC predictions. This exceptional behaviour is
already present in the raw data spectra for each trigger. The fraction of bb̄ dijets predicted
by Pythia seems to be on average 20% to 30% underestimated.
Such a ratio measurement is another approach sensitive to deviations between data and
QCD. Any model of new phenomena bears the possibility to be sensitive to the different
quark generations and to favour one over the other in its decay modes. The relative fraction
between inclusive jets and a chosen type of jets is a excellent contact point. However, in
the measured phase space the QCD predictions are able to describe data.
From an experimental point of view the advantage of a ratio measurement is that it
193
11 Results of the cross section measurements
106 1
s=7TeV, ∫ Ldt=34 pb-1 Data + stat. error s=7TeV, ∫ Ldt=34 pb-1 Data + stat. error
105 Sys. uncertainty Anti-k t R=0.4 EM+JES Sys. uncertainty
4 POWHEG 0.110 |y|<2.1, p >40GeV
POWHEG
T
Pythia (x 0.65) Pythia
103
0.01
2 Anti-k10 t
 R=0.4 EM+JES
|y|<2.1, p >40GeV
T
1.24
1.80 100 200 300 400 500 600 700 0 100 200 300 400 500 600 7001.2 Stat. error 3 Stat. error
1.61 2 bb dijet mass [GeV]
01..48 1.51
01..62
10 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700
1.5 Shaded areas: theo. sys. unc.
3 Shaded areas: theo. sys. unc.
0.8 Shaded areas: sys. theo. unc.
0.6 statistical error only
dijet mass [GeV] statistical error only dijet mass [GeV]
21
0.41
0.2 1
0 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700
dijet mass [GeV] dijet mass [GeV]
Figure 11.5: The inclusive dijet cross section as a function of dijet mass with pT ¡ 40 GeV
and |y|   2.1 is presented on the left hand side. On the right hand side the ratio between the
dijet cross sections of b-jets and inclusive jets with pT ¡ 40 GeV and |y|   2.1 is presented. The
data are compared to MC predictions from Powheg and Pythia. Only the central values of the
theoretical predictions are drawn. The leading-order Pythia prediction is scaled to the measured
integrated cross section in case of the inclusive dijet cross section. The lower parts of the plots
present the corresponding ratios between data and the MC simulations. The shaded areas around
the MC prediction indicate the systematic theoretical uncertainty (except for Pythia). The
statistical error is calculated from the uncorrelated statistical errors from MC and data.
194
DDaattaa// DDaattaa//
Pythia dσ /dM [pb GeV
-1]
POWHEG incl
DDaattaa// DDaattaa// ddσσ //ddMM  //  ddσσiinnccll  //ddMMPythia POWHEG bbbb  
11.2 Ratio measurement between bb̄ dijets and inclusive dijets
reduces theoretical and experimental systematic uncertainties. This is exploited in case of
the theoretical uncertainties. But the reduction in case of data is marginal. This comes
from the overwhelming contribution of b-tagging related uncertainties which are present
exclusively on the bb̄ measurement. As long as these dominate, the effect of the reduction
and cancellation of uncertainties like luminosity and jet energy scale uncertainty on the
total uncertainty is only at a few per cent.
195

12 Search for resonances in the cross
section
The measurement of the dijet cross section of b-jets as a function of dijet mass has shown
that the production of pairs at high-energies from two incoming hadrons is well described
in terms of QCD in the Standard Model. The dijet mass spectrum predicted from QCD
falls smoothly with increasing dijet mass. Many extensions beyond the Standard Model
predict new massive particle states, which are localised at a given mass and could be
observed as resonances in the dijet mass spectrum. In addition a new force manifesting
itself at very high centre-of-mass energies could enhance the event rate.
Models in which quarks are composite particles [20] predict excited quarks states which
decay into dijets. Models which embed the QCD into a large gauge group and higher
symmetries often contain yet unobserved heavier gauge bosons [143, 16, 17]. Also models
of extra dimensions [21] can manifest itself in an excess of dijet events at an invariant
mass.
To test the measured mass spectrum, a statistical method sensitive on the presence or
absence of a resonance in the mass spectrum is used. In this method the region above
760 GeV which had to be ignored in the cross section measurement is also exploited.
Recent ATLAS results on the search for resonances in the inclusive dijet spectrum have not
found an evidence for a resonance signal [144]. Without the observation of a signal from
new physics, an exclusion limit on their production can be obtained. Recently ATLAS
excluded most of the important models with new physics below about 2 TeV [145].
In the following this statistical method and its application on the bb̄ cross section measure-
ment is explained. Changes to the event selection and the trigger efficiency as a function
of the dijet mass for the search are briefly presented. Finally, a model independent limit
on the event yield of a new resonance is determined from data and put into context of
a hypothetical signal of a new resonance predicted from a model beyond the Standard
Model.
12.1 Statistical method
The goal of the statistical method, called BumpHunter [146], is to find the most significant
excess of events above background (bkg) using a window of varying width. Such localised
effects are colloquially called bumps. The advantage of this method, is that it respects
the trial factors (also called look elsewhere effect). In case of any hypothesis test where
the data is tested for its consistency to a hypothesis, the trial factors account for the
possibility that any bin (= trial) can contain a discovery by mere fluctuations, reflecting
the fact that the resonance has an unknown mass. A brief description of BumpHunter
is given and its application to the bb̄ dijet mass spectrum is explained.
197
12 Search for resonances in the cross section
12.1.1 The BUMPHUNTER method
The BumpHunter algorithm is in detail explained in Ref. [146] in the context of other
hypothesis tests. The brief description here focuses on the aspects important for this
investigation. BumpHunter is a hypothesis test, which quantifies the consistency of
a hypothesis with an observation. A discovery, which is generally a disqualification of
a null hypothesis, is usually claimed in case of the inconsistency to a background hy-
pothesis H0 (=null hypothesis) like the Standard Model. But the statistical method
only establishes the inconsistency of data to the hypothesis H0, it does not address the
amount of signal residing in the bump. So in general any hypothesis test follows three steps:
1. The data D are compared to a hypothesis H0, resulting in a quantity t0, called
test statistic, which describes the differences between both. By convention a bad
agreement is given by a large t0.
2. Pseudo-data are generated allowing for bin-wise Poisson fluctuations, following the
H0 hypothesis. For each pseudo-data spectrum the test statistic t is calculated which
quantifies the difference between the pseudo-data and the hypothesis H0.
3. Then the probability is calculated that the test statistic t is equal or greater than the
test statistic t0 from data assuming the hypothesis H0. This probability is referred
to as p-value:
p-value  P pt ¥ t0|H0q. (12.1)
This p-value is not a statement about how likely H0 is, but it is identical to the
probability to mistakenly rule out the background hypothesis (Type-I error).
Besides the observed data distribution D and the background hypothesis H0, the Bum-
pHunter method requires a minimal set of information to calculate the test statistic
t. The minimum and maximum number of consecutive bins is required in which the
consistency of data is checked against the background hypothesis. These numbers define
the range of widths allowed for the search window. The mass region measured in data is
determined on which BumpHunter evaluates the test statistic. Quality criteria on an
excess found in data may be imposed, for example that an excess has to be surrounded by
non-discrepant regions. With these information the BumpHunter algorithm calculates
the test statistic and the p-value with the following steps:
 Iterate over the mass range by shifting the configured search window and varying
the search window between the minimum and maximum width. For each window
width and for each mass, the data or pseudo-data events d are compared with the
background events b. For each window i the p-valuei following this prescription is
calculated:
&$
% 1 if di ¤ bip-valuei (12.2)Γp q  °8 bnd i bii, bi nd e otherwisei di!
(12.3)
198
12.1 Statistical method
 Among all calculated p-values find the smallest value and set the test statistic of the
BumpHunter method according to:
t   log p-valuemin, (12.4)
where the p-valuemin is the smallest of all p-values found in the previous step. The
mass region with the smallest p-value is the window with the smallest probability,
that the deviation from the background is caused by a statistical fluctuation.
The output of BumpHunter consists of the interval with the most interesting prop-
?erties (smallest p-value), the p-value according to Eq. 12.1 and the significance σp 
2  Erf1p1 2  p-valueq of this p-value which are corrected for the trial factor.1 A nega-
tive significance corresponds to a p-value ¡ 0.5 and significant deviations are characterised
by small p-values (  0.001), corresponding to significances above 3.
Systematic uncertainties on the background may shift the background and decrease the
significance of any bump. To account for these uncertainties BumpHunter performs
pseudo-experiments in which the background is allowed to shift according to a Gaussian
distribution with width of the uncertainty. In case of several uncertainties, they need
to be merged into one uncertainty by adding them in quadrature. The BumpHunter
algorithm searches for the maximum of the product of two probabilities, namely from
the most interesting bump and from the Gaussian probability for observing the shifted
background.
12.1.2 Application to bb̄ dijet mass spectrum
The investigation on significant deviations from the Standard Model (=background hy-
pothesis) is performed on the dijet mass spectrum of b-jets with a minimum window size
of one mass bin. In general the maximum window size corresponds to half the mass range
spanned by the data. No quality requirement on the surrounding region of an observed
excess is set.
The background normalisation and shape is extracted from the observed spectrum in data
by fitting a smooth function [19]
fpxq  p p1 xqp1xp2 lnpxqp30 , (12.5)
?
where x  M{ s and pt0,1,2,3u are free parameters. The parameters are constrained to
describe the behaviour of the dijet cross section. The function falls monotonically and
describes the behaviours in the limit fp0q   8. Although this function is not inspired
by theory, it has proven to describe the dijet mass spectrum well [144].
To properly use the BumpHunter method, data and background distributions are required
to follow the Poisson statistics. This means that the spectrum with prescale-corrected
events is not applicable to this hypothesis test. Therefore, the prescale-corrected spectrum
is only used to extract the background hypothesis H0 with the above mentioned fit. The
result from the fit is subsequently corrected back to raw background events by scaling
Ndata
bin-wise with an effective prescale pseff  uncorrectedNdata obtained from data. The asymmetriccorrected
1The function Erf1 is the inverse of the err³or function. The error function maps the p-value to the8
significance σp and is given by: p-value  ?1 ex
2{2
 dx. The Erf
1 function gets the p-value as
σp 2 π
input and returns the corresponding σp.
199
12 Search for resonances in the cross section
 ∆N
statistical uncertainty N high∆N on the raw data events is taken from the 68% confidence-low
level on Poisson-distributed events Ndatauncorrected [3, 147]:
 

∆N Ndata 1 1 68.27% datalow uncorrected  F ; 2 N2 χ2 2 uncorre
cted ,
1 1  68.27%∆Nhigh F 2 1 ; 2  pNdata data
2 χ 2 uncorrected
  1q Nuncorrected, (12.6)
where F1 is the quantile of the χ2 distribution or the inverse of the cumulative distribution
χ2
of Poisson distributed events.2 The statistical uncertainty on the prescale-corrected events
is calculated from error propagation with trigger prescale ps:¸ ¸ ¸
Variance Ni  psi  VariancepNi  psiq  ps2i VariancepNiq, (12.7)
trigger i trigger i trigger i
where the Variance(Ni) is given by the error of Poisson distributed events Ni evaluated
at 68% confidence-level (cf. Eq. 12.6). The statistical error on the effective prescales is
Ndata
evaluated from the error propagation of the statistical uncertainties on uncorrected
Ndata
.
corrected
To demonstrate the BumpHunter method, it is shown that an artificially injected
signal, whose cross section is smaller than the QCD cross section, is immediately tracked by
the BumpHunter method. An arbitrary background hypothesis is chosen with parameters
p 41  1  10 , p2  10, p3  6.3 and p4  0.1. This background hypothesis is fluctuated
bin-by-bin according to a Poisson distribution to simulate a data observation. Two signals
following a Gaussian distribution are injected into this simulated data with a cross section
of 0.2 per mill of the total cross section:
 With a mean at 480 GeV and a width of 20 GeV.
 With a mean of 1000 GeV and a width of 100 GeV.
Examples of the BumpHunter results for the solely Poisson fluctuated data and for
the two data distributions with injected signals are presented in Fig. 12.1(left). In the
spectrum without an injected signal the determined most interesting interval should be
equally distributed over the dijet mass range and the p-values fluctuating around the
value 0.5, which is equivalent to a significance of zero. On the top of the right hand
side of Fig. 12.1, the mean value of the p-value distribution as a function of dijet mass
after 1000 pseudo-experiments is presented. In the dijet mass spectra with injected signal
Fig. 12.1(middle and bottom), the p-values in the pseudo-experiments are not uniformly
distributed. They are all below 0.1 ( σp  1.3) and the most interesting interval is
Gaussian distributed around the injected signal mass.
12.2 Search for an excess in the dijet mass spectrum
New resonances in the dijet mass spectrum of b-jets are searched for with the help of
BumpHunter. This section presents the adjustments and extensions to the former cross
2The quantile xa is the value of the random variable x at which the cumulative distrib³ution is equal to a.a
The cumulative distribution function F paq is the probability that x ¤ a: F paq  8 fpxqdx, where
fpxq is the probability density function. Taken from Ref. [3].
200
12.2 Search for an excess in the dijet mass spectrum
107 0.7
106 Observed Statistic: 3.98 Pseudo-data Pseudo-experiments
105 0.65
104 Background No Signal
0.6
103
Most interesting interval: Significance σp = 0
102
260 GeV - 370 GeV 0.55
10
1
0.5
10-1
10-20 500 1000 1500 2000 2500 0.45
2
0.4
0
0.35
0 500 1000 1500 2000 2500 0 200 400 600 800 1000 1200 1400
bb dijet mass bb dijet mass [GeV]
1
106
Observed Statistic: 6.41 Pseudo-data+Signal Pseudo-experiments
105 10
Background
104
Injected Signal Signal at 1000 GeV
103
-1
2 Most interesting interval: 1010
950 GeV - 1310 GeV
10
1
1
10-1
10-2 10
-2
0 500 1000 1500 2000 2500
2
0
-3 -1
0 500 1000 1500 2000 2500 10 0 200 400 600 800 1000 1200 14001600 1800 2000 10
bb dijet mass bb dijet mass [GeV]
1
106
Observed Statistic: 8.11 Pseudo-data+Signal Pseudo-experiments
105 10
Background
104
Injected Signal Signal at 480 GeV
103
10-1
102
Most interesting interval:
10
440 GeV - 670 GeV
1
1
10-1
-2
10-2 100 500 1000 1500 2000 2500
2
0
-3 -1
0 500 1000 1500 2000 2500 10 0 200 400 600 800 1000 1200 14001600 1800 2000 10
bb dijet mass bb dijet mass [GeV]
Figure 12.1: The BumpHunter results for pseudo-data generated by Poisson fluctuations with
no injected signal (top), with injected signal with a mean at 1000 GeV (middle) and with injected
signal with a mean at 480 GeV (bottom). On the left side a typical examples of a BumpHunter
result is presented. In the top right corner the mean p-value as a function of dijet mass is
presented and in the middle and the bottom on the right side the distributions of the p-values as
a function the most interesting interval are presented.
201
(Data-Bkg)/σBkg EEvveennttss (Data-Bkg)/σBkg EEvveennttss (Data-Bkg)/σBkg EEvveennttss
p-value of interest p-value of interest 〈 p-value of interest 〉
Number of pseudo-experiments Number of pseudo-experiments
12 Search for resonances in the cross section
section measurement to increase the sensitivity to new phenomena.
12.2.1 Event selection and trigger
For the searches the BumpHunter method is given the uncorrected mass spectrum without
the application of b-tagging related correction factors as well as the bin-by-bin unfolding.
This is important as these corrections are capable of concealing new phenomena because
they are derived under assumption of QCD only. In addition to the mass spectrum, which
has been used to derive the dijet cross section, two other selections have been developed to
increase the sensitivity to s-channel processes. A full mass spectrum is derived using all jet
triggers but restricting the rapidity correlation to |∆y|   1 between the two leading jets.
This diminishes the dominating contribution of bb̄ pairs from gluon fusion in the t-channel
and the selection focuses on the region in which s-channel processes such as decays of heavy
resonances are important. This selection criteria is motivated by the rapidity correlation
of the outgoing partons in the gluon-fusion process shown in Fig. 3.3(b). Furthermore, to
study the higher mass regions with a homogeneous selection, an additional event selection
based on the unprescaled trigger with lowest threshold is validated. The trigger efficiency
for the L1 J95 trigger is determined using the bootstrap method (cf. Section 7.3) as a
function of inclusive dijet mass for the event selection presented in Section 7.4 and using
the requirement of |∆y|   1. The trigger plateau for L1 J95 is reached at a dijet mass of
440 GeV as can be seen in Fig. 12.2. To account for possible biases between inclusive and
b-jets due to different rapidity correlations a safety margin is chosen. The measurement of
b-tagged jets is performed for dijet masses above 510 GeV. In summary three searches are
1.2
1
0.8
Inclusive jets
0.6 Bootstrap method: L1_J55
L1_J95
0.4
0.2
0 200 400 600 800 1000
dijet mass [GeV]
Figure 12.2: Trigger efficiency of the L1 J95 as a function of inclusive dijet mass determined
with the bootstrap method and L1 J55. The events are required to obey |∆y|   1.
performed:
 On the full mass spectrum used in the cross section measurement ( 250000 events).
 On the full mass spectrum with an acceptance cut on the rapidity correlation |∆y|   1
( 75000 events).
 On the mass spectrum obtained with the unprescaled trigger L1 J95 and an accep-
tance cut on the rapidity correlation |∆y|   1 ( 210 events).
202
∈trig
12.2 Search for an excess in the dijet mass spectrum
12.2.2 Results on the search for resonances
The first step is to extract the background hypothesis with the dijet mass function given
in Eq. 12.5. All three spectra with the corresponding fit are presented in Fig. 12.3. The
fitted parameter values are presented in Table L.1. The data are well described by the
corresponding fit with χ2{DoF  1 and with p-values greater than 0.35.3
To evaluate the uncertainty on the fit result in each bin, pseudo-experiments are performed
in which the data points are fluctuated according to their statistical uncertainty and this
new spectrum is re-fitted. The root mean square of all fit results in each bin is determined
and is identified with the fit uncertainty. Compared to the statistical uncertainty from the
prescale correction, this uncertainty is small and neglected in the following.
The distributions of the BumpHunter statistic can be seen on the left hand side in
Fig. 12.4. Besides the broad distribution of the pseudo-experiments, the BumpHunter
statistic for data is indicated by the blue arrow. From these distributions the p-value for
each event selection can be obtained by using Eq. 12.1. In the full spectrum (top) without
any restrictions the significance is sizable in contrast to the full spectrum with the rapidity
difference cut (middle) and the mass spectrum measured with L1 J95 (bottom) in which
the BumpHunter statistic of data is well below the median of the pseudo-data. The
resulting p-values and the corresponding significances are summarised in Table 12.1. The
p-value of the full spectrum is 0.02, whereas the other selections have p-values above 0.4
and the distributions are in good agreement with the background hypothesis. On the right
hand side in Fig. 12.4 the data distributions and the most interesting intervals in data
are indicated by the vertical lines. None of the interesting intervals between those three
selections are identical, supporting the conclusion that no significant deviation from QCD
is observed. The plots on the bottom of Fig. 12.4 show the difference between observed
and expected events normalised to the uncertainty on the background expectation.
Selection Interval p-value Significance
[GeV]
Full spectrum 1310- 0.02 2.02
2330
Full spectrum with 310- 0.44 0.14
|∆y|   1 370
Spectrum with 510- 0.53 -0.06
L1 J95 and 590
|∆y|   1
Table 12.1: Summary of the BumpHunter results for different fitting procedures.
From this method, it is concluded that no evidence is found for new phenomena in the
dijet mass spectrums with different sensitivity to s-channel processes. The deviations
seen in the bb̄ dijet mass spectrum and in the ratio measurement around 400 GeV are
not significant. Due to time constrains the effects of the systematic uncertainties are not
evaluated. However, qualitatively speaking their inclusion will decrease the significances
even more. The deviations without the uncertainties are already not significant and they
3DoF stands for the number of degrees of freedom.
203
12 Search for resonances in the cross section
106 106
5 χ2/DoF = 10/12 5 χ2/DoF = 8.7/1010 10
s=7 TeV s=7 TeV
104 ∫Ldt=34 pb-1 104 ∫Ldt=34 pb-1
3 Data 3 Data10 10
Background fit Background fit
102 102
10 10
1 1
10-1 10-1
10-2 10-2
10-3 -30 500 1000 1500 2000 2500 10 0 500 1000 1500 2000 2500
bb dijet mass [GeV] bb dijet mass [GeV]
(a) Full spectrum (b) Full spectrum with |∆y|   1
102
χ2/DoF = 5.5/5
s=7 TeV
∫Ldt=34 pb-1
Data
10 Background fit
1
10-10 500 1000 1500 2000 2500
bb dijet mass [GeV]
(c) Mass spectrum from L1 J95
Figure 12.3: Fits on observed mass spectrum in data to obtain the background hypotheses on
(a) the full spectrum, (b) the full spectrum with |∆y|   1 and (c) the mass spectrum measured
with L1 J95.
will not be afterwards.
204
Events (prescale corrected)
Events (prescale corrected)
Events (prescale corrected)
12.2 Search for an excess in the dijet mass spectrum
500
s=7 TeV, ∫ Ldt=34 pb-1 450 s=7 TeVObserved Statistic: 5.84
Ldt=34 pb-1
Pseudo-experiments 400 ∫
104 DataValue in Data 350 Background
p-value: 0.02 300 Bkg uncertainty
250
103
200
150 Most interesting interval:
102 100 1310 GeV - 2330 GeV
50
0
0 500 1000 1500 2000 2500
10 2
1
0
1 -1
0 2 4 6 8 10 12 14 0 500 1000 1500 2000 2500
BumpHunter statistic bb dijet mass
200
104 s=7 TeV, ∫ Ldt=34 pb-1 180 s=7 TeVObserved Statistic: 2.83
∫Ldt=34 pb-1Pseudo-experiments 160 Data
Value in Data 140 Background
3 p-value: 0.44 120 Bkg uncertainty10
100
80
60 Most interesting interval:
102
40 310 GeV - 370 GeV
20
0
10 0 500 1000 1500 2000 2500
2
1
0
1 -1
0 2 4 6 8 10 12 14 16 0 500 1000 1500 2000 2500
BumpHunter statistic bb dijet mass
104 s=7 TeV, ∫ Ldt=34 pb-1 140 Observed Statistic: 2.19 s=7 TeV
Pseudo-experiments 120 ∫Ldt=34 pb-1
Value in Data Data
100
103 p-value: 0.53 Background
80
60
102 Most interesting interval:40
510 GeV - 590 GeV
20
10 0 500 1000 1500 2000 2500
2 bb dijet mass [GeV]
1
0
1 -1
0 2 4 6 8 10 12 0 500 1000 1500 2000 2500
BumpHunter statistic bb dijet mass
Figure 12.4: From top to bottom: Full spectrum, full spectrum with |∆y|   1 and mass spectrum
from L1 J95 and with |∆y|   1. On the left side the resulting BumpHunter statistics from
the pseudo-experiments and the BumpHunter statistic observed in data (arrow) are presented.
On the right side the mass spectra with most interesting interval are presented. The plots on
the bottom show the difference between data and background hypothesis normalised to the total
uncertainty on the background.
205
Pseudo-experiments Pseudo-experiments Pseudo-experiments
(Data-Bkg)/σBkg EEvveennttss (Data-Bkg)/σBkg EEvveennttss (Data-Bkg)/σBkg EEvveennttss
12 Search for resonances in the cross section
12.3 Model independent limit setting
There is no evidence for a resonance signal in the dijet mass spectrum of b-jets. However,
from the observed data spectrum in context of the Standard Model (= background hy-
pothesis) it is possible to deduce a limit on the maximum number (= maximum cross
section) of events reconstructed from a new resonance which are excluded by the data.
Using the assumption that any new resonance is likely to be detected as a Gaussian
signal from the calorimeters, a limit can be calculated which is independent from any
model. Such a limit could be used to estimate the current sensitivity of the measurement
to any model. A recipe for this application is briefly described and finally the model
for a heavy gauge boson, called Z 1, assuming the same couplings to leptons and quarks
as that of the Standard Model Z is tested with the help of the model-independent limit [148].
12.3.1 Bayesian limit on generic Gaussian signals
To calculate a limit on a resonance signal with Gaussian shape, Bayesian methods are
applied. Further details on Bayesian limit setting can be found in Ref. [149]. The likelihood
function Lm dependent on the signal mass m is given by
¹
p | q  pbi   sm,iq
di
L d b, s epbi sm,iqm m , (12.8)
d
i i
!
where the product runs over all bins i. The likelihood function describes the probability
to observe d data events with the condition of b background events and sm signal events
from a massive resonance with mass m. This likelihood function is maximised with respect
to the data events. Assuming a flat prior for all possible number of signal events, the
95% confidence-level (CL) to exclude a signal with strength sm or bigger is calculated by
integrating the likelihood over the prior. The 95% CL upper limit is parametrised by the
mass of the resonance and this limit is usually dependent on the signal width. This limit
calculates the maximum number of events of a given resonance which are at 95% confidence-
level excluded. This is then usually expressed in smpexcludedq{L  σ BR  Acc, where
BR stands for the branching ratio of the resonance into bb̄. In case of a measurement which
is subject to a selection efficiency as the b-tagging algorithm, the result of the Bayesian
limit is identical to smpexcludedq{L  σ BR  Acc efficiency.
A hypothetical resonance which decays into all flavours of quark-antiquark pairs can
have a non-zero branching ratio into top-antitop pairs if mZ1 ¡ 2mt. The bb̄ dijets from
these decays are also likely to be identified by the b-tagging algorithm. Depending on
the transverse momenta of the top- and antitop-quark, which increase with increasing Z 1
mass, the decay products become more collimated. As long as they are well separated
(mZ1 Á 2mt), the invariant mass distribution of the bb̄ dijets does not reflect the invariant
mass of the resonance due to the decay of the top. This solely leads to a broad distribution
which would contribute to the Gaussian signal mainly in the tails. If the resonance mass
is in the region of 1 TeV, merged objects become more likely and the invariant mass shifts
towards the resonance mass.
Besides these irreducible top-antitop events, signal events from light-flavour jets (u,
d, s) and c-jets can be mis-tagged. A simple calculation shows that the fraction of
mis-tagged events in the signal is negligible: Assuming SV0 b-tagging performance and
a signal with a cross section of 10 pb which decays democratically into all types of
206
12.3 Model independent limit setting
quarks (msig ¡ 350 GeV), the fraction of events reconstructed from this signal consist of:
BR   BR 
σ  L  light mistag c c 1sig ATLAS   ! 1. It should be noted that their effect would onlyBRbb̄ bb̄ 17
be beneficial for the limit calculation in the first place, so disregarding them makes the
calculation conservative.
In summary, in the core region of the Gaussian signal events from top-antitop decays are
negligible and the fraction of signal events which are mis-tagged is small. So the limit
can be simply expressed in terms of σ BR  Acc b-tagging, where the b-tagging term
stands solely for the b-tagging efficiency.
The limit calculation uses the measured prescale-corrected dijet mass spectrum with the
rapidity correlation selection cut |∆y|   1. The background hypothesis is again extracted
from a fit with Eq. 12.5 to data. The systematic uncertainties affecting the Bayesian limit
are the statistical uncertainty on the data points arising from the prescale correction, the
uncertainty on the luminosity, the uncertainty on the signal templates from the jet energy
scale and the jet energy resolution.
Each data point is shifted according to the statistical uncertainty and the background
fit is redone. From the sample of fit results the root mean square in each bin is taken
as systematic uncertainty. The systematic uncertainty on the luminosity is 3.4%. The
systematic uncertainties related to the jet reconstruction affect the signal templates only.
The signal shape for each signal mass is varied according to the jet energy scale uncertainty
and the uncertainty on the jet energy resolution. These uncertainties are evaluated in the
limit setting by varying all the sources according to a Gaussian probability distribution
and convoluting these with the likelihood function.
The signal templates for masses M between the 200 GeV and 1300 GeV are generated
with six different signal widths σpMq. The signal widths are expressed in multiples of the
detector resolution. The signal widths chosen are: σdetector, 2σdetector, 2.5σdetector, 3σdetector,
3.5σdetector and 5σdetector. The detector resolution has been calculated with the help of
Pythia QCD simulation samples with a full-simulation of the ATLAS detector. The
resolution as a function of dijet mass is fitted and this parametrisation is used to determine
the signal width as function of multiple detector resolutions. The resulting parametrisation
can be found in Appendix Fig. L.1. For signal widths of the detector resolution the ratio
σpMq{M ranges from 5% to 15% for high and low resonances mass respectively.
To estimate the shift of the signal template due to the jet energy scale uncertainty, it is
assumed that the emerging jets from the decay are balanced back-to-back in transverse
momentum (pT,1  pT,2 M{2) and the uncertainty on the transverse momentum is the
maximum jet energy scale uncertainty determined in the rapidity region |y|   2.1. The
resulting shift of the core region of the Gaussian signal is between 3.5% and 4.8%. The
variation from the uncertainty on the jet energy resolution is estimated to be 15% for all
signal masses. The uncertainty from the jet energy resolution causes the signal to become
narrower or broader. An example of a resulting signal template with a resonance mass of
350 GeV and a signal width of twice the detector resolution and its variations is presented
in Fig. 12.5(a). The resulting observed limit in data from these signal templates as a
function of the invariant dijet mass for six different signal widths is shown in Fig. 12.5(b).
The expected limit and the 68% uncertainty band for a signal template with a signal width
of the detector resolution is calculated from the background distribution using statistical
fluctuations. The area above each curve is excluded from data. The curves are falling
with increasing dijet mass. In general, it is expected that a signal template with a broad
signal width has a worse exclusion limit than a signal template with a more narrow signal
width. Consequently, the curves should be ordered from top to bottom with decreasing
207
12 Search for resonances in the cross section
signal width. However, fluctuations in the same direction in data, which extend over
more than one bin, can change this. If two or more bins show a deficit, then the limit
on a signal with broad signal width is improved. As can be seen in Fig. E.3(b) between
200 GeV and 500 GeV there a neighbouring bins which fluctuate in the same direction
and their appearance can be tracked in the limit curves as well. The expected limit has
been calculated with a small number of pseudo-experiments due to time constraints. This
makes the uncertainty band less smooth and lets the error band increase in the last bin
due to this small statistics.
These limits can be used for any new physics model with a new massive particle decaying
1 103
s=7 TeV,
Signal mass at 350 GeV ∫
 Ldt=34 pb-1
0.9
Gaussian Signal: σ(M)/M:
σ(M)/M = 2σ
detector
0.8 nominal
= 1.0σdetector
+JES 102 = 2.0σdetector
0.7 -JES = 2.5σdetector
+Resolution = 3.0σdetector
0.6 -Resolution = 3.5σdetector
10 = 5.0σdetector
0.5
Expected Limit (1σdetector)
0.4
0.3 1
0.2
0.1
10-1
0
0 100 200 300 400 500 600 700 800 200 300 400 500 600 700 800 900 1000
signal mass [GeV] mass [GeV]
(a) (b)
Figure 12.5: (a) Example of assumed signal shape at an resonance mass of 350 GeV and
a width of twice the detector resolution with the variations in the shape from the systematic
uncertainties jet energy scale (JES) and jet energy resolution. (b) The 95% CL upper limits
on σ BRAcc b-tagging observed in data for simple Gaussian resonances decaying into bb̄
dijets as a function of the invariant dijet mass. The expected limit (dashed line) and the 68%
uncertainty band are computed using statistical uncertainties alone.
into bb̄ dijets. The signal events and corresponding reconstructed jets from a new resonance
have to be selected according to the event selections applied to obtain the limit. The dijet
mass spectrum for these events need to obtained. The dijet mass distribution has to be
convoluted with the detector resolution and resulting tails have to be removed because a
Gaussian shape has been assumed. From the resulting Gaussian core of the resonance the ac-
ceptance of the signal has to be calculated and for the core the b-tagging performance has to
be estimated. Then the theoretical value for σTheoryBRTheoryAccTheoryb-taggingTheory
can be determined and conservatively compared to the observed limit in Fig. 12.5(b) by
choosing the limit curve with corresponding signal width by rounding up and the nearest
mass point from rounding down. This procedure is used in the following section to obtain
the theoretical curve for a heavy gauge boson decaying into bb̄.
208
arbitrary units
σσ  ××  BBRR  ××  AAcccc  ××  bb--ttaaggggiinngg  [[ppbb]]
12.3 Model independent limit setting
12.3.2 Limit on new heavy gauge boson Z 1
The model-independent limit which was obtained in the previous section is compared to a
signal from a Z 1 decay. This hypothetical gauge boson refers to a new massive copy of the
well-known Z boson in the context of the Standard Model. MC events containing Z 1’s
are generated with Pythia without the full-detector simulation under the assumption of
identical couplings to leptons and quarks as the Z bos	on. The resonance width of the Z 1
M
therefore increases linearly with its mass: Γ  Z1Z1 ΓZ .MZ
Firstly, a range of Z 1 masses is generated with σTheory  BRTheory and the events are
selected in accordance to the data in the observed limit. For all masses the generated
mass, the dijet mass of anti-kt R  0.4 jets on particle level and on calorimeter level are
obtained. The dijet mass at calorimeter level reflects the energy of particles visible to
the calorimeters. In Fig. 12.6(a) all three masses for a Z 1 at 420 GeV are presented. The
generated mass with its small width describes a Breit-Wigner function. The reconstructed
dijet masses of jets with resolution parameter R  0.4 at particle level already measure a
smaller mass due to particle losses from the hadronisation as well as a more distinct tail
for smaller masses. The exclusion of neutrinos and muons which are not part of the visible
energy at calorimeter level make these effects even worse. The next step is to convolute the
reconstructed dijet mass with the detector resolution using pseudo-experiments in which
each jet is smeared according to the resolution presented in Fig. 8.23(a). As can be seen
in Fig. 12.6(b) for a Z 1 signal at 420 GeV the detector resolution shifts the asymmetric
distribution to smaller masses and makes the signal symmetric. In the core region the
resonance looks like a Gaussian distribution. The mass window in which the signal is
Gaussian is extracted and is used as an additional selection cut on the signal. The events
which pass this additional selection cut are used to calculate the acceptance AccTheory.
Because the jet calibration applied to data is determined from truth jets at calorimeter
level, it is a valid approximation to treat these smeared jets as pseudo-data.
To estimate the b-tagging performance, the full-simulated QCD Pythia events are used.
The b-tagging efficiency for the SV0 algorithm is obtained as a function of jet pT only
for b-jets originating from the hard scatter to suppress the b-jets from GSP which are
not contained in the signal sample. For the rapidity region 0.8   |y|   1.2 the b-tagging
efficiency is shown in Fig. 12.7(a) as a function of dijet mass. The efficiencies are fitted by
a Landau function because all efficiency curves favour this shape and the obtained χ2’s
are close to one. The b-tagging efficiencies are slowly decreasing with increasing rapidity.
All curves are generally rising in the lower pT region to a maximum between 0.5 to 0.7 at
around 200 GeV and decreasing with increasing pT to about 0.2 to 0.3 at around 800 GeV.
Each event in the mass window is weighted by the product of both efficiencies for each jet.
From the unweighted dijet mass spectrum and the efficiency-weighted spectrum, which are
shown for a Z 1 mass at 420 GeV in Fig. 12.7(b), the b-tagging efficiency Theory is obtained.
The effective b-tagging efficiency for the case of the Z 1 signal at 420 GeV as shown in
Fig. 12.7(b) is about 0.33.
The effective b-taggingTheory values for all generated dijet masses are presented in
Fig. 12.8 and summaries in Table L.2. The b-tagging efficiency as a function of signal mass
shows the same behaviour as the b-tagging efficiency as a function of pT, it rises to around
0.35 at a mass of 350 GeV and then decreases to values smaller than 0.18 at 1300 GeV.
This is due to the rising transverse momentum of the decay products.
The resulting theoretical values of σTheory BRTheory and AccTheory for all generated mass
points are presented in Appendix as Fig. L.2. The values of σTheory BRTheory starting
209
12 Search for resonances in the cross section
6000
10000
Pythia, s=7 TeV Pythia, s=7 TeV
5000
0.25 × Z' (420 GeV) Signal Z' (420 GeV)
8000
Reconstruction level with Anti-k  R=0.4: Fit to Gaussian coret
4000
Anti-k t R=0.4: calorimeter jets Mass window 150-500 GeV
6000 particle jets Pseudo data
calorimeter jets 3000 Gaussian fit
4000
2000
2000 1000
0 0
100 200 300 400 500 600 100 200 300 400 500 600
mass [GeV] dijet mass [GeV]
(a) (b)
Figure 12.6: (a) Pythia Z 1 signal at various levels: generated Z 1 mass at 420 GeV, after
applying the event and jet selection of anti-kt jets at particle level and at calorimeter level. (b)
Generating from the reconstructed Z 1 signal at calorimeter level pseudo-data which simulate the
detector resolution. The core region with Gaussian shape of this pseudo-data is extracted via a fit
and determines the mass window.
at around 100 pb decrease rapidly with increasing signal mass over more than 4 orders
magnitude until the highest signal mass of 1200 GeV. The acceptance falls with increasing
signal mass from 20% to 10%. This has several reasons. The production of Z 1 off the
resonance peak increases with increasing mass due to the sea quark PDF and the fraction of
events in the mass window, which defines the core region with a Gaussian shape, decreases
with increasing mass. A sample of Toy-MC predictions for three different Z 1 masses are
plotted with the observed data dijet mass spectrum in Fig. 12.9(a). With increasing
signal mass the signal widths and the shift between the generated and reconstructed mass
with detector resolution increase rapidly. For the smallest signal mass in Fig. 12.9(a)
the measurement observed more than 10000 events in the mass bin of interest and the
predicted number of events are 450.
With these numbers the theoretical curve of σTheoryBRTheoryAccTheoryb-taggingTheory
is obtained and compared to the observed limit in data. This is presented in Fig. 12.9(b).
The points of the Z 1 signals represent the reconstructed dijet mass, not the generated
resonance mass. In Table L.2 the generated and the corresponding reconstructed masses
are presented. Any exclusion region obtained has to be translated into generated resonance
mass. The Z 1 signal points are coloured corresponding to the signal width obtained in
the Toy-MC. For the Z 1 signal with smallest resonance mass, the signal width already is
more than twice the detector resolution. It can be seen that with the available data set
the Z 1 with identical quark couplings as the Z cannot be ruled out in any mass region. In
special cases in which the Z 1 coupling to leptons is suppressed or even zero, the sensitivity
of this observed limit may be increased. In the hypothetical case in which the branching
ratio into bb̄ of a new heavy gauge boson is 100%, the sensitivity is increased by a factor
of  100%{15.12%  6.6 [3]. The theoretical values of the Z 1 signal are shifted up by this
210
arbitrary units
arbitrary units
12.3 Model independent limit setting
1.2 6000
Pythia
Toy Monte-Carlo from Z' (420 GeV)
1 5000
Pythia, s=7 TeV
Fit
Anti-k t R=0.4:
0.8 4000 Pseudo data
Pseudo b-tagged data
0.6 3000
0.4 2000
0.8<|y|<1.2
0.2 1000
χ2/DoF = 33/35
0 0
0 100 200 300 400 500 600 700 800 100 200 300 400 500 600
p  [GeV]
T dijet mass [GeV]
(a) (b)
Figure 12.7: (a) From QCD Pythia simulation the b-tagging efficiency as a function of jet pT
in four different rapidity ranges is calculated using b-hadrons produced in the hard scatter. (b)
The b-tagging performance is simulated on pseudo-data to determine the b-tagging efficiency on
signal events and the resulting pseudo-b-tagged data is plotted against the pseudo-data.
factor in Fig. 12.9(b). In this case an exclusion limit for a heavy gauge boson with a mass
around 260 GeV can be found. This exclusion region obtained from Fig. 12.9(b) is already
translated into terms of Z 1 mass using Table L.2.
Compared to exclusion limits with charged leptons, the experimental sensitivities in the
hadronic decay channels are much weaker. The sensitivity in the lepton sector arises
from trigger selections and smaller systematic uncertainties on the measurement. With
charged leptons ATLAS has excluded a Z 1 with the same lepton and quark couplings
as the Z boson up to 2.21 TeV [150]. Measurements on the hadronic decay channels
using inclusive dijets have excluded the following regions: MZ1 ¡ 237 GeV [151] and
320 GeV  MZ1   740 GeV [19]. A measurement from CDF on a final state with bb̄ using
data corresponding to an integrated luminosity of 87 pb1 is also not able to exclude the
Z 1 [152]. Their sensitivity is in the same regime as this measurement.
An improvement in the sensitivity in searches with bb̄ final states can be achieved with a
more advanced b-tagging algorithm. A realistic achievement is an improvement of 50%
to 70% in the b-tagging efficiency with constant light-jet rejection (cf. Fig. 6.7). This
means roughly an improvement of 40%. However, pseudo-experiments, which estimate the
95% CL upper limit assuming this b-tagging performance, show that with 2010 ATLAS
data (L  34 pb1) the Z 1 cannot be excluded. Of much more importance, is therefore
the amount of integrated luminosity recorded in 2011 data. The expected limit with an
integrated luminosity of 5 fb1 is calculated to demonstrate the sensitivity of 2011 ATLAS
data. The expected limit for reconstructed resonances with a signal width of 2.5 and 3.5
detector resolutions is presented in Fig. 12.10. These signal widths are chosen due to
Fig. 12.9(b) as they are important for masses below 500 GeV. In this limit calculation, the
performance of the b-tagging algorithm is assumed to be identical to the SV0 algorithm
and the jet energy scale uncertainty is improved by 20%. These are rather conservative
211
∈
b(b)
arbitrary units
12 Search for resonances in the cross section
0.5
0.45 s=7 TeV
0.4 Pythia: Z' signal
0.35 b-tagging efficiency
0.3
0.25
0.2
0.15
0.1
200 400 600 800 1000
signal mass [GeV]
Figure 12.8: Effective b-tagging efficiency for each generated resonance as a function of signal
mass.
assumptions. The expected limit shows that with the recorded data from 2011, the Z 1
can be excluded in final states with pairs of b-jets. The exclusion region can be estimated
to be around 260 GeV  MZ1   700 GeV for 2011 ATLAS data. This prognosis for the
exclusion region obtained from Fig. 12.10 is already translated into terms of Z 1 mass using
Table L.2.
212
∈
bb
12.3 Model independent limit setting
105 102
s=7 TeV,∫ Ldt=34 pb-1
104 10 s=7 TeV, Ldt=34 pb
-1
Anti-k t R=0.4 EM+JES
∫
Data
Toy-MC: Z' (220 GeV)
103 Toy-MC: Z' (420 GeV) 1
Toy-MC: Z' (800 GeV)
102 10-1 σ(M)/M:
= 1.0σdetector
= 2.0σ
-2 detector10 10 = 2.5σdetector
= 3.0σdetector
= 3.5σdetector
1 10-3 = 5.0σdetector
Z' signal
10-1 -4200 300 400 500 600 700 800 900 1000 1100 10 200 300 400 500 600 700 800 900 1000
dijet mass [GeV] mass [GeV]
(a) (b)
Figure 12.9: (a) The measured dijet mass spectrum of b-jets is shown with predictions from
Toy-MC of Pythia Z 1 for masses 220, 420 and 800 GeV using the SV0 b-tagging algorithm. (b)
The 95% CL upper limits on σ BRAcc b-tagging for simple Gaussian resonances decaying
into bb̄ dijets as a function of the invariant dijet mass and the determined σBRAccb-tagging
values for the heavy gauge boson Z 1. The colours of the Z 1 signals indicate the corresponding
signal width obtained in the Toy-MC.
10
s=7 TeV,∫ Ldt=5 fb-1 (2011)
1 Expected Limit
10-1
10-2 σ(M)/M:
= 2.5σdetector
10-3 = 3.5σdetector
Z' signal
10-4 200 300 400 500 600 700 800 900 1000
dijet mass [GeV]
Figure 12.10: Expected limit for data corresponding to a total integrated luminosity of 5 fb1
which has been recorded by ATLAS in the LHC running period in 2011. The evaluated expected
limits are calculated for two signal widths: 2.5σdetector and 3.5σdetector. The empty signal markers
indicate that the signal width is larger than the ones for which the expected limit is calculated.
213
Events
σ × BR × Acc × b-tagging [pb]
σ × BR × Acc × b-tagging [pb]

13 Conclusion and outlook
The Large Hadron Collider (LHC) began regular operation at a centre-of-mass energy of
7 TeV in 2010. The run period in 2010 set up a new world record in the beam energy at
a particle accelerator. The commissioning of the LHC offers the opportunity to explore
unprecedented kinematic regimes. With this machine precision measurements in the TeV
regime of the Standard Model (SM) and the search for new phenomena in the multi-TeV
region are achievable. ATLAS is a multi-purpose detector built for high-energy particle
p?hysics at the LHC. The full data set recorded by ATLAS during 2010 LHC operation at
s  7 TeV corresponds to an integrated luminosity of 45 pb1.
This thesis presented the measurement of the production rate of bottom-quark pairs with
the ATLAS experiment. It made intensive use of the capabilities of the calorimeters and the
precision of the tracking system of the ATLAS detector. The bb̄ cross section is determined
as a function of the invariant dijet mass, the azimuthal angle between the bb̄ pairs and
their polar angle correlation in the variable χ. Bottom-flavoured jets are measured above
a transverse momentum of 40 GeV and within the rapidity region |y|   2.1. For the cross
section measurements the data is corrected to particle level, making it independent of
detector effects. It is then compared to next-to-leading order QCD predictions. Physics
phenomena beyond the Standard Model of particle physics have been searched for in the
bb̄ invariant mass spectrum, and the 95% confidence-level upper limits on a resonance
signal with a Gaussian shape have been calculated.
Jet production is by far the dominant process at the LHC. In proton-proton collisions,
jet studies can therefore usually benefit from small statistical uncertainties. The total jet
production rate is of interest to test the QCD description as well as to understand them as
a background source in various numbers of analyses. But jets can also be used to search
for new phenomena which would manifest themselves in an excess or deficit of events at a
given invariant dijet mass or in an excess at high masses. Bottom-flavoured jets are an
excellent tool to test QCD. They are the most direct probe of the hard scatter and its
kinematic properties. Their production at large transverse momentum is only subject to
small contamination from non-perturbative effects. The fragmentation of bottom-flavour
hadrons in high-pT jets can be studied by means of perturbation theory since the momenta
involved are typically large enough. The ratio of heavy-quark jets relative to generic jets
could be an indicator for new physics if the coupling to quarks is sensitive to the quark
generation.
For the measurement of jets with bottom-flavour content three ingredients are essential: the
absolute scales of the calorimeter measurement of the energies of inclusive jets and of b-jets,
and the calibration of the heavy-flavour identification (b-tagging). In ATLAS, the inclusive
jet energy scale is established using data-driven techniques and test-beam measurements
and used as a baseline in this analysis. For the cross section measurement performed
in this thesis, an additional contribution to the jet energy scale uncertainty taking into
account the difference in fragmentation between bottom-flavour jets and light-quark and
gluon-initiated jets has been derived with the help of the tracking system. The b-tagging
calibration is determined with the help of semi-leptonic b-hadron decays into muons. The
215
13 Conclusion and outlook
resulting scale factors, which adjust the b-tagging performance in Monte-Carlo simulation
(MC) to comply with data, are shown to be valid assuming a conservative uncertainty in
the higher kinematic regions which were aimed for in this measurement. The uncertainties
on this measurement are dominated by systematic uncertainties related to b-tagging. The
second largest uncertainties arise from the jet energy scale uncertainty.
The MC studies have shown that the dijet cross section of b-jets is dominated by the
production via flavour creation. The next-to-leading-order calculations (NLO) are capable
of describing the measured differential cross sections very well. They are also essential to
understand the differential cross sections. It has been shown that the QCD production
mechanism is also valid in the energy regime of the LHC. However, first evidence for
deficiencies in the description of data have been found in the azimuthal angle correlation
between b-jets. These have been discussed in the context of other discrepancies found
at the LHC in the description of b-hadron production and modelling. As good as the
next-to-leading QCD calculations are, there is still room for improvements. One goal
would be to describe higher jet multiplicities at leading order (LO) while maintaining
the NLO accuracy for the hard scatter. New approaches are investigated to achieve
next-to-leading-order accuracy for parton shower algorithms. However, the measurement
and the determination of corrections could have not been so straightforward if not for the
good modelling of the underlying event, the multiple parton interactions and hadronisation
in the parton shower generators. The studies on tracks within jets have impressively
shown the power of the phenomenological models on the non-perturbative processes during
hadronisation.
Additionally, the same data was used to search for physics beyond the SM. Three different
event selections with different sensitivities to processes in the s-channel, which join into
an intermediate state, have been investigated for the presence of an excess or a deficit in
the invariant mass spectrum. It has been shown that there is no evidence for such new
physics. A model independent limit on the event yield of a process forming a resonance
with a Gaussian shape with different widths has been calculated at 95% confidence-level.
A neutral heavy gauge boson with the same couplings as the Z boson cannot be excluded
in any mass region. In scenarios in which the heavy gauge boson exceptionally decays only
into bb̄ pairs, the sensitivity is increased and may even be excluded using this data set of
34 pb1.
In ?2011 an integrated luminosity of 5 fb1 has been recorded by the ATLAS experiment
at s  7 Te?V. After surveying the perspectives for 2012, it has been decided to operate
the LHC at s  8 TeV in 2012. This run period has begun in April 2012. In 2013 the
LHC will shutdown to prepare running at design center-of-mass energy of 13-14 TeV. This
includes months of repair work and an intensive training of the magnets to reach their
maximum magnetic field.
Improvements from the b-tagging performance and the jet energy scale uncertainty are ex-
pected in measurements using 2011 and 2012 data. High-performance b-tagging algorithms
can achieve an increase in efficiency from 50% to 70% with the same light jet rejection as
the SV0 b-tagging algorithm used in this analysis. These new algorithms will allow for
refined searches of new phenomena with low production cross sections. Equivalently, the
light jet rejection at the point of 50% b-tagging efficiency can be increased by a factor
of 3. The inclusive jet energy scale uncertainty has been improved during the last year
and already reached the 1% level in the central rapidity region for intermediate jet pT.
As a consequence a reduction of the jet energy scale uncertainty on the cross section of
almost 50% in the low dijet mass region can be achieved in an inclusive jet measurement.
216
To take advantage of the correlation of experimental and theoretical uncertainties in a
cross section ratio measurement the b-tagging related uncertainties have to be reduced to
the level of the jet energy scale uncertainties. When this is accomplished, the production
ratio of heavy-quark jets relative to generic jets can get very sensitive to new physics. The
additional contribution to account for the differences in heavy-flavour fragmentation has
already been reduced on the basis of MC studies. This additional uncertainty is about
2% for jets with pT  100 GeV and decreases to below 1% for higher-pT jets. The jet
energy scale for b-jets could also be improved and validated using (anti-)top quark decays
for the intermediate transverse momentum region. The prospects of the search with the
integrated luminosity available in 2011 data have been shown. It can be expected that
with 2011 data first limits on the heavy gauge boson with the same couplings as the Z
boson in the bb̄ decay channel can be extracted.
Because the number of interactions per beam crossing has increased to more than 20 in
data in 2011 and to almost 30 in 2012, the analyses face new challenges. But still the
performance of ATLAS is expected to increase in terms of calibration and simulation
efforts leading to smaller experimental uncertainties. The coming years particle physics
will be strongly affected by the results of the LHC and its experiments.
217

List of acronyms
ALFA Absolute Luminosity for ATLAS
ALICE A Large Ion Collider Experiment
AMBT1 ATLAS Minimum Bias Tune 1
ATLAS A Toroidal LHC ApparatuS
AUET1 ATLAS Underlying Event Tune 1
BC Before Christ
BKG Background
BR Branching Ratio
BS Beam Spot
CDF Collider Detector at Fermilab
CERN Centre Européen pour la Recherche Nucléaire
CKM Cabibbo-Kobayashi-Maskawa
CL Confidence level
CMS Compact Muon Solenoid
CPU Computer Processing Unit
CSC Cathode Strip Chambers
CTEQ Coordinated Theoretical-Experimental Project on QCD
CTP Central Trigger Processor
DAQ Data Acquisition
DCS Detector Control System
DGLAP Dokshitzer-Gribov-Lipatov-Altarelli-Parisi
DoF Number of Degrees of Freedom
DQ Data Quality
EF Event Filter
EM Electromagnetic
EMB Electromagnetic Barrel Calorimeter
EMEC Electromagnetic End-cap Calorimeter
FCal Forward Calorimeter
FCR Flavour Creation
FEX Flavour Excitation
FONLL Fixed Order plus Next-to-Leading Logarithms
219
13 Conclusion and outlook
GSP Gluon Splitting
GUT Grand Unified Theory
HAD Hadronic
HEC Hadronic End-cap Calorimeter
HLT High-level Trigger
ID Inner Detector
JES Jet Energy Scale
LAr Liquid Argon
LEP Large Electron-positron Collider
LHAPDF The Les Houches Accord PDF Interface
LHC Large Hadron Collider
LHCb LHC-beauty
LHCf LHC-forward
LO Leading Order
LUCID LUminosity Cherenkov Integrating Detector
MBTS Minimum Bias Trigger Scintillators
MC Monte-Carlo
MCFM Monte Carlo for Femtobarn Processes
MDT Monitored Drift Chambers
MNR Mangano-Nason-Ridolfi
MPI Multiple Parton Interactions
MRST Martin-Roberts-Stirling-Thorne
MSTW Martin-Stirling-Thorne-Watt Parton Distribution Functions
NI Non-interacting
NLO Next-to-leading Order
NNLO Next-next-to-leading Order
NP Non-perturbative
PDF Parton Density Functions
POWHEG POsitive Weight Hard Event Generator
pQCD Perturbative QCD
PS Prescale
PV Primary Vertex
QCD Quantum Chromodynamics
QED Quantum Electrodynamics
220
QGSP Quark Gluon String model
RMS Root Mean Square
RoI Region-of-Interest
RPC Resistive Plate Chambers
SCT Silicon Microstrip Tracker
SLD Stanford Linear Collider Large Detector
SM Standard Model
SV Secondary Vertex
TGC Thin Gap Chambers
TOTEM Total Elastic and Diffractive Cross Section Measurement
TRT Transition Radiation Tracker
UE Underlying Event
ZDC Zero Degree Calorimeter
221

A Appendix: Analysis binning
Following conventions for the variable binning are used:
 Binning of jet pT in GeV: {0,5, 10, 20, 30, 40, 60, 80, 110, 160, 210, 260, 310, 400,
500, 600, 800, 1000, 1200, 1500, 1800, 2500}
 Binning of dijet mass in GeV: { 0, 30, 70, 110, 160, 210, 260, 310, 370, 440, 510, 590,
670, 760, 850, 950, 1060, 1180, 1310,1450, 1600, 1760, 1940, 2120, 2330, 2550, 2780,
3040, 3310, 3610, 3930, 4270, 4640, 5040, 5470, 5940, 6440, 7000}
 Binning of ∆φ in rad: {0,π/2,2.5,2.8,2.9,3.0,3.1,π}
 Binning of χ  e|y1y2|: {1,3,5,10,30}
B Appendix: Monte-Carlo samples
The beam spot used in the MC samples with the MC10 tune is the measured beam spot
from data period D. The ATLAS geometry used in the samples is called GEO-16-00-00
with particle ID (s934).
Baseline Pythia samples:
 No pile-up setup (150 ns bunch spacing) with reconstruction tags r1653.
 Pile-up: double bunch trains with 225ns separation, within trains there are 8 filled
bunches with 150ns bunch separation and   number of pile-up interactions ¡ 2.2
with reconstruction tag r1833.
223
MC dataset p̂T [GeV] Cross section [nb] Number of events
J0 8-17 9860100 16343508
J1 17-35 678140 7384565
J2 35-70 40981 2795084
J3 70-140 2193.1 2792379
J4 140-280 87.707 2786179
J5 280-560 2.3502 2773476
J6 560-1120 3.3618102 2774601
J7 1120-2240 1.3744104 1381026
Table B.1: Summary of pile-up Pythia samples studied.
×103
2500 Data 1
Pythia
2000 0.8
1500 0.6
1000 0.4
500 0.2
0 0
-200 -100 0 100 200 -200 -100 0 100 200
zPV [mm] zPV [mm]
(a) (b)
Figure B.1: (a) The z-distribution of reconstructed primary vertices zPV in data and Pythia
simulation. (b) The reweighing factors as a function of zPV which are applied to Pythia MC.
C Appendix: Data quality
requirements
Colour scheme used in the data quality assessment [97]:
 Green colour: Data can be non-restrictively used for physic analysis.
 Yellow colour: Data is not used for public analysis unless explicitly stated. This
status indicates that the corresponding data are flawed relative to green data
224
AArrbbiittrraarryy  uunniittss
Data/MC
quality but possibly recoverable. A recovery may be possible due to adjusted offline
reconstruction.
 Red colour: Unrecoverable data which is lost due to major problems for data analysis.
 Grew colour: For very short runs with insufficient statistics or due to problems in
the monitoring or assessment software, it may occur that a clear statement cannot
be made.
 Black colour: System disabled.
A summary of the data quality requirements on accelerator parameters, detector opera-
tion and the analysis-based quality criteria in use in this analysis:
 Accelerator parameters: LHC delivered stable beams with an energy of 3.5 TeV.
 Detector-level quality criteria:
– The L1 trigger processor has green data quality.
– The L1 calorimeter trigger has green data quality.
– The toroid magnet is at nominal voltage.
– The solenoid magnet is at nominal voltage.
– The Pixel, SCT and TRT work at nominal parameters.
– The luminosity monitors and counters work at nominal parameters.
– Good beam spot data is available with a full beam spot determination including
the (resolution-corrected) beam spot size.
 Analysis-based quality criteria:
– The monitored tracking properties behave as expected.
– The muon algorithms and monitored muon reconstruction properties behave as
expected.
– For every calorimeter region, the inspected jet and missing transverse energy
variables behave as expected.
225
D Appendix: Jet energy calibration
The values of the correction factor 1F p EMq| are illustrated in Fig. D.1 for three repre-calib E η
sentative η-intervals.
The jet energy response of jets in the inclusive sample is derived separately for gluon- and
quark-initiated jets and presented in Fig. D.2.
ATLAS simulation 0.3 ≤ |η| < 0.82
2.1 ≤ |η| < 2.8
3.6 ≤ |η| < 4.4
1.8
1.6
1.4
1.2
Anti-k  R = 0.6, EM+JES
t
1
3 3
20 30 102 2 102× 10 2×10
jet
p  [GeV]
T
Figure D.1: Average jet energy scale correction as a function of the calibrated jet transverse
momentum for three representative η-intervals obtained from the nominal Monte-Carlo simulation
sample. The correction is only shown over the accessible kinematic range. Taken from Ref. [60].
Figure D.2: Response as a function of particle jet transverse momenta (ptruthT ) for all jets in the
QCD sample (black solid circles), gluon-jets (red open squares), and light-quark jets (blue open
circles) falling in the barrel in MC simulation. Jets are reconstructed with the anti-kt algorithm
with distance parameter R=0.4 and calibrated with the EM+JES calibration scheme. Taken from
Ref. [110].
226
Average JES correction
E Appendix: Monte-Carlo
comparisons
1 1
Inclusive jets: Inclusive jets:
Data Data
10-1 Pythia 10-1 Pythia
MC stat. unc. MC stat. unc.
10-2
∫Ldt = 34 pb-1 10-2 ∫Ldt = 34 pb-1
10-3
10-3
10-4
0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8
2 2
1 1
0 0
0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8
∆Rj3,j1 ∆Rj3,j2
(a) (b)
Figure E.1: The ∆R distribution between the third leading jet in the event and the leading jets.
Inclusive jets: Inclusive jets:
10-1 Data 10-1 Data
Pythia Pythia
-2 MC stat. unc. MC stat. unc.10 10-2
∫Ldt = 34 pb-1 ∫Ldt = 34 pb-1
10-3 10-3
10-4 10-4
0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8
2 2
1 1
0 0
0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8
∆Rj4,j1 ∆Rj4,j2
(a) (b)
Figure E.2: The ∆R distribution between the fourth leading jet in the event and the leading
jets.
227
Data/MC 111///NNN   dddNNN///ddd∆∆∆RRR Data/MC 111///NNN   dddNNN///ddd∆∆∆RRR
Data/MC 111///NNN   dddNNN///ddd∆∆∆RRR Data/MC 111///NNN   dddNNN///ddd∆∆∆RRR
102
∫Ldt = 34 pb-1 Inclusive jets: 10 ∫Ldt = 34 pb-1 Inclusive jets:10 Data Data
Pythia 1 Pythia1 MC stat. unc. MC stat. unc.
-1
10-1 10
-2
10-2 10
10-3 10
-3
10-4 10-4
1.4-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.-410 -8 -6 -4 -2 0 2 4 6 8 10
1.2 1.2
1 1
0.8 0.8
0.6 0.6
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 -10 -8 -6 -4 -2 0 2 4 6 8 10
z  (leading jets) [mm] z0/σ(z ) (leading jets) [mm]0 0
(a) (b)
Figure E.3: The reconstructed longitudinal impact parameter ((a)) and its significance ((b))
are presented for tracks associated to a jet and fulfilling b-tagging quality cuts.
F Appendix: Calibration of
bottom-tagging algorithms
Summary of the systematic uncertainties on the b-tagging efficiency measurement with
the prelT method given in Table F.1 and Table F.2.
The resulting scale factors for the JetProb tagger using the 50% efficiency working point
and their uncertainties are given in the following:
20   pT   30 GeV : 0.83 0.06(stat) 0.09(syst)
30   pT   60 GeV : 0.89 0.03(stat) 0.07(syst)
60   pT   90 GeV : 0.87 0.04(stat) 0.03(syst)
90   pT   140 GeV : 0.89 0.09(stat) 0.07(syst)
Systematic uncertainties from the SV0 mass method for the mistag rate calibration of SV0
and JetProb tagging algorithm at 50% efficiency are given in Table F.3 and Table F.4.
Systematic uncertainties from the negative tag method for the mistag rate calibration of
SV0 and JetProb tagging algorithm at 50% efficiency are given in Table F.5 and Table F.6.
The resulting mistag rate for the JetProb tagger is given in Table F.7.
228
Data/MC 111///NNN   dddNNN///ddd(((zzz )))   [[[mmmmmm
---111]]]
000
Data/MC 111///NNN   dddNNN///ddd(((ddd )))   [[[mmmmmm
---111]]]
000
Figure F.1: Example of a template fit in data to the prelT distribution after the JetProb b-tagging
cut. The template fit is performed on all jets. Uncertainties shown are for data statistics only.
The discrepancies between the data and the sum of the templates are fully covered by the systematic
uncertainties on the template shapes. Taken from Ref. [103].
Jet pT[GeV]
Source 20-30 30-60 60-90 90-140
Statistical 7.5 2.9 4.6 9.8
Measurement:
Jet Energy Scale 4.3 0.5 1.3 1.2
Method:
Template statistics 5.1 1.4 1.8 2.2
Non-b template modelling 0.8 0.8 0.7 0.3
b-template modelling 1.4 0.2 0.3 0.1
Validity for all b-hadrons 3.5 5.6 0.7 2.9
MC model dependence:
b-hadron direction 2.5 0.1 1.4 3.6
Muon pmuonT -spectrum 4.7 3.6 1.8 3.3
b-fragmentation 0.4 0.1   0.1 0.5
b-decay modelling (spectrum) 5.3 0.3 0.6 0.1
b-decay modelling (branching frac- 1.0 0.4 0.1   0.1
tions)
Modelling of b/c-production 2.4/1.1 0.1/1.4 0.6/1.0 0.8/7.2
Total 11.1 7.1 3.6 9.5
Table F.1: Relative statistical and systematic uncertainties for the SV0 tagger at working point
SV0 weight ¡ 5.85.
229
F Appendix: Calibration of bottom-tagging algorithms
Jet pT[GeV]
Source 20-30 30-60 60-90 90-140
Statistical 7.7 2.9 4.6 9.5
Measurement:
Jet Energy Scale 2.3 0.5 1.3 0.5
Method:
Template statistics 5.4 1.4 1.8 2.5
Non-b template modelling 0.8 0.8 0.7 0.5
b-template modelling 1.4 0.2 0.4 0.2
Validity for all b-hadrons 4.9 5.7 0.5 3.0
MC model dependence:
b-hadron direction 1.7 0.4 1.4 3.9
Muon pmuonT -spectrum 4.7 4.6 1.8 2.4
b-fragmentation 0.4 0.1   0.1 0.4
b-decay modelling (spectrum) 5.3 0.3 0.6 0.4
b-decay modelling (branching frac- 1.0 0.4 0.1   0.1
tions)
Modelling of b/c-production 2.9/1.3 0.1/1.6 0.6/1.1 0.5/4.1
Total 11.2 7.7 3.6 7.4
Table F.2: Relative statistical and systematic uncertainties for the JetProb tagger at working
point JetProb weight ¡ 3.25.
Jet pT[GeV]
Source 40-60 60-90 90-140 140-200 200-300 300-500
|η|   1.2
Simulation statistics 14.7 16.1 8.4 7.7 7.7 7.1
b-tagging efficiencies 3.0 3.9 3.2 2.8 2.4 1.4
b-, c-template shapes 1.6 1.7 1.0 0.7 0.3 0.6
Light-template shapes 6.8 7.1 9.2 11.0 12.4 16.7
Long-lived particles and 3.2 3.2 3.2 3.2 3.2 3.2
material interactions
Total 16.9 18.4 13.2 14.1 15.1 18.5
1.2   |η|   2.5
Simulation statistics 9.6 10.1 8.5 8.3 11.5 24.5
b-tagging efficiencies 1.8 2.2 2.1 2.0 2.2 2.5
b-, c-template shapes 0.5 0.3 0.4 0.1 0.4 1.2
Light-template shapes 5.9 6.4 11.0 9.9 11.3 18.7
Long-lived particles and 3.2 3.2 3.2 3.2 3.2 3.2
material interactions
Total 11.9 12.5 14.4 13.4 16.6 31.1
Table F.3: Relative systematic uncertainties (in %) of the SV0 mass measurement for the SV0
tagger at working point SV0 weight ¡ 5.85.
230
Jet pT[GeV]
Source 40-60 60-90 90-140 140-200 200-300 300-500
|η|   1.2
Simulation statistics 6 7.6 3.5 3.3 4.0 4.7
b-tagging efficiencies 2.2 3.4 2.8 2.6 3.0 2.8
b-, c-template shapes 0.7 1.6 0.9 1.0 1.0 1.0
Light-template shapes 2.4 2.8 3.8 4.7 6.2 6.5
Long-lived particles and 3.2 3.2 3.2 3.2 3.2 3.2
material interactions
Total 7.5 9.5 6.7 7.1 8.6 9.1
1.2   |η|   2.5
Simulation statistics 6.6 4.2 3.9 3.7 4.5 13.4
b-tagging efficiencies 1.6 1.6 2.0 1.6 2.0 0.8
b-, c-template shapes 0.6 0.7 0.9 0.4 0.2 0.2
Light-template shapes 2.1 2.6 3.1 3.6 3.9 2.9
Long-lived particles and 3.2 3.2 3.2 3.2 3.2 3.2
material interactions
Total 7.8 6.1 6.3 6.3 7.0 14.1
Table F.4: Relative systematic uncertainties (in %) of the SV0 mass measurement for the
JetProb tagger at working point JetProb weight ¡ 3.25.
Jet pT[GeV]
Source 40-60 60-90 90-140 140-200 200-300 300-500
|η|   1.2
Simulation statistics 7.2 5.3 4.8 4.3 4.0 3.8
b-tagging efficiencies 4.1 5.9 6.6 7.1 8.8 8.4
Heavy flavour fraction 1.0 2.0 2.1 2.3 2.9 3.0
Track multiplicity 1.0 0.4 0.2 0.3 1.1 2.2
Long-lived particles and 1.5 2.0 1.8 0.8 0.5 0.5
material interactions
Impact parameter resolu- 3.6 3.0 12.7 5.4 9.8 7.1
tion
Total 9.3 9.0 15.4 10.2 14.1 12.3
1.2   |η|   2.5
Simulation statistics 16.6 8.8 8.8 7.8 5.1 10.4
b-tagging efficiencies 3.9 3.7 6.6 4.0 4.3 3.9
Heavy flavour fraction 1.1 0.9 2.5 1.2 1.2 1.2
Track multiplicity 1.7 4.8 2.1 0.7 1.2 2.2
Long-lived particles and 2.3 0.7 1.0 0.5 0.7 0.2
material interactions
Impact parameter resolu- 7.3 13.4 6.5 16.7 19.2 12.1
tion
Total 18.8 17.2 13.2 18.9 20.4 16.6
Table F.5: Relative systematic uncertainties (in %) of the negative tag measurement for the
SV0 tagger at working point SV0 weight ¡ 5.85.
231
F Appendix: Calibration of bottom-tagging algorithms
Jet pT[GeV]
Source 40-60 60-90 90-140 140-200 200-300 300-500
|η|   1.2
Simulation statistics 3.8 2.8 2.3 2.1 1.9 1.6
b-tagging efficiencies 10.0 11.8 13.0 15.2 15.4 12.8
Heavy flavour fraction 3.3 4.0 4.2 4.9 4.7 4.1
Track multiplicity 6.2 0.3 0.1 0.3 0.4 1.3
Long-lived particles and 2.0 1.1 0.6 0.8 1.0 0.5
material interactions
Impact parameter resolu- 6.0 0.6 3.1 2.5 2.8 2.4
tion
Total 14.3 12.8 14.2 16.3 16.5 13.8
1.2   |η|   2.5
Simulation statistics 4.4 3.2 3.2 2.9 2.2 3.4
b-tagging efficiencies 4.5 5.4 7.4 7.5 7.2 5.6
Heavy flavour fraction 1.2 1.7 2.5 2.9 2.5 2.1
Track multiplicity 0.7 1.0 0.4 0.4 0.5 1.6
Long-lived particles and 1.0 0.9 0.9 0.3 0.6 0.4
material interactions
Impact parameter resolu- 13.8 3.5 6.5 0.5 7.8 9.4
tion
Total 15.3 7.5 10.8 8.5 11.1 11.7
Table F.6: Relative systematic uncertainties (in %) of the negative tag measurement for the
JetProb tagger at working point JetProb weight ¡ 3.25.
Jet pT[GeV]
40-60 60-90 90-140 140-200 200-300 300-500
|η|   1.2
1.30.4 1.20.3 1.00.1 0.90.1 1.10.3 1.20.3
|η|   1.2
1.20.4 1.10.2 1.00.2 1.00.2 1.10.3 1.00.4
Table F.7: The resulting mistag rate scale factors for the JetProb tagger for the selection cuts
yielding 50% efficiency in tt̄ events as function of jet pT and |η|.
232
G Appendix: Extension of calibration
Figure G.1: Distribution of the transverse impact parameter in experimental data for tracks
without shared hits and for tracks with shared hits. Both plots are normalised to unity. Taken
from Ref. [153].
233
H Appendix: Jet energy scale
1 20 GeV<p <30 GeV Pythia: incl. jets 1 30 GeV<p <40 GeV Pythia: incl. jets 1 40 GeV<p <60 GeV Pythia: incl. jets
T T T
Jet trigger data Jet trigger data Jet trigger data
Minimum bias data Minimum bias data Minimum bias data
10-1 10-1 10-1
10-2 10-2 10-2
10-3 10-3 10-3
10-4 -4 -40 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
rtrk rtrk rtrk
1 60 GeV<p <80 GeV Pythia: incl. jets 1 80 GeV<p <110 GeV Pythia: incl. jets 1 110 GeV<p <160 GeV Pythia: incl. jets
T T T
Jet trigger data Jet trigger data Jet trigger data
Minimum bias data Minimum bias data Minimum bias data
10-1 10-1 10-1
10-2 10-2 10-2
10-3 10-3 10-3
10-4 -4 -40 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
rtrk rtrk rtrk
1 160 GeV<p <210 GeV Pythia: incl. jets 1 210 GeV<p <260 GeV Pythia: incl. jets 1 260 GeV<p <310 GeV Pythia: incl. jets
T T T
Jet trigger data Jet trigger data Jet trigger data
Minimum bias data Minimum bias data Minimum bias data
10-1 10-1 10-1
10-2 10-2 10-2
10-3 10-3 10-3
10-4 -4 -40 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
rtrk rtrk rtrk
1 310 GeV<p <400 GeV Pythia: incl. jets 1 400 GeV<p <500 GeV Pythia: incl. jets 1 500 GeV<p <600 GeV Pythia: incl. jets
T T T
Jet trigger data Jet trigger data Jet trigger data
Minimum bias data Minimum bias data Minimum bias data
10-1 10-1 10-1
10-2 10-2 10-2
10-3 10-3 10-3
10-4 -4 -40 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
rtrk rtrk rtrk
Figure H.1: rtrk distributions for all pT bins for the inclusive jet sample for |y|   1.2.
234
11//NN  ddNN//ddrrttrrkk 11//NN  ddNN//ddrrttrrkk 11//NN  ddNN//ddrrttrrkk 11//NN  ddNN//ddrrttrrkk
11//NN  ddNN//ddrrttrrkk 11//NN  ddNN//ddrrttrrkk 11//NN  ddNN//ddrrttrrkk 11//NN  ddNN//ddrrttrrkk
11//NN  ddNN//ddrrttrrkk 11//NN  ddNN//ddrrttrrkk 11//NN  ddNN//ddrrttrrkk 11//NN  ddNN//ddrrttrrkk
1 20 GeV<p <30 GeV Pythia: incl. jets 1 30 GeV<p <40 GeV Pythia: incl. jets 1 40 GeV<p <60 GeV Pythia: incl. jets
T T T
Jet trigger data Jet trigger data Jet trigger data
Minimum bias data Minimum bias data Minimum bias data
10-1 10-1 10-1
10-2 10-2 10-2
10-3 10-3 10-3
10-4 10-4 -40 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
rtrk rtrk rtrk
1 60 GeV<p <80 GeV Pythia: incl. jets 1 80 GeV<p <110 GeV Pythia: incl. jets 1 110 GeV<p <160 GeV Pythia: incl. jets
T T T
Jet trigger data Jet trigger data Jet trigger data
Minimum bias data Minimum bias data Minimum bias data
10-1 10-1 10-1
10-2 10-2 10-2
10-3 10-3 10-3
10-4 10-4 10-40 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
rtrk rtrk rtrk
1 160 GeV<p <210 GeV Pythia: incl. jets 1 210 GeV<p <260 GeV Pythia: incl. jets 1 260 GeV<p <310 GeV Pythia: incl. jets
T T T
Jet trigger data Jet trigger data Jet trigger data
Minimum bias data Minimum bias data Minimum bias data
10-1 10-1 10-1
10-2 10-2 10-2
10-3 10-3 10-3
10-4 10-4 -40 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
rtrk rtrk rtrk
1 310 GeV<p <400 GeV Pythia: incl. jets 1 400 GeV<p <500 GeV Pythia: incl. jets 1 500 GeV<p <600 GeV Pythia: incl. jets
T T T
Jet trigger data Jet trigger data Jet trigger data
Minimum bias data Minimum bias data Minimum bias data
10-1 10-1 10-1
10-2 10-2 10-2
10-3 10-3 10-3
10-4 -4 -40 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
rtrk rtrk rtrk
Figure H.2: rtrk distributions for all pT bins for the inclusive jet sample for 1.2   |y|   2.1.
235
11//NN  ddNN//ddrrttrrkk 11//NN  ddNN//ddrrttrrkk 11//NN  ddNN//ddrrttrrkk 11//NN  ddNN//ddrrttrrkk
11//NN  ddNN//ddrrttrrkk 11//NN  ddNN//ddrrttrrkk 11//NN  ddNN//ddrrttrrkk 11//NN  ddNN//ddrrttrrkk
11//NN  ddNN//ddrrttrrkk 11//NN  ddNN//ddrrttrrkk 11//NN  ddNN//ddrrttrrkk 11//NN  ddNN//ddrrttrrkk
H Appendix: Jet energy scale
1 1 1
20 GeV<p <30 GeV Pythia: b-tagged jets 30 GeV<p <40 GeV Pythia: b-tagged jets 40 GeV<p <60 GeV Pythia: b-tagged jets
T T T
Jet trigger data Jet trigger data Jet trigger data
10-1 Minimum bias data 10-1 Minimum bias data 10-1 Minimum bias data
10-2 10-2 10-2
10-3 10-3 10-3
10-4 -4 -40 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
rtrk rtrk rtrk
1 1 1
60 GeV<p <80 GeV Pythia: b-tagged jets 80 GeV<p <110 GeV Pythia: b-tagged jets 110 GeV<p <160 GeV Pythia: b-tagged jets
T T T
Jet trigger data Jet trigger data Jet trigger data
10-1 Minimum bias data 10-1 Minimum bias data 10-1 Minimum bias data
10-2 10-2 10-2
10-3 10-3 10-3
10-4 -4 -40 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
rtrk rtrk rtrk
1 1 1
160 GeV<p <210 GeV Pythia: b-tagged jets 210 GeV<p <260 GeV Pythia: b-tagged jets 260 GeV<p <310 GeV Pythia: b-tagged jets
T T T
Jet trigger data Jet trigger data Jet trigger data
10-1 Minimum bias data 10-1 Minimum bias data 10-1 Minimum bias data
10-2 10-2 10-2
10-3 10-3 10-3
10-4 -4 -40 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
rtrk rtrk rtrk
1 1 1
310 GeV<p <400 GeV Pythia: b-tagged jets 400 GeV<p <500 GeV Pythia: b-tagged jets 500 GeV<p <600 GeV Pythia: b-tagged jets
T T T
Jet trigger data Jet trigger data Jet trigger data
10-1 Minimum bias data 10-1 Minimum bias data 10-1 Minimum bias data
10-2 10-2 10-2
10-3 10-3 10-3
10-4 10-4 -40 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
rtrk rtrk rtrk
Figure H.3: rtrk distributions for all pT bins for the b-tagged jet sample for |y|   1.2.
236
11//NN  ddNN//ddrrttrrkk 11//NN  ddNN//ddrrttrrkk 11//NN  ddNN//ddrrttrrkk 11//NN  ddNN//ddrrttrrkk
11//NN  ddNN//ddrrttrrkk 11//NN  ddNN//ddrrttrrkk 11//NN  ddNN//ddrrttrrkk 11//NN  ddNN//ddrrttrrkk
11//NN  ddNN//ddrrttrrkk 11//NN  ddNN//ddrrttrrkk 11//NN  ddNN//ddrrttrrkk 11//NN  ddNN//ddrrttrrkk
1 1 1
20 GeV<p <30 GeV Pythia: b-tagged jets 30 GeV<p <40 GeV Pythia: b-tagged jets 40 GeV<p <60 GeV Pythia: b-tagged jets
T T T
Jet trigger data Jet trigger data Jet trigger data
10-1 Minimum bias data 10-1 Minimum bias data 10-1 Minimum bias data
10-2 10-2 10-2
10-3 10-3 10-3
10-4 -4 -40 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
rtrk rtrk rtrk
1 1 1
60 GeV<p <80 GeV Pythia: b-tagged jets 80 GeV<p <110 GeV Pythia: b-tagged jets 110 GeV<p <160 GeV Pythia: b-tagged jets
T T T
Jet trigger data Jet trigger data Jet trigger data
10-1 Minimum bias data 10-1 Minimum bias data 10-1 Minimum bias data
10-2 10-2 10-2
10-3 10-3 10-3
10-4 -4 -40 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
rtrk rtrk rtrk
1 1 1
160 GeV<p <210 GeV Pythia: b-tagged jets 210 GeV<p <260 GeV Pythia: b-tagged jets 260 GeV<p <310 GeV Pythia: b-tagged jets
T T T
Jet trigger data Jet trigger data Jet trigger data
10-1 Minimum bias data 10-1 Minimum bias data 10-1 Minimum bias data
10-2 10-2 10-2
10-3 10-3 10-3
10-4 -4 -40 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
rtrk rtrk rtrk
1 1 1
310 GeV<p <400 GeV Pythia: b-tagged jets 400 GeV<p <500 GeV Pythia: b-tagged jets 500 GeV<p <600 GeV Pythia: b-tagged jets
T T T
Jet trigger data Jet trigger data Jet trigger data
10-1 Minimum bias data 10-1 Minimum bias data 10-1 Minimum bias data
10-2 10-2 10-2
10-3 10-3 10-3
10-4 -4 -40 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
rtrk rtrk rtrk
Figure H.4: rtrk distributions for all pT bins for the b-tagged jet sample for 1.2   |y|   2.1.
237
11//NN  ddNN//ddrrttrrkk 11//NN  ddNN//ddrrttrrkk 11//NN  ddNN//ddrrttrrkk 11//NN  ddNN//ddrrttrrkk
11//NN  ddNN//ddrrttrrkk 11//NN  ddNN//ddrrttrrkk 11//NN  ddNN//ddrrttrrkk 11//NN  ddNN//ddrrttrrkk
11//NN  ddNN//ddrrttrrkk 11//NN  ddNN//ddrrttrrkk 11//NN  ddNN//ddrrttrrkk 11//NN  ddNN//ddrrttrrkk
I Appendix: Correction factors and
systematics
2 60
1.5 50
1
40
0.5
0 30
-0.5
20
-1
-1.5 10
-2 0
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
y
leading jet
Figure I.1: Illustration of the acceptance cut 12 |y1   y2|   1.1 for the measurement of the dijet
cross section as a function of the angular variable χ.
∆φ bin [rad] b-tagging Statistical Fractional sys. uncertainty
efficiency error [%]
π{2-2 0.25 0.00 17
2-3 0.25 0.00 16
3-3 0.22 0.00 16
3-3 0.21 0.00 16
3-π 0.19 0.00 17
Table I.1: The b-tagging efficiency as a function of the difference in azimuthal angle ∆φ. The
statistical error is of the order of 1  104.
238
y
subleading jet
χ
110 GeV   M   370 GeV 370 GeV   M   850 GeV
χ bin
b-tagging Stat. Sys. un- b-tagging Stat. Sys. un-
efficiency error certainty efficiency error certainty
[%] [%]
1-3 0.26 0.00 17 0.35 0.01 44
3-5 0.22 0.00 16 0.35 0.01 42
5-10 0.20 0.00 16 0.29 0.01 39
10-30 0.23 0.00 15 0.28 0.00 28
Table I.2: The b-tagging efficiency as a function of angular variable χ for both mass ranges.
∆φ bin [rad] b-tagging Total Fractional tot.
purity uncertainty uncertainty [%]
π{2-2.5 0.72 0.21 29
2.5-2.8 0.58 0.17 29
2.8-2.9 0.59 0.13 21
2.9-3.0 0.55 0.16 29
3.0-π 0.59 0.13 21
Table I.3: The b-tagging purity and systematic uncertainty as a function of ∆φ.
239
I Appendix: Correction factors and systematics
×103
160 b-template Fit: 50000 b-template Fit:
40000 b-template Fit:
140 110 GeV < M < 160 GeV Mean: 3.914 ± 0.002 160 GeV < M < 210 GeV Mean: 3.969 ± 0.003 35000 210 GeV < M < 260 GeV Mean: 4.155 ± 0.005
120 Sigma: 1.336 ± 0.001 40000 Sigma: 1.283 ± 0.002 30000 Sigma: 1.286 ± 0.003
100 Pythia Pythia 25000 Pythia
30000
80 20000
60 20000 15000
40 10000
10000
20 5000
0 0 0
0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10
SV0 mass sum [GeV] SV0 mass sum [GeV] SV0 mass sum [GeV]
b-template Fit: 14000 b-template Fit: b-template Fit:
12000
260 GeV < M < 310 GeV Mean: 3.967 ± 0.007 12000 310 GeV < M < 370 GeV Mean: 4.142 ± 0.009 2500 370 GeV < M < 440 GeV Mean: 3.647 ± 0.014
10000 Sigma: 1.199 ± 0.005 Sigma: 1.155 ± 0.006 Sigma: 1.090 ± 0.010
10000 2000
8000 Pythia Pythia Pythia
8000
1500
6000
6000
1000
4000 4000
2000 2000 500
0 0 0
0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10
SV0 mass sum [GeV] SV0 mass sum [GeV] SV0 mass sum [GeV]
700 b-template Fit:
800 b-template Fit: 140 b-template Fit:
440 GeV < M < 510 GeV Mean: 3.734 ± 0.029 700 510 GeV < M < 590 GeV Mean: 3.960 ± 0.031 120 590 GeV < M < 670 GeV Mean: 3.139 ± 0.074
600
Sigma: 1.153 ± 0.021 600 Sigma: 1.155 ± 0.022 Sigma: 0.616 ± 0.038100
500
Pythia 500 Pythia Pythia
400 80
400
300 60300
200 200 40
100 100 20
0 0 0
0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10
SV0 mass sum [GeV] SV0 mass sum [GeV] SV0 mass sum [GeV]
140 b-template Fit:
120 670 GeV < M < 760 GeV Mean: 3.761 ± 0.110
Sigma: 1.435 ± 0.082
100
Pythia
80
60
40
20
0
0 2 4 6 8 10
SV0 mass sum [GeV]
Figure I.2: Construction of templates for b-contribution in the SV0 mass sum distribution from
simulation for the measurement of the dijet cross section as a function of dijet mass.
240
EEvveennttss  //  ((00..66  GGeeVV)) EEvveennttss  //  ((00..66  GGeeVV)) EEvveennttss  //  ((00..66  GGeeVV))
EEvveennttss  //  ((00..66  GGeeVV)) EEvveennttss  //  ((00..66  GGeeVV)) EEvveennttss  //  ((00..66  GGeeVV)) EEvveennttss  //  ((00..66  GGeeVV))
EEvveennttss  //  ((00..66  GGeeVV)) EEvveennttss  //  ((00..66  GGeeVV)) EEvveennttss  //  ((00..66  GGeeVV))
25000
non-b template Fit: non-b template Fit: 10000 non-b template Fit:50000
110 GeV < M < 160 GeV Mean: 1.985 ± 0.003 20000 160 GeV < M < 210 GeV Mean: 2.600 ± 0.004 210 GeV < M < 260 GeV Mean: 2.662 ± 0.008
40000 Sigma: 0.451 ± 0.001 Sigma: 0.935 ± 0.003 8000 Sigma: 1.083 ± 0.006
Pythia 15000 Pythia Pythia
30000 6000
10000
20000 4000
10000 5000 2000
0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10
SV0 mass sum [GeV] SV0 mass sum [GeV] SV0 mass sum [GeV]
12000
non-b template Fit: non-b template Fit: 1400 non-b template Fit:
7000
10000 260 GeV < M < 310 GeV Mean: 2.360 ± 0.008 310 GeV < M < 370 GeV Mean: 1.619 ± 0.006 1200 370 GeV < M < 440 GeV Mean: 2.521 ± 0.019
Sigma: 0.898 ± 0.006 6000 Sigma: 0.274 ± 0.003 Sigma: 1.045 ± 0.014
8000 1000
Pythia 5000 Pythia Pythia
6000 4000 800
3000 600
4000
2000 400
2000
1000 200
0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10
SV0 mass sum [GeV] SV0 mass sum [GeV] SV0 mass sum [GeV]
1000 non-b template Fit: 140800 non-b template Fit: non-b template Fit:
440 GeV < M < 510 GeV Mean: 2.282 ± 0.025 700 510 GeV < M < 590 GeV Mean: 2.493 ± 0.026 120 590 GeV < M < 670 GeV Mean: 1.884 ± 0.059
800 Sigma: 0.885 ± 0.019 Sigma: 0.954 ± 0.020 Sigma: 0.496 ± 0.031
600 100
Pythia 500 Pythia Pythia600 80
400
400 60300
40
200
200
100 20
0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10
SV0 mass sum [GeV] SV0 mass sum [GeV] SV0 mass sum [GeV]
120
non-b template Fit:
100 670 GeV < M < 760 GeV Mean: 1.843 ± 0.059
Sigma: 0.383 ± 0.029
80
Pythia
60
40
20
0 2 4 6 8 10
SV0 mass sum [GeV]
Figure I.3: Construction of templates for non-b contribution in the SV0 mass sum distribution
from simulation for the measurement of the dijet cross section as a function of dijet mass.
60000
35000 b-template Fit: b-template Fit: b-template Fit:35000
30000 1.6 rad < ∆φ < 2.5 rad Mean: 3.967 ± 0.004
50000 2.5 rad < ∆φ < 2.8 rad Mean: 4.121 ± 0.003 2.8 rad < ∆φ < 2.9 rad Mean: 3.999 ± 0.005
Sigma: 1.244 ± 0.003 Sigma: 1.284 ± 0.002 30000 Sigma: 1.158 ± 0.002
25000 40000 25000
Pythia Pythia Pythia
20000 30000 20000
15000 15000
20000
10000 10000
10000
5000 5000
0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10
SV0 mass sum [GeV] SV0 mass sum [GeV] SV0 mass sum [GeV]
b-template Fit: 60000 b-template Fit:
40000
2.9 rad < ∆φ < 3.0 rad Mean: 3.853 ± 0.004 50000 3.0 rad < ∆φ < 3.1 rad Mean: 4.012 ± 0.00335000
Sigma: 1.260 ± 0.003 Sigma: 1.249 ± 0.002
30000 40000
Pythia Pythia
25000
20000 30000
15000 20000
10000
10000
5000
0 2 4 6 8 10 0 2 4 6 8 10
SV0 mass sum [GeV] SV0 mass sum [GeV]
Figure I.4: Construction of templates for b-contribution in the SV0 mass sum distribution from
simulation for the measurement of the dijet cross section as a function of ∆φ.
241
EEvveennttss  //  ((00..66  GGeeVV)) EEvveennttss  //  ((00..66  GGeeVV)) EEvveennttss  //  ((00..66  GGeeVV)) EEvveennttss  //  ((00..66  GGeeVV))
EEvveennttss  //  ((00..66  GGeeVV))
EEvveennttss  //  ((00..66  GGeeVV)) EEvveennttss  //  ((00..66  GGeeVV)) EEvveennttss  //  ((00..66  GGeeVV)) EEvveennttss  //  ((00..66  GGeeVV)) EEvveennttss  //  ((00..66  GGeeVV))
EEvveennttss  //  ((00..66  GGeeVV))
EEvveennttss  //  ((00..66  GGeeVV)) EEvveennttss  //  ((00..66  GGeeVV)) EEvveennttss  //  ((00..66  GGeeVV)) EEvveennttss  //  ((00..66  GGeeVV))
I Appendix: Correction factors and systematics
4500
non-b template Fit: non-b template Fit: non-b template Fit:
4000 30000 14000
1.6 rad < ∆φ < 2.5 rad Mean: 2.445 ± 0.659 2.5 rad < ∆φ < 2.8 rad Mean: 2.741 ± 0.429 2.8 rad < ∆φ < 2.9 rad Mean: 2.314 ± 0.428
3500
Sigma: 1.232 ± 0.253 25000 Sigma: 0.809 ± 0.137
12000 Sigma: 0.802 ± 0.295
3000 10000
Pythia Pythia Pythia
2500 20000
8000
2000 15000
6000
1500
10000
1000 4000
500 5000 2000
0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10
SV0 mass sum [GeV] SV0 mass sum [GeV] SV0 mass sum [GeV]
18000 non-b template Fit: 35000 non-b template Fit:
16000 2.9 rad < ∆φ < 3.0 rad Mean: 2.541 ± 0.578 30000 3.0 rad < ∆φ < 3.1 rad Mean: 1.925 ± 0.401
14000 Sigma: 1.106 ± 0.318 Sigma: 0.379 ± 0.143
25000
12000 Pythia Pythia
10000 20000
8000 15000
6000
10000
4000
2000 5000
0 2 4 6 8 10 0 2 4 6 8 10
SV0 mass sum [GeV] SV0 mass sum [GeV]
Figure I.5: Construction of templates for non-b contribution in the SV0 mass sum distribution
from simulation for the measurement of the dijet cross section as a function of ∆φ.
χ bin b-tagging Total Fractional tot.
purity uncertainty uncertainty [%]
110 GeV   M   370 GeV
1-3 0.67 0.17 25
3-5 0.48 0.27 56
5-10 0.58 0.18 31
10-30 0.76 0.18 24
370 GeV   M   850 GeV
1-3 0.38 0.26 17
3-5 0.34 0.24 55
5-10 0.36 0.19 27
10-30 0.38 0.13 29
Table I.4: The b-tagging purity and systematic uncertainty as a function of χ.
242
EEvveennttss  //  ((00..66  GGeeVV))
EEvveennttss  //  ((00..66  GGeeVV))
EEvveennttss  //  ((00..66  GGeeVV))
EEvveennttss  //  ((00..66  GGeeVV))
EEvveennttss  //  ((00..66  GGeeVV))
90000 b-template Fit: 45000 b-template Fit:
80000 40000
1.0 < χ < 3.0 Mean: 4.010 ± 0.510 3.0 < χ < 5.0 Mean: 3.950 ± 0.483
70000 Sigma: 1.328 ± 0.172 35000 Sigma: 1.206 ± 0.228
60000 30000
Pythia Pythia
50000 25000
40000 20000
30000 15000
20000 10000
10000 5000
0 2 4 6 8 10 0 2 4 6 8 10
SV0 mass sum [GeV] SV0 mass sum [GeV]
35000 b-template Fit: 20000 b-template Fit:
18000
30000 5.0 < χ < 10.0 Mean: 4.259 ± 0.507 10.0 < χ < 30.0 Mean: 3.797 ± 0.510
16000
Sigma: 1.335 ± 0.315 Sigma: 1.247 ± 0.247
25000 14000
Pythia Pythia
20000 12000
10000
15000 8000
10000 6000
4000
5000
2000
0 2 4 6 8 10 0 2 4 6 8 10
SV0 mass sum [GeV] SV0 mass sum [GeV]
b-template Fit: b-template Fit:
500
1.0 < χ < 3.0 Mean: 4.019 ± 0.500 250 3.0 < χ < 5.0 Mean: 3.630 ± 0.464
400 Sigma: 1.378 ± 0.273 Sigma: 1.210 ± 0.187
200
Pythia Pythia
300 150
200 100
100 50
0 2 4 6 8 10 0 2 4 6 8 10
SV0 mass sum [GeV] SV0 mass sum [GeV]
1800
800 b-template Fit: b-template Fit:
1600
700 5.0 < χ < 10.0 Mean: 3.745 ± 0.424 10.0 < χ < 30.0 Mean: 3.629 ± 0.419
1400
600 Sigma: 0.956 ± 0.145 Sigma: 0.902 ± 0.152
1200
500 Pythia Pythia1000
400 800
300 600
200 400
100 200
0 2 4 6 8 10 0 2 4 6 8 10
SV0 mass sum [GeV] SV0 mass sum [GeV]
Figure I.6: Construction of templates for b-contribution in the SV0 mass sum distribution from
simulation for the measurement of the dijet cross section as a function of χ for the lower and
higher mass region.
243
EEvveennttss  //  ((00..66  GGeeVV)) EEvveennttss  //  ((00..66  GGeeVV)) EEvveennttss  //  ((00..66  GGeeVV)) EEvveennttss  //  ((00..66  GGeeVV))
EEvveennttss  //  ((00..66  GGeeVV)) EEvveennttss  //  ((00..66  GGeeVV)) EEvveennttss  //  ((00..66  GGeeVV)) EEvveennttss  //  ((00..66  GGeeVV))
I Appendix: Correction factors and systematics
30000
non-b template Fit: non-b template Fit:
25000 1.0 < χ < 3.0 Mean: 2.476 ± 0.478 10000 3.0 < χ < 5.0 Mean: 3.010 ± 0.489
Sigma: 1.025 ± 0.205 Sigma: 1.134 ± 0.216
20000 8000
Pythia Pythia
15000 6000
10000 4000
5000 2000
0 2 4 6 8 10 0 2 4 6 8 10
SV0 mass sum [GeV] SV0 mass sum [GeV]
18000 non-b template Fit: 9000 non-b template Fit:
16000 5.0 < χ < 10.0 Mean: 2.544 ± 0.450 8000 10.0 < χ < 30.0 Mean: 2.477 ± 0.453
14000 Sigma: 0.946 ± 0.226 7000 Sigma: 0.899 ± 0.258
12000 Pythia 6000 Pythia
10000 5000
8000 4000
6000 3000
4000 2000
2000 1000
0 2 4 6 8 10 0 2 4 6 8 10
SV0 mass sum [GeV] SV0 mass sum [GeV]
450
350 non-b template Fit: non-b template Fit:
400
300 1.0 < χ < 3.0 Mean: 2.716 ± 0.574 3.0 < χ < 5.0 Mean: 2.436 ± 0.625
Sigma: 1.262 ± 0.275 350 Sigma: 1.200 ± 0.201
250 300
Pythia Pythia
200 250
150 200
150
100
100
50 50
0 2 4 6 8 10 0 2 4 6 8 10
SV0 mass sum [GeV] SV0 mass sum [GeV]
400
non-b template Fit: non-b template Fit:
350 1200
5.0 < χ < 10.0 Mean: 2.435 ± 0.528 10.0 < χ < 30.0 Mean: 1.952 ± 0.385
300 Sigma: 0.555 ± 0.270 1000 Sigma: 0.319 ± 0.160
250 Pythia 800 Pythia
200
600
150
400
100
50 200
0 2 4 6 8 10 0 2 4 6 8 10
SV0 mass sum [GeV] SV0 mass sum [GeV]
Figure I.7: Construction of templates for non-b contribution in the SV0 mass sum distribution
from simulation for the measurement of the dijet cross section as a function of χ for the lower
and higher mass region.
244
EEvveennttss  //  ((00..66  GGeeVV)) EEvveennttss  //  ((00..66  GGeeVV)) EEvveennttss  //  ((00..66  GGeeVV)) EEvveennttss  //  ((00..66  GGeeVV))
EEvveennttss  //  ((00..66  GGeeVV)) EEvveennttss  //  ((00..66  GGeeVV)) EEvveennttss  //  ((00..66  GGeeVV)) EEvveennttss  //  ((00..66  GGeeVV))
50 110 GeV < M < 160 GeV
80 160 GeV < M < 210 GeV 80 210 GeV < M < 260 GeV
70 70
40 χ2/DoF: 18.6/23 60 χ2/DoF: 20.8/23 60 χ2/DoF: 25.2/23
P : 0.89±0.06 50 P : 0.72±0.05 50 P : 0.60±0.06
30 bb bb bb
Data 40 Data 40 Data
20 b-template 30 b-template 30 b-template
non-b template 20 non-b template 20 non-b template
10
10 10
00 2 4 6 8 10 12 14 00 2 4 6 8 10 12 14 00 2 4 6 8 10 12 14
3 3 3
2 SV0 mass sum [GeV] 2 SV0 mass sum [GeV] 2 SV0 mass sum [GeV]
1 1 1
0 0 0
0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14
SV0 mass sum [GeV] SV0 mass sum [GeV] SV0 mass sum [GeV]
80
70 260 GeV < M < 310 GeV 100 310 GeV < M < 370 GeV 80 370 GeV < M < 440 GeV
70
60 χ2/DoF: 27.3/23 80 χ2/DoF: 69.0/23 60 χ2/DoF: 69.9/23
50 P : 0.59±0.05 P : 0.65±0.04 50 P : 0.70±0.06bb 60 bb bb40
Data Data 40 Data
30 b-template 40 b-template 30 b-template
20 non-b template non-b template 20 non-b template
20
10 10
00 2 4 6 8 10 12 14 00 2 4 6 8 10 12 14 00 2 4 6 8 10 12 14
3 3 3
2 SV0 mass sum [GeV] 2 SV0 mass sum [GeV] 2 SV0 mass sum [GeV]
1 1 1
0 0 0
0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14
SV0 mass sum [GeV] SV0 mass sum [GeV] SV0 mass sum [GeV]
70 35
60 440 GeV < M < 510 GeV
60 510 GeV < M < 590 GeV 30 590 GeV < M < 670 GeV
50
50 χ2/DoF: 22.2/23 χ2/DoF: 28.9/23 25 χ2/DoF: 16.2/23
40 P : 0.54±0.07
40 P : 0.50±0.06 P : 0.65±0.11
bb bb 20 bb
30 Data 30 Data 15 Data
b-template 20 b-template b-template20 non-b template non-b template 10 non-b template
10 10 5
00 2 4 6 8 10 12 14 00 2 4 6 8 10 12 14 00 2 4 6 8 10 12 14
3 3 3
2 SV0 mass sum [GeV] 2 SV0 mass sum [GeV] 2 SV0 mass sum [GeV]
1 1 1
0 0 0
0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14
SV0 mass sum [GeV] SV0 mass sum [GeV] SV0 mass sum [GeV]
24
22 670 GeV < M < 760 GeV
20
18 2
16 χ /DoF: 6.8/23
14 P : 0.80±0.15bb
12
10 Data
8 b-template
6 non-b template
4
2
00 2 4 6 8 10 12 14
3
2 SV0 mass sum [GeV]
1
0
0 2 4 6 8 10 12 14
SV0 mass sum [GeV]
Figure I.8: Final template fits on data using a binned maximum likelihood fit (TFractionFitter)
in bins of dijet mass. The uncertainty on Pbb̄ denotes the statistical uncertainty from the likelihood
fit. DoF stands for the number of degrees of freedom. The single contributions are drawn stacked
on top of each other.
245
Data / MC EEEEnnnnttttrrrriiiieeeessss    ////    ((((0000....6666    GGGGeeeeVVVV)))) Data / MC EEEEnnnnttttrrrriiiieeeessss    ////    ((((0000....6666    GGGGeeeeVVVV)))) Data / MC EEEEnnnnttttrrrriiiieeeessss    ////    ((((0000....6666    GGGGeeeeVVVV))))
Data / MC EEEEnnnnttttrrrriiiieeeessss    ////    ((((0000....6666    GGGGeeeeVVVV)))) Data / MC EEEEnnnnttttrrrriiiieeeessss    ////    ((((0000....6666    GGGGeeeeVVVV)))) Data / MC EEEEnnnnttttrrrriiiieeeessss    ////    ((((0000....6666    GGGGeeeeVVVV)))) Data / MC EEEEnnnnttttrrrriiiieeeessss    ////    ((((0000....6666    GGGGeeeeVVVV))))
Data / MC EEEEnnnnttttrrrriiiieeeessss    ////    ((((0000....6666    GGGGeeeeVVVV)))) Data / MC EEEEnnnnttttrrrriiiieeeessss    ////    ((((0000....6666    GGGGeeeeVVVV)))) Data / MC EEEEnnnnttttrrrriiiieeeessss    ////    ((((0000....6666    GGGGeeeeVVVV))))
I Appendix: Correction factors and systematics
100
45 1.6 rad < ∆φ < 2.5 rad 2.5 rad < ∆φ < 2.8 rad 70 2.8 rad < ∆φ < 2.9 rad
40 80
35 60χ2/DoF: 28.0/23 χ2/DoF: 22.1/23 χ2/DoF: 15.6/23
30 P : 0.73±0.08 60 P : 0.59±0.05 50 P : 0.60±0.05bb bb bb
25 40
20 Data 40 Data Data
15 b-template b-template
30 b-template
10 non-b template non-b template
20 non-b template
20
5 10
0 0 0
0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14
3 3 3
2 SV0 mass sum [GeV] 2 SV0 mass sum [GeV] 2 SV0 mass sum [GeV]
1 1 1
0 0 0
0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14
SV0 mass sum [GeV] SV0 mass sum [GeV] SV0 mass sum [GeV]
120 2.9 rad < ∆φ < 3.0 rad 200180 3.0 rad < ∆φ < 3.1 rad
100
χ2 160/DoF: 55.6/23 χ2/DoF: 36.4/23
80 140P : 0.57±0.05 P : 0.59±0.03
bb 120 bb
60 Data 100 Data
40 b-template
80 b-template
non-b template 60 non-b template
20 40
20
0 0
0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14
3 3
2 SV0 mass sum [GeV] 2 SV0 mass sum [GeV]
1 1
0 0
0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14
SV0 mass sum [GeV] SV0 mass sum [GeV]
Figure I.9: Final template fits on data using a binned maximum likelihood fit (TFractionFitter)
in bins of ∆φ. The uncertainty on Pbb̄ denotes the statistical uncertainty from the likelihood fit.
DoF stands for the number of degrees of freedom. The single contributions are drawn stacked on
top of each other.
160 90 501.0 < χ < 3.0 80 3.0 < χ < 5.0 5.0 < χ < 10.0
140 110 GeV < M < 370 GeV 110 GeV < M < 370 GeV 40 110 GeV < M < 370 GeV
120 χ2
70
/DoF: 38.5/23 χ2/DoF: 35.4/23 χ2/DoF: 23.9/23
100 P : 0.67±0.04
60 P : 0.50±0.08 P : 0.59±0.07
bb 50 bb 30 bb
80 Data 40 Data Data
60 b-template 30 b-template
20 b-template
40 non-b template 20 non-b template non-b template10
20 10
0 0 0
0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14
3 3 3
2 SV0 mass sum [GeV] 2 SV0 mass sum [GeV] 2 SV0 mass sum [GeV]
1 1 1
0 0 0
0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14
SV0 mass sum [GeV] SV0 mass sum [GeV] SV0 mass sum [GeV]
100
14 10.0 < χ < 30.0 1.0 < χ < 3.0 60 3.0 < χ < 5.0
12 110 GeV < M < 370 GeV 80 370 GeV < M < 850 GeV 50 370 GeV < M < 850 GeV
χ2/DoF: 22.2/23 χ2/DoF: 32.9/23 χ2/DoF: 29.4/23
10 P : 0.75±0.12 60 P : 0.39±0.06 40 P : 0.35±0.09bb bb bb
8
6 Data 40 Data
30 Data
b-template b-template 20 b-template
4 non-b template non-b template non-b template
20
2 10
0 0 0
0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14
3 3 3
2 SV0 mass sum [GeV] 2 SV0 mass sum [GeV] 2 SV0 mass sum [GeV]
1 1 1
0 0 0
0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14
SV0 mass sum [GeV] SV0 mass sum [GeV] SV0 mass sum [GeV]
45 5.0 < χ < 10.0 30 10.0 < χ < 30.0
40 370 GeV < M < 850 GeV 25 370 GeV < M < 850 GeV35 χ2/DoF: 27.6/23 χ2/DoF: 18.4/23
30 P : 0.37±0.10 20 P : 0.38±0.11
bb bb
25
20 Data 15 Data
15 b-template 10 b-template
10 non-b template non-b template
5 5
0 0
0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14
3 3
2 SV0 mass sum [GeV] 2 SV0 mass sum [GeV]
1 1
0 0
0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14
SV0 mass sum [GeV] SV0 mass sum [GeV]
Figure I.10: Final template fits on data using a binned maximum likelihood fit (TFractionFitter)
in bins of χ. The uncertainty on Pbb̄ denotes the statistical uncertainty from the likelihood fit.
DoF stands for the number of degrees of freedom. The single contributions are drawn stacked on
top of each other.
246
Data / MC EEEEnnnnttttrrrriiiieeeessss    ////    ((((0000....6666    GGGGeeeeVVVV)))) Data / MC EEEEnnnnttttrrrriiiieeeessss    ////    ((((0000....6666    GGGGeeeeVVVV)))) Data / MC EEEEnnnnttttrrrriiiieeeessss    ////    ((((0000....6666    GGGGeeeeVVVV))))
Data / MC EEEEnnnnttttrrrriiiieeeessss    ////    ((((0000....6666    GGGGeeeeVVVV)))) Data / MC EEEEnnnnttttrrrriiiieeeessss    ////    ((((0000....6666    GGGGeeeeVVVV))))
Data / MC EEEEnnnnttttrrrriiiieeeessss    ////    ((((0000....6666    GGGGeeeeVVVV)))) Data / MC EEEEnnnnttttrrrriiiieeeessss    ////    ((((0000....6666    GGGGeeeeVVVV)))) Data / MC EEEEnnnnttttrrrriiiieeeessss    ////    ((((0000....6666    GGGGeeeeVVVV))))
Data / MC EEEEnnnnttttrrrriiiieeeessss    ////    ((((0000....6666    GGGGeeeeVVVV)))) Data / MC EEEEnnnnttttrrrriiiieeeessss    ////    ((((0000....6666    GGGGeeeeVVVV))))
Data / MC EEEEnnnnttttrrrriiiieeeessss    ////    ((((0000....6666    GGGGeeeeVVVV)))) Data / MC EEEEnnnnttttrrrriiiieeeessss    ////    ((((0000....6666    GGGGeeeeVVVV)))) Data / MC EEEEnnnnttttrrrriiiieeeessss    ////    ((((0000....6666    GGGGeeeeVVVV))))
35000 ∫Ldt = 34 pb-1 Data 40000 ∫Ldt = 34 pb-1 Data ∫Ldt = 34 pb-1 DataPythia: b-jets Pythia: b-jets Pythia: b-jets
30000 Pythia: c-jets 35000 Pythia: c-jets 25000 Pythia: c-jets
Pythia: light jets Pythia: light jets Pythia: light jets
MC stat. unc. 30000 MC stat. unc. MC stat. unc.25000 20000
25000
20000
20000 15000
15000
15000 10000
10000
10000
5000 50005000
0 0 0
0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10
SV0 mass of b-tagged jets (double tag,2 tracks) [GeV] SV0 mass of b-tagged jets (double tag,3 tracks) [GeV] SV0 mass of b-tagged jets (double tag,4 tracks) [GeV]
12000 ∫Ldt = 34 pb-1
12000
Data ∫Ldt = 34 pb-1 Data Ldt = 34 pb-1 DataPythia: b-jets Pythia: b-jets 4000 ∫ Pythia: b-jets
Pythia: c-jets 10000 Pythia: c-jets Pythia: c-jets
10000 Pythia: light jets Pythia: light jets 3500 Pythia: light jets
MC stat. unc. MC stat. unc. MC stat. unc.
8000 30008000
2500
6000 6000 2000
4000 4000 1500
1000
2000 2000
500
0 0 0
0 2 4 6 8 10 0 2 4 6 8 10 0 2 4 6 8 10
SV0 mass of b-tagged jets (double tag,5 tracks) [GeV] SV0 mass of b-tagged jets (double tag,6 tracks) [GeV] SV0 mass of b-tagged jets (double tag,7 tracks) [GeV]
4000 ∫Ldt = 34 pb-1 DataPythia: b-jets
Pythia: c-jets
3500 Pythia: light jets
MC stat. unc.
3000
2500
2000
1500
1000
500
0
0 2 4 6 8 10
SV0 mass of b-tagged jets (double tag,at least 8 tracks) [GeV]
Figure I.11: Distribution of the invariant mass of the charged tracks in bins of track multiplicity
in the secondary vertex (SV0 mass) found in the b-tagged jets in events in which both leading jets
are b-tagged. Simulated data is normalised to the number of b-tagged jets in data. The single
contributions are drawn stacked on top of each other.
247
NNuummbbeerr  oojj  jjeettss NNuummbbeerr  oojj  jjeettss
NNuummbbeerr  oojj  jjeettss NNuummbbeerr  oojj  jjeettss NNuummbbeerr  oojj  jjeettss
NNuummbbeerr  oojj  jjeettss NNuummbbeerr  oojj  jjeettss
I Appendix: Correction factors and systematics
1 2.4
10-1 ∫Ldt = 34 pb-1 Inclusive jets: 2.2 Pythia
10-2 Data
10-3 2Herwig++ Herwig++
10-4 1.8
10-5 1.6
10-6
10-7
1.4
10-8 1.2
10-9 1
10-10 0.8
0 200 400 600 800 1000 1200 1400 1600 1800 0 100 200 300 400 500 600 700
2 1
1 0.5
0 0
0 200 400 600 800 1000 1200 1400 1600 1800 0 100 200 300 400 500 600 700
p  (leading jets) [GeV]
T bb dijet mass [GeV]
(a) (b)
Figure I.12: (a) The leading jet pT distribution compared to Herwig++ simulation on the basis
of Fig. 8.1(a) and (b) the corresponding unfolding correction CHerwig  unf compared to Pythia on
the basis of Fig. 9.20.
0.07
Pythia: b-jets
0.06 p:1, q: 0.33 p:-0.5, q: 0.33
0.05 p:1, q: 1.00 p:-0.5, q: 1.00
p:1, q: 3.00 p:-0.5, q: 3.00
0.04
0.03
0.02
0.01
0
-0.01
-0.02
0 100 200 300 400 500 600 700
bb dijet mass [GeV]
Figure I.13: The resulting effect on the unfolding correction factors from the shape variations
from the function Eq. 9.8 for the bb̄ cross section as a function of dijet mass. The variations are
fitted and the deviation to the nominal unfolding correction symmetrised.
248
Data/MC 11//NN  ddNN//ddpp   [[GGeeVV
--11]]
TT
nom weightCunf -Cunf
Pythia Herwig
C /C UUUnnnfffooollldddiiinnnggg   cccooorrrrrreeeccctttiiiooonnn   CCCunf unf uuunnnfff
Dijet mass bin [GeV] Cunf Sys. Fractional
uncertainty sys.
uncertainty
[%]
110-160 1.24 0.06 5
160-210 1.24 0.06 4
210-260 1.24 0.05 4
260-310 1.24 0.05 4
310-370 1.25 0.05 4
370-440 1.25 0.05 4
440-510 1.25 0.04 4
510-590 1.25 0.05 4
590-670 1.25 0.05 4
670-760 1.26 0.05 4
Table I.5: The unfolding correction and systematic uncertainty as a function of dijet mass.
∆φ bin [rad] Cunf Stat. Fractional sys.
error uncertainty [%]
π{2-2 1.30 0.08 1.8
2.5-3 1.31 0.06 1.3
2.8-3 1.26 0.08 7.1
2.9-3 1.27 0.07 4.7
3.0-π 1.22 0.07 7.1
Table I.6: The unfolding correction and systematic uncertainty as a function of ∆φ.
249
I Appendix: Correction factors and systematics
χ bin Cunf Stat. error Fractional sys.
uncertainty [%]
110 GeV   M   370 GeV
1-3 1.21 0.04 0.2
3-5 1.31 0.07 0.7
5-10 1.37 0.15 0.6
10-30 1.54 0.15 0.6
370 GeV   M   850 GeV
1-3 1.19 0.05 0.7
3-5 1.33 0.11 2.0
5-10 1.41 0.16 0.7
10-30 1.33 0.10 1.6
Table I.7: The unfolding correction and systematic uncertainty as a function of χ.
250
Dijet mass bin [GeV] Cleaning efficiency Statistical error Fractional sys.
uncer-
tainty[%]
110-160 0.96 0.00 +0.3-1.0
160-210 0.97 0.00 +0.3-0.9
210-260 0.97 0.00 +0.3-1.0
260-310 0.98 0.00 +0.3-1.0
310-370 0.99 0.00 +0.3-1.0
370-440 0.99 0.00 +0.2-1.0
440-510 1.00 0.00 +0.1-1.0
510-590 1.00 0.00 +0.1-0.9
590-670 1.00 0.00 +0.0-0.7
670-760 1.00 0.00 +0.0-0.6
Table I.8: The jet cleaning efficiency and systematic uncertainty as a function of dijet mass for
inclusive jets.
251
I Appendix: Correction factors and systematics
Dijet mass bin [GeV] Unfolding Statistical error Fractional sys.
correction uncertainty
[%]
110-160 0.99 0.00 1.8
160-210 0.99 0.01 1.8
210-260 0.99 0.01 1.8
260-310 1.02 0.01 1.8
310-370 1.00 0.01 2.1
370-440 0.99 0.01 1.9
440-510 1.01 0.01 2.0
510-590 1.00 0.01 2.3
590-670 1.00 0.01 2.2
670-760 1.00 0.01 2.2
Table I.9: The unfolding correction and systematic uncertainty as a function of dijet mass for
inclusive jets.
252
J Appendix: Cross section
measurement
Dijet mass bin Central value Statistical error Systematic error
[GeV] [pb GeV1] [pb GeV1] [pb GeV1]
110-160 341.69 6.55 +115.82- 131.44
160-210 122.36 2.94 +52.23- 42.82
210-260 42.90 1.48 +21.94- 18.04
260-310 19.29 0.82 +9.18- 6.74
310-370 9.28 0.49 +4.90- 3.44
370-440 5.02 0.25 +2.80- 1.94
440-510 1.24 0.10 +0.73- 0.48
510-590 0.44 0.03 +0.27- 0.17
590-670 0.20 0.01 +0.14- 0.09
670-760 0.12 0.01 +0.08- 0.05
Table J.1: Results from the dijet cross section measurement of b-jets as a function of invariant
dijet mass.
∆φ bin [rad] Central value Statistical error Systematic error
[rad1] [rad1] [rad1]
π{2-2.5 0.06 0.01 +0.02- 0.02
2.5-2.8 0.60 0.09 +0.24- 0.22
2.8-2.9 1.34 0.25 +0.47- 0.42
2.9-3.0 1.94 0.30 +0.76- 0.70
3.0-3.1 2.90 0.38 +0.99- 0.89
3.1-π 3.56 0.87 +1.47- 1.36
Table J.2: Results from the dijet cross section measurement of b-jets as a function of ∆φ.
253
J Appendix: Cross section measurement
χ bin Central value [GeV1] Statistical error Systematic error
[GeV1] [GeV1]
5
1-3 65.5  105 5.9  105 +23.0  10
- 20.6  105
5
3-5 47.0  105 5.5  105 +29.2  10
- 28.1  105
5
5-10 23.3  105 3.7  105 +9.3  10
- 8.6  105
5
10-30 2.1  105 0.5  105 +0.8  10
- 0.7  105
Table J.3: Results from the cross section measurement as a function of χ for
110 GeV   M   370 GeV.
χ bin Central value [GeV1] Statistical error Systematic error
[GeV1] [GeV1]
1-3 11.3  105 1.2  105 +12.1  105
- 8.8  105
3-5 10.9  105 1.7  105 +10.2  105
- 8.5  105
5
5-10 10.8  105 2.1  105 +9.1  10
- 6.7  105
10-30 5.5  105  51.3  105 +3.0  10
- 2.4  105
Table J.4: Results from the cross section measurement as a function of χ for
370 GeV   M   850 GeV.
Dijet mass bin Central value Statistical error Systematic error
[GeV] [pb GeV1] [pb GeV1] [pb GeV1]
110-160 29706.92 216.75 +4362.04- 3762.42
160-210 13207.69 165.69 +1874.75- 1753.06
210-260 6039.29 73.98 +880.88- 790.08
260-310 3041.64 49.82 +449.45- 419.44
310-370 1460.01 30.89 +236.41- 196.89
370-440 621.58 14.82 +85.67- 82.63
440-510 279.33 7.00 +39.31- 34.05
510-590 128.07 3.24 +17.44- 15.60
590-670 59.03 1.61 +8.72- 8.04
670-760 28.23 0.76 +3.88- 3.65
Table J.5: Results from the dijet cross section measurement of inclusive jets as a function of
invariant dijet mass.
254
Dijet mass bin Central value Statistical error Systematic error
[GeV] [pb GeV1] [pb GeV1] [pb GeV1]
3
110-160 11.5  103 0.2  103 +3.5  10
- 4.2  103
160-210 9.3  103 0.3  103 +3.7  103
- 3.0  103
210-260 7.1  103 0.3  103 +3.5  103
- 2.9  103
260-310 6.3  103 0.3  103 +2.9  103
- 2.1  103
3
310-370 6.4  103 0.4  103 +3.2  10
- 2.2  103
370-440 8.1  103 0.4  103 +4.4  103
- 3.0  103
3
440-510 4.4  103 0.4  103 +2.6  10
- 1.7  103
3
510-590 3.4  103 0.2  103 +2.1  10
- 1.3  103
3
590-670 3.5  103 0.2  103 +2.3  10
- 1.5  103
3
670-760 4.3  103 0.3  103 +2.8  10
- 1.6  103
Table J.6: Results from the dijet cross section ratio measurement of b-jets and inclusive jets as
a function of invariant dijet mass.
255
K Appendix: NLO calculation
1.2
Simulation: Bowler (high)
Pythia (default) Bowler (low)
1.1 Perugia (soft) Peterson
Perugia (hard) Herwig++
1
0.9
0.8
110 GeV < M < 370 GeV
0.7
Systematic uncertainty
0.6
5 10 15 20 25 30
χ
Figure K.1: The non-perturbative corrections as a function of the angular variable χ in the
mass range 110 GeV   M   370 GeV with resulting uncertainty envelop around the default
Pythia correction.
L Appendix: Resonance search
Selection p0 p1 p2 p3
Full spectrum 1.61010  2.6  1010 5.51011  8.1 13.31.1 1.40.2
Full spectrum with 1.11010  2.6  1010 6.21011  31.8 11.71.5 1.00.2
|∆y|   1
Spectrum with 1.61010  2.3  1010 13.11011  11.2 21.51.6 3.80.5
L1 J95
Table L.1: Summary of the background fits for the BumpHunter on different event selections.
256
PPNNPP
0.18
0.16 Pythia:
0.14 Inclusive jets
0.12
Fit
0.1
0.08
0.06
0.04
0.02
0 200 400 600 800 1000 1200 1400 1600
dijet mass [GeV]
Figure L.1: Relative resolution as a function of dijet mass determined with the help of Pythia
QCD samples.
s=7 TeV
102 Pythia: Z' signal
(σ × BR)/pb
10
Acceptance
1
10-1
10-2
10-3 200 400 600 800 1000
signal mass [GeV]
Figure L.2: The acceptance and the product of cross section and branching ratio for each
resonance mass of a Z 1 boson are presented.
257
arbitrary units σ(M)/M
L Appendix: Resonance search
Generated Z 1 mass Reconstructed Z 1 mass SV0 b-tagging
efficiency
220 175.11 0.34
310 242.134 0.37
420 327.659 0.37
520 403.999 0.36
620 480.782 0.34
720 555.921 0.32
800 616.385 0.30
930 713.374 0.26
1020 780.272 0.24
1120 847.952 0.22
1300 969.715 0.18
1500 1098.49 0.15
Table L.2: Summary of the generated and corresponding reconstructed mass of a Z 1 boson and
of the SV0 b-tagging efficiency obtained by Toy-MC.
258
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