Prototype development for a new readout
of the CB/A2 setup
and
Analysis of the relative branching fraction
of the η′ → ωγ decay
Dissertation
zur Erlangung des Grades
„Doktor der Naturwissenschaften“
am Fachbereich Physik, Mathematik und Informatik
der Johanndes Gutenberg-Universität
in Mainz
Andreas Neiser
geboren in Boppard
Mainz, August 2017
Erster Berichterstatter:
Zweiter Berichterstatter:
Datum der mündlichen Prüfung: 9. November 2018
ii
Abstract
The A2 collaboration at the electron accelerator MAMI in Mainz uses an
energy-tagged photon beam to produce light mesons off the nucleon to study
quantum chromodynamics, the underlying theory of the strong interaction, in
the low-energy regime below 1GeV. The A2 detector system mainly consists
of the 4π calorimeter Crystal Ball (CB) and the TAPS calorimeter in forward
direction, which are ideally suited to detect final state photons in the given
energy range. In 2014, three dedicated beam-times for the production of η′
mesons off unpolarized protons yielded a data sample of (5.12± 0.19)× 106
η′ mesons within an incident photon energy range of Eγ = 1.42 . . . 1.58GeV.
This thesis consists of two parts: First, the prototype development to
assess possible upgrades of the existing data acquisition system and, second,
the analysis of the branching fraction of the decay η′ → ωγ relative to the
reference channel η′ → γγ. To achieve the results, numerous improvements
and innovations related to deployed hardware and software were developed
and implemented.
The prototype development for the CB/A2 experiment setup is based on
the GSI TRB3 platform, primarily consisting of a multi-purpose 4 + 1 FPGA
printed circuit board. In this thesis, a feature extraction firmware for an already
existing sampling analog-to-digital converter extension board is developed and
successfully tested at the CB calorimeter, showing a sufficiently precise time and
energy measurement at the limit of the given analog signal quality. Additionally,
the applicability of a charge-to-time conversion front-end is investigated for
other components of the A2 detector system.
The pseudoscalar-vector-gamma decay η′ → ωγ serves as an input to effective
field theories of the strong interaction, in particular concerning η-η′-mixing
and the consistent inclusion of vector mesons. In this thesis, a new analysis
framework has been developed providing advanced calibration and tuning
methods including kinematic fitting for photo-production experiments. The
final result BR(η′ → ωγ) = (1.82 ± 0.19stat) × 10−2 is inconsistent with the
current PDG world average at 4.3σstat. Systematic studies for this deviation
are discussed and future work is outlined.
iii
Kurzzusammenfassung
Die A2 Kollaboration am Elektronenbeschleuniger MAMI in Mainz nutzt
einen energiemarkierten Photonenstrahl zur Produktion leichter Mesonen an
Nukleonen, um die Theorie der starken Wechselwirkung, genannt Quantenchro-
modynamik, im Niedrigenergiebereich unterhalb von 1GeV zu untersuchen.
Das A2 Detektorsystem besteht hauptsächlich aus dem 4π Kalorimeter Crystal
Ball (CB) und dem TAPS Kalorimeter in Vorwärtsrichtung, die ideal dazu
geeignet sind, Photonen im gegebenen Energiebereich zu detektieren. Im Jahr
2014 lieferten drei dedizierte Strahlzeiten für die Produktion von η′ Mesonen an
unpolarisierten Protonen einen Datensatz von (5.12± 0.19)× 106 η′ Mesonen
im Energiebereich von Eγ = 1.42 . . . 1.58GeV der eingehenden Photonen.
Diese Arbeit besteht aus zwei Teilen: Erstens, eine Prototypentwicklung
um mögliche Verbesserungen der existierenden Datenerfassung zu beurteilen
und, zweitens, die Analyse des Verzweigungsverhältnisses des Zerfalls η′ →
ωγ relativ zum Referenzkanal η′ → γγ. Um diese Ergebnisse zu erhalten,
wurden zahlreiche Verbesserungen und Innovationen im Zusammenhang mit
der eingesetzten Hardware und Software entwickelt und umgesetzt.
Die Protoypentwicklung für den CB/A2 Experimentaufbau basiert auf der
GSI TRB3 Plattform, die im Wesentlichen aus einer vielseitig einsetzbaren
4 + 1 FPGA Elektronikplatine besteht. In dieser Arbeit wurde eine Firmware
zur Merkmalextraktion für eine bereits existierende Erweiterungsplatine mit
einem abtastenden Analog-Digital-Umsetzer entwickelt und erfolgreich am CB
Kalorimeter getestet. Es wurde eine ausreichende Energie- und Zeitauflösung
begrenzt durch die vorgegebene Analogsignalqualität bestimmt. Zusätzlich
wurde die Anwendbarkeit einer weiteren Ladungs-Zeit-Umsetzer-Vorplatine
auch für andere Teile des A2 Detektorsystems untersucht.
Der Pseudoskalar-Vektor-Gamma-Zerfall η′ → ωγ dient als Test von ef-
fektiven Feldtheorien der starken Wechselwirkung, insbesondere die η-η′-
Mischung und die konsistente Integration von Vektormesonen betreffend.
In dieser Arbeit wurde eine neue Analyseumgebung entwickelt, die fort-
schrittliche Kalibrations- und Feinabstimmungsmethoden sowie kinemati-
sches Fitten für Photoproduktionsexperimente bereitstellt. Das Endergebnis
BR(η′ → ωγ) = (1.82± 0.19stat)× 10−2 ist um 4.3σstat inkonsistent mit dem
aktuellen weltweiten Durchschnitt laut PDG. Systematische Studien für diese
Abweichung werden diskutiert und zukünftige Arbeiten werden dargestellt.
iv
Contents
1. Introduction 1
1.1. Motivation and overview . . . . . . . . . . . . . . . . . . . . . . 1
1.2. Theory of the strong interaction . . . . . . . . . . . . . . . . . 3
1.3. Physics of the η′ → ωγ decay . . . . . . . . . . . . . . . . . . . 11
2. Experimental setup 15
2.1. The electron accelerator MAMI . . . . . . . . . . . . . . . . . . 15
2.2. The end-point tagger (EPT) . . . . . . . . . . . . . . . . . . . . 19
2.3. The liquid hydrogen target system . . . . . . . . . . . . . . . . 22
2.4. The Crystal Ball (CB) detector system . . . . . . . . . . . . . . 22
2.5. The two-arm photon spectrometer (TAPS) . . . . . . . . . . . 26
2.6. Upgrade and improvements in October 2013 . . . . . . . . . . . 27
2.6.1. Streamlined VME readout scheme . . . . . . . . . . . . 33
2.6.2. TAPS efficient readout scheme . . . . . . . . . . . . . . 34
3. Hardware upgrade design studies 37
3.1. Experimental requirements . . . . . . . . . . . . . . . . . . . . 37
3.2. The TRB3 platform . . . . . . . . . . . . . . . . . . . . . . . . 38
3.3. Charge-to-time conversion front-end PaDiWa AMPS . . . . . . 42
3.4. Sampling ADC firmware development and measurements . . . 48
3.5. Summary and outlook . . . . . . . . . . . . . . . . . . . . . . . 56
4. Analysis of the η′ → ωγ branching fraction 59
4.1. Introduction to photo-production experiments . . . . . . . . . . 59
4.2. Software environment . . . . . . . . . . . . . . . . . . . . . . . 64
4.3. Event reconstruction . . . . . . . . . . . . . . . . . . . . . . . . 68
4.4. Event calibration and quality checks . . . . . . . . . . . . . . . 73
4.5. Kinematic fitting . . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.6. Selection of η′ → γγ events . . . . . . . . . . . . . . . . . . . . 97
4.7. Selection of η′ → ωγ events . . . . . . . . . . . . . . . . . . . . 102
4.8. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
5. Conclusion 119
v
Contents
A. Supplementary figures for η′ → γγ 121
B. Supplementary figures for η′ → ωγ 125
Glossary 127
vi
List of Figures
1.1. Pseudo-scalar meson octet . . . . . . . . . . . . . . . . . . . . . 9
2.1. A2 experiment hall . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2. RTM principle and MAMI HDSM . . . . . . . . . . . . . . . . 17
2.3. MAMI accelerator facility floorplan . . . . . . . . . . . . . . . . 18
2.4. End-point tagger . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.5. EPT QDC measurement . . . . . . . . . . . . . . . . . . . . . . 21
2.6. Liquid hydrogen target geometry . . . . . . . . . . . . . . . . . 23
2.7. A2 detector system . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.8. CB icosahedron geometry . . . . . . . . . . . . . . . . . . . . . 25
2.9. TAPS BaF2 module . . . . . . . . . . . . . . . . . . . . . . . . 26
2.10. Simplified detector/DAQ layout . . . . . . . . . . . . . . . . . . 28
2.11. CB/PID read-out components . . . . . . . . . . . . . . . . . . . 29
2.12. CB hum on analog sum signal . . . . . . . . . . . . . . . . . . . 30
2.13. CATCH TDC overflow of raw units . . . . . . . . . . . . . . . . 31
2.14. VITEC PCB image . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.15. VME timing measurement . . . . . . . . . . . . . . . . . . . . . 35
2.16. SpeedTAPS readout scheme . . . . . . . . . . . . . . . . . . . . 36
3.1. CB signal measurement . . . . . . . . . . . . . . . . . . . . . . 39
3.2. TRB3 PCB image . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.3. TRB3 DAQ integration . . . . . . . . . . . . . . . . . . . . . . 43
3.4. Threshold scanning for V refthr determination . . . . . . . . . . . . 44
3.5. PaDiWa AMPS building blocks . . . . . . . . . . . . . . . . . . 45
3.6. PaDiWa AMPS LTspice simulation verification . . . . . . . . . 47
3.7. PaDiWa AMPS time interval vs. charge . . . . . . . . . . . . . 48
3.8. TRB3 ADC firmware building blocks . . . . . . . . . . . . . . . 50
3.9. TRB3 ADC timings at fsampling = 64MHz, 80MHz . . . . . . . 51
3.10. TRB3 ADC external timing measurement . . . . . . . . . . . . 53
3.11. TRB3 ADC Acqu DAQ comparison . . . . . . . . . . . . . . . 55
3.12. TRB3 ADC timing resolution . . . . . . . . . . . . . . . . . . . 56
4.1. Total photo-production cross-section . . . . . . . . . . . . . . . 60
4.2. EPT prompt-random timing windows . . . . . . . . . . . . . . 62
vii
List of Figures
4.3. Scattered proton kinematics for η′ production . . . . . . . . . . 64
4.4. Ant analysis framework processing flow chart . . . . . . . . . . 67
4.5. Clustering performance on MC . . . . . . . . . . . . . . . . . . 72
4.6. Calibration modules and dependencies . . . . . . . . . . . . . . 74
4.7. CB time-walk calibration . . . . . . . . . . . . . . . . . . . . . 76
4.8. PID pedestals and timings . . . . . . . . . . . . . . . . . . . . . 77
4.9. Ant fit GUI for CB energy calibration . . . . . . . . . . . . . . 79
4.10. Time-dependent calibration MC toy model . . . . . . . . . . . 81
4.11. Run-dependent energy calibration for CB and TAPS . . . . . . 82
4.12. Calorimeter cluster reconstruction . . . . . . . . . . . . . . . . 83
4.13. Invariant mass spectrum after calibration . . . . . . . . . . . . 84
4.14. Element status in CB and TAPS . . . . . . . . . . . . . . . . . 87
4.15. Impact of kinematic fitting . . . . . . . . . . . . . . . . . . . . 89
4.16. Kinematic fitter parametrization . . . . . . . . . . . . . . . . . 90
4.17. Fitter uncertainties for photons in CB, Data . . . . . . . . . . . 93
4.18. Fitter uncertainties for photons in CB, MC . . . . . . . . . . . 94
4.19. Fitter probabilities for Data and MC . . . . . . . . . . . . . . . 95
4.20. 2γ, 3γ, 6γ invariant mass before/after kinematic fit . . . . . . . 96
4.21. Processing of η′ → γγ events . . . . . . . . . . . . . . . . . . . 98
4.22. MC Weighting of η′ production . . . . . . . . . . . . . . . . . . 99
4.23. Cuts for η′ → γγ . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.24. Signal extraction for η′ → γγ . . . . . . . . . . . . . . . . . . . 103
4.25. Fit parameters for η′ → γγ . . . . . . . . . . . . . . . . . . . . 104
4.26. Systematic cut studies for η′ → γγ . . . . . . . . . . . . . . . . 105
4.27. Processing of η′ → ωγ events . . . . . . . . . . . . . . . . . . . 106
4.28. 2γ out of 4γ invariant mass after kinematic fit . . . . . . . . . . 107
4.29. Phase space of η′ → ωγ photons . . . . . . . . . . . . . . . . . . 107
4.30. Fit probability cuts for η′ → ωγ . . . . . . . . . . . . . . . . . . 108
4.31. Kinematic cut of bachelor photons in η′ → ωγ . . . . . . . . . . 110
4.32. PID cut for η′ → ωγ . . . . . . . . . . . . . . . . . . . . . . . . 111
4.33. Cut on ω invariant mass for η′ → ωγ . . . . . . . . . . . . . . . 111
4.34. Fit for η′ → ωγ . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
4.35. Systematic error estimation for η′ → ωγ . . . . . . . . . . . . . 115
viii
List of Tables
1.1. Quark masses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.1. A2 detector signal properties . . . . . . . . . . . . . . . . . . . 39
3.2. TRB3 ADC Acqu channel mapping . . . . . . . . . . . . . . . . 53
3.3. TRB3 upgrade options for A2 detectors . . . . . . . . . . . . . 57
4.1. Nominal beam time conditions . . . . . . . . . . . . . . . . . . 65
4.2. Overview of data-taking periods . . . . . . . . . . . . . . . . . 85
4.3. Overview of setup parameters . . . . . . . . . . . . . . . . . . . 88
4.4. Overview of cut variables . . . . . . . . . . . . . . . . . . . . . 99
4.5. Cuts for η′ → ωγ . . . . . . . . . . . . . . . . . . . . . . . . . . 112
4.6. Fit parameters for η′ → ωγ . . . . . . . . . . . . . . . . . . . . 113
4.7. Cut variations for η′ → ωγ . . . . . . . . . . . . . . . . . . . . . 114
ix

1. Introduction
1.1. Motivation and overview
The strong interaction is one of the four fundamental forces in physics, besides
gravitation, electromagnetism and the weak interaction. A huge spectrum of
strongly interacting particles has been discovered since the 1950s in cosmic
rays and at accelerator facilities all over the world. The properties of those
unstable particles are mainly determined by the investigation of their decay
into stable particles, for example, photons, electrons or protons, allowing the
reconstruction of Lorentz-invariant quantities. To this end, detectors and
read-out systems are built to measure the kinetic energy, momentum and the
direction of flight, possibly including particle type identification. This modern
era of experimental particle physics began in 1952 with the invention of the
bubble chamber [1] as an improvement of the cloud chamber, and the most
recent highlight was reached with the detection of the Higgs boson in 2012
measured with state-of-the-art detector systems consisting of many million
channels [2, 3]. Over this timespan, particle accelerator technology increased
the maximum available energies from MeV to TeV and integrated luminosities
from 1/µb to 1/fb, both improvements of many orders of magnitude. Detector
technology advanced accordingly to distinguish interesting reactions from
already known backgrounds with segmented calorimeters and particle tracking
on the micrometer scale inside magnetic fields of a few Teslas. Moreover,
computer technology crucially supported the recording and subsequent analysis
of huge amounts of event data. Thus, experimental particle physics and, on
the other side, technology and society mutually benefit from efforts to answer
fundamental questions about nature, such as what is matter made of.
Nowadays, the strong interaction is excellently described by quantum chro-
modynamics (QCD), establishing quarks as the elementary constituents and
gluons as force carriers. However, those degrees of freedom do not exist freely
in nature due to the so-called confinement, but only their complex bound states
are observed, such as protons or pions. Furthermore, QCD in the low-energy
regime can neither be solved analytically nor perturbatively, but only ab-initio
numerical approaches on the lattice or chiral effective field theories are avail-
able. A perturbative treatment of QCD becomes feasible for energies beyond
1
1. Introduction
a few GeV owing to the decreasing coupling constant of the strong interaction,
a phenomenon called asymptotic freedom. Despite those complex features,
the underlying symmetries of the theory help to organize qualitatively the
rich “particle zoo” as observed today and even have led to the prediction and
subsequent discovery of missing particles to complete the expected symmetry-
degenerate multiplets. The correct description of experimental observations
by QCD with sub-percent precision is still a current topic of research, which is
presented in greater detail in section 1.2.
Photo-production experiments with bremsstrahlung from an electron beam
were first conducted in the early 1950s [4], but became valuable for nuclear
and particle physics only after the construction of reliable and high energy
electron accelerators, such as the Mainzer Mikrotron (MAMI). A photon beam
represents a well-defined quantum state of point-like particles interacting elec-
tromagnetically, which is well-understood in terms of quantum electrodynamics
(QED). Since they impinge on fixed targets, the initial state of the particle
reaction is precisely known, including the polarization of the photon and the
target nucleus if desired. Furthermore, owing to the bremsstrahlung spectrum,
a range of photon energies is available concurrently within the experiment,
which are determined statistically via so-called photon-tagging. This makes
such experiments ideally suited to study nucleon resonances, to probe the
internal structure of nucleons, and to produce a clean sample of various mesons
and their subsequent decays. All those different topics have been covered in the
past decade within the A2 collaboration at the MAMI electron accelerator lead-
ing to an improved understanding of QCD in the low-energy regime, together
with similar experiments at Jefferson Lab, Virginia, U. S. and at ELSA in
Bonn, Germany. Complimentary experiments using Compton backscattering
of optical laser photons from electrons in storage rings are LEGS at BNL, New
York, U. S. and GRAAL at ESRF in Grenoble, France. These combined efforts
eventually contribute to a consistent test of QCD predictions over a large
energy scale, which is the key to reduce systematic uncertainties in precision
measurements probing the limits of QCD and the Standard Model of particle
physics.
A main component of the current A2 detector setup is the well-known
Crystal Ball (CB) calorimeter, which was built in the 1970s to precisely study
the charmonium excitation spectrum, leading to the discovery of the ηc meson.
After it was moved to Mainz in 2003, a read-out system was installed from
already existing electronics components. In order to reach future physics goals,
a prototype development for the CB has been successfully finished within the
scope of this thesis, as well as possible upgrades of other detector components
of the A2 setup. Based on this knowledge, the existing data acquisition system
2
1.2. Theory of the strong interaction
(DAQ) has been improved significantly before the high-statistics run in 2014
with the end-point tagger (EPT). Furthermore, many diagnosis tools were
established in order to detect problems during beam-time and enhance data
quality. The acquired data are analyzed to extract the relative branching
fraction of the η′ → ωγ decay, which serves as a valuable input to models
describing low-energy QCD, as detailed in section 1.3.
This thesis is structured as follows: The experimental setup of the A2
collaboration is presented in chapter 2 including a detailed description of the
substantially upgraded data acquisition. Further hardware upgrade feasibility
studies are described in chapter 3. In chapter 4, the analysis of the relative
branching fraction of η′ → ωγ is presented.
Throughout this thesis, natural units in powers of eV are used, that means
ℏ = c = 1. A glossary with abbreviations used here and henceforth is given on
page 127.
1.2. Theory of the strong interaction
The strong interaction is described by the SU(3)c color-charge gauge theory
QCD, where the degrees of freedom are massive quarks interacting via massless
gluons. To understand this statement in detail, the simpler construction of
the QED Lagrangian describing the interaction of electrons1 with photons
is presented first. This section is loosely based on [6–10], as it is merely a
suitably adapted summary of textbook knowledge.
Quantum electrodynamics (QED)
The Lagrangian yielding the Dirac equation of a free fermion with mass m,
such as the electron, is given by2
L0 = ψ̄(iγµ∂µ −m)ψ , (1.1)
where ψ(x) is a complex four-component bispinor field with its adjoint ψ̄ = ψ†γ0
and where γµ, µ = 0 . . . 3, are the 4× 4 gamma matrices satisfying the defining
anti-commutation relation
{γµ, γν} ≡ γµγν + γνγµ = 2gµν ≡ 2 diag(1,−1,−1,−1) . (1.2)
Equation (1.1) is clearly inva(riant )under the globa(l tr)ansformation
ψ → exp −ieξ ψ , ψ̄ → exp ieξ ψ̄ , (1.3)
1Including their anti-particles positrons, which were predicted by Dirac [5].
2The sum over repeated indices, such as µ in equation (1.1), is implied in the following.
3
1. Introduction
where the electric charge e has been introduced as part of the real transfor-
mation parameter ξ. The field transformation (1.3) can also be seen as a
realization of the group U(1) = {eiϕ, ϕ ∈ R} acting as a phase rotation of the
complex fields (ψ, ψ̄) by an angle (eξ,−eξ) in the complex plane. As the result
of applying two of those rotations successively does not depend on their order,
U(1) is called “abelian” or “commutative”.
Elevating the global inv(ariance t)o a local U(1) t(ransfor)mation,
ψ → exp −ieξ(x) ψ , ψ̄ → exp ieξ(x) ψ̄ , (1.4)
where ξ(x) now depends on the space-time coordinate xµ, yields for the free
Lagrangian in equation (1.1)
L = ψ̄(iγµ0 ∂µ −m)ψ → L′0 = ψ̄(iγµ∂µ + eγµ∂µξ −m)ψ . (1.5)
Since the extra term eγµ∂µξ looks surprisingly similar to a so-called gauge
transformation of the four-vector potential,
Aµ → Aµ + ∂µξ , (1.6)
known from classical electrod(ynamics, a locally U()1) invariant Lagrangian isfound as
L = ψ̄ iγµ(∂µ − ieAµ)−m ψ , (1.7)
which is indeed invariant under the transformations (1.4) and (1.6) for ψ and
Aµ, respectively. Adding the dynamics of the field Aµ, which is identified as
the photon field after quantization, the complete QED Lagrangian is eventually
found as ( )
LQED = ψ̄ iγµDµ −m ψ −
1
Fµν4 Fµν , (1.8)
where the field strength tensor Fµν = ∂µAν − ∂νAµ and the so-called covariant
derivative Dµ ≡ ∂µ − ieAµ are introduced. As already known from classical
electrodynamics, Fµν is invariant under transformation (1.6).
Quantization of a classical Lagrangian, referring to the transition from a
field to a particle interpretation, can be carried out within the so-called path
integral formalism. By assigning each term in the Lagrangian a corresponding
Feynman rule, the quantization has a compelling graphical interpretation. For
QED, besides propagators for the electron (or positron as interpreted traveling
backwards in time) and the photon,
= Electron, = Positron, = Photon,
there is only one fundamental vertex given by the local gauge coupling,
4
1.2. Theory of the strong interaction
.
From those graphical building blocks, electron-positron scattering is described
by an infinite series of all possible diagrams matching the initial and final state
topology:
+ + + . . .
√
Fortunately, each vertex introduces a small factor of α, where α = e2/(4π) ≈
1/137 is the so-called fine structure or electromagnetic coupling constant,
such that terms with more vertices are suppressed and the infinite number
of diagrams can be seen as a series converging to the scattering process as
realized in nature. ∫
The loop diagrams represent an integration d4k over the complete four-
momentum space of the “unfixed” momentum kµ, as indicated by a dashed
circle in the last diagram above. In general, this causes logarithmic divergences
to appear. It can be shown for local gauge theories that those divergences
can always be absorbed by appropriately redefining the finite number of
fields and coupling parameters in the “bare” Lagrangian, a technique called
renormalization, but to this end an arbitrarily chosen energy scale µ must
be introduced at which the renormalization is carried out. The resulting
dependence of the coupling constant α on the scale µ is described by the
so-called β-function as
( ) = ∂αβ α (log ) . (1.9)∂ µ
It can be shown that β does not depend explicitly on the energy scale µ, but
only implicitly through the “running” coupling constant α(µ). For QED, the
β-function is positive, which means that the effective coupling increases with
the scale µ. Similarly, as distance scales inversely with energy, the effective
charge decreases if measured from larger distances. This can be interpreted
qualitatively as a screening of charge by virtually created electron-positron
pairs and is studied rigorously within renormalization group theory. In order
to achieve a fast convergence of the perturbative series, the scale µ is typically
chosen to match experimental energy scales, such as the four-momentum
transfer qµ in scattering experiments, so q2 ≈ µ2. This sometimes leads
to the wrong conclusion that the scale µ has some experimentally relevant
5
1. Introduction
interpretation or would somehow influence experimental observables, such as
cross sections. In other words, if one could calculate physical quantities in
QED non-perturbatively by some other means than path integral formalism,
the “hidden” scale µ would have never been introduced, and thus remains a
merely theoretical quantity.
In conclusion, the coupling of the electrons to photons mediated by the
electric charge e is uniquely determined by requiring local U(1) gauge invariance,
and, as this coupling turns out to be small, a perturbative treatment after
quantization is meaningful and feasible. However, as U(1) is an abelian group,
the mathematical structure of transformation (1.3) and equation (1.8) is rather
simple. In the following, this recipe is extended to the non-abelian gauge theory
QCD, which leads to important consequences for its perturbative treatment.
Quantum chromodynamics (QCD)
As an example for a non-abelian group, the “special unitary group in three
dimensions” is defined as the{ fol⏐⏐lowing set of complex 3}× 3 matrices,SU(3) = U U †U = 13×3, detU = 1 , (1.10)
where the term “special” refers to the condition detU = 1. As it is well-known
from Lie group theory, the elements of SU(3) can be parametrized by 32−1 = 8
real numbers Θa, ( )
U = exp −iΘaλa/2 , (1.11)
where the Hermitian, traceless generators λa are the so-called Gell-Mann
matrices. The Gell-Mann matrices satisfy the Lie algebra given by
[λa, λb] ≡ λaλb − λbλa = 2ifabcλc , (1.12)
where the so-called structure constants fabc uniquely encode the mathematical
properties of SU(3).
In formal analogy to the QED Lagrangian in equation (1.8), the complete
QCD Lagrangian is therefore constructed as an SU(3)c color-charge gauge
theory [11, 12],
∑6 1 ( )LQCD = q̄f (iγµDµ −m µνf )qf − 2 Trc GµνG , (1.13)
f=1
where ⎛ ⎞
qf = ⎜⎝qf,r⎟ ( )q † † † †f,g⎠ , q̄f = qfγ0 = qf,rγ0 qf,gγ0 qf,bγ0 , (1.14)
qf,b
6
1.2. Theory of the strong interaction
is the Dirac bispinor quark field and its adjoint, respectively, written down
explicitly as a SU(3)c “rgb” color triplet for each of the six quark flavors f ,
usually denoted up (u), down (d), strange (s), charm (c), bottom (b) and
top (t). In analogy to transformation (1.4), the fields are required to locally
transform using the parametrization in equation (1.11), again introducing the
flavor-independent color-charge g by replacing the parameters Θa with gΘa(x).
In addition, the quantity
a
A a λµ ≡ Aµ 2 (1.15)
represents the 32 − 1 = 8 gluon fields decomposed in the so-called adjoint
representation of SU(3). In analogy to equation (1.8), the covariant derivative
is given as
Dµqf ≡ (∂µ − igAµ)qf , (1.16)
which transforms as the object it acts on by definition. According to equa-
tion (1.16), the basis vectors of the decomposition in equation (1.15), in this
case the Gell-Mann matrices, should match the potentially arbitrary choice
for the representation of the matter fields, which are the quarks in this case.
In contrast, the basis vectors of the gluon fields (Aaµ)a=1...8 is always of dimen-
sionality N2c − 1 = 8 due to the underlying SU(Nc = 3) gauge group. Finally,
the gluon field strength tensor is given by
a
Gµν ≡ Ga
λ
µν 2 = (∂µAν − ∂νAµ − ig[Aµ,Aν ] ) a (1.17)
= λ∂ Aa a abc b cµ ν − ∂νAµ + gf AµAν 2 ,
where fabc are the SU(3) structure constants as defined in equation (1.12).
In contrast to QED, there are additional three- and four-vertex interactions
of the gluon fields Aaµ due to the non-vanishing structure constants fabc in
equation (1.17), which stem from the non-abelian nature of the gauge group
SU(3)c. This key feature dramatically changes the asymptotic behavior of QCD,
as the QCD β-function describing the scaling of the strong coupling constant
αs = g2/(4π) analogously to equation (1.9) becomes negative. Thus, the
coupling αs decreases with higher energy scales, which is known as “asymptotic
freedom”. Moreover, below energy scales of µ ≈ 1GeV, the coupling becomes
larger than 1, which renders a perturbative treatment in powers of g in the low-
energy regime impossible, as higher order diagrams with more vertices cannot
be neglected as it was the case for QED. The diverging coupling constant
manifests itself experimentally by the fact that no free gluons or quarks but
only “color-neutral” bound states called hadrons are observed, which is denoted
as confinement [13, 14].
7
1. Introduction
Light flavors / MeV Heavy flavors / GeV
m = 2.2+0.6u −0.4 mc = 1.27± 0.03
m = 4.7+0.5 m = 4.18+0.04d −0.4 b −0.03
m +8s = 96−4 mt = 160+5−4
Table 1.1.: The “current-quark” masses for the light flavors u, d, s and the
“running” masses for the heavy flavors c, b, t from [17], all given in
the mass-independent MS subtraction scheme at scale µ ≈ 2GeV.
As quarks are confined, their masses should be interpreted as
parameters within certain theoretical frameworks, see the review
in [17] for details.
Still, non-perturbative approaches to QCD exist, such as ab-initio numerical
calculations on the lattice [15, 16] or effective field theories. The latter are
presented in more detail in the following to explore the rich physics of the
strong interaction in the low-energy regime.
Chiral effective field theories
Since the experimental values of the quark masses given in table 1.1 accidentally
divide them into “light” and “heavy” flavors, the limit mu, d, s → 0 and
mc, b, t → ∞ should be a good approximation of QCD in the low-energy
regime. In this so-called chiral limit, the Lagrangian reads
0 ∑ µ 1 (L µν)QCD = q̄f iγ Dµqf − 2 Tr GµνG
f=∑u,d,s( ) 1 ( ) (1.18)= q̄Rf iγµD qR + q̄Lµ f f iγµD qL µνµ f − 2 Trc GµνG ,
f=u,d,s
where the left- and right-handed quark fields R/Lq 1f = 2(1 ± γ5)qf with γ5 =
iγ0γ1γ2γ3 are introduced. Thus, in this chiral, or “handedness”, representation,
it is easily seen that L0 ∼QCD is invariant under a U(3)R × U(3)L = SU(3)R ×
SU(3)L×U(1)V=R+L×U(1)A=R−L symmetry group in flavor space. According
to Noether’s theorem [18], (32 − 1) + (32 − 1) + 1 + 1 = 18 currents jµ with
vanishing total divergence∫, ∂ jµµ = 0, are expected, each associated to a
conserved quantity Q(t) = j0(x⃗, t)d3x.
However, it is not trivial that the symmetries present in the classical La-
grangian as given by equation (1.18) are still realized after quantization. In
8
1.2. Theory of the strong interaction
Figure 1.1.: The pseudo-scalar meson octet JP = 0− amended by the η′ and
arranged by the quantum numbers Q (electric charge) and S
(strangeness). The approximate masses in MeV are taken from
[17] and indicate that SU(3) flavor symmetry for flavors f = u, d, s
is not as well realized as the embedded SU(2) symmetry for flavors
f = u, d. This is related to the non-vanishing current masses of
the light quarks in table 1.1. See section 1.3 for mixing of the η
and η′ mesons.
fact, as first shown in [19–21], the axial singlet current associated with U(1)A
is not conserved and hence its divergence is given in the chiral limit by [7]
3g2
∂ jµ = ϵµνρσGa aµ axial 32 2 µνGρσ ̸= 0 , (1.19)singlet π
which is called the chiral quantum anomaly. Thus, QCD in the chiral limit
possesses the symmetry
SU(3)R × SU(3)L×U(1)V , (1.20)
chiral symmetry
where the U(1)V is associated with the conservation of baryon number B,
giving rise to the classification of hadrons into mesons with B = 0 and baryons
with B = 1.
9
1. Introduction
Moreover, according to the chiral symmetry in (1.20), one naively expects
an approximate arrangement of hadrons in irreducible multiplets of SU(3)
with positive, V = R+ L, and negative parity, A = R− L. However, as the
experimentally observed low-energy baryons can be arranged in approximately
degenerate multiplets of positive parity only, the chiral symmetry is assumed
to be spontaneously broken to SU(3)V=R+L. This gives rise to 32 − 1 = 8
Goldstone bosons identified as the pseudo-scalar meson octet consisting of
π±, π0, K±, K0, K̄0 and the η, see figure 1.1. In the chiral limit, the mass
of the Goldstone bosons vanishes. Their experimentally observed small mass,
compared to a typical QCD mass scale of 1GeV, is thus attributed to the
explicit breaking of the chiral symmetry by the non-vanishing mass of the light
quarks, see table 1.1.
As already mentioned, QCD cannot be solved perturbatively as a quantum
field theory of quarks and gluons in the low-energy regime since the coupling
diverges at this energy scale. Fortunately, a solution to this problem is given
by Steven Weinberg as a so-far unproven “theorem” [22]:
The “theorem” says that although individual quantum field
theories have of course a good deal of content, quantum field
theory itself has no content beyond analyticity, unitarity, cluster
decomposition, and symmetry. This can be put more precisely in
the context of perturbation theory: if one writes down the most
general possible Lagrangian, including all terms consistent with
assumed symmetry principles, and then calculates matrix elements
with this Lagrangian to any given order of perturbation theory, the
result will simply be the most general possible S-matrix consistent
with analyticity, perturbative unitarity, cluster decomposition and
the assumed symmetry principles.
In this sense, so-called effective field theories use the experimentally observed
hadrons as degrees of freedom and construct the most general Lagrangian
consistent with the underlying symmetries. In particular, the so-called chiral
perturbation theory describes Goldstone bosons ϕa as a non-linear realization3
of SU(3), (
( ) = exp ϕ(x)
)
U x i , (1.21)
F0
3It is non-linear as the unitary elements U(x) in equation (1.21) do not form a vector space.
10
1.3. Physics of the η′ → ωγ decay
with the explicit representati⎛on of the pseudo-scalar mesons f⎞rom figure 1.1,√ √
∑ ⎜⎜π0 + √
1
3η 2π
+ 2K+
8
ϕ = ϕaλa = ⎝⎜ √ √ ⎟2π− −π0 + √1 η 2K0⎟⎟ , (1.22)
a=1 √ √
3 ⎠
2K− 2K̄0 −√23η
to implement the spontaneously broken chiral symmetry as [7, 22]
2
L F0eff = 4 ⟨∂ U∂
µ
µ U
†⟩+ · · · , (1.23)
where ⟨. . .⟩ denotes the trace over flavor indices and only the lowest order term
with a minimal number of derivatives and without any external currents is
given. The effective Lagrangian in equation (1.23) contains an infinite number
of terms with a-priori unknown low-energy constants (LECs) as coefficients,
such as the pion decay constant F0. To restore predictive power of the theory,
each term in the effective Lagrangian—leading to a Feynman rule to construct
corresponding Feynman diagrams—is given an order according to the power
of a small expansion parameter δ, which is the Goldstone boson momentum in
this case. This procedure is known as Weinberg’s power counting. Still, the
remaining finite number of LECs, whose numerical values depend also on the
employed renormalization scheme, need to be determined from experimental
values. The theory can be extended to include the proton and neutron as
isospin partners of the nucleon as well as vector mesons, such as the ρ and the
ω mesons [23, 24], and the coupling to photons is realized as external vector
currents. However, establishing a consistent power counting scheme for this
extended case is non-trivial due to the separate mass scales introduced by the
nucleon or the vector mesons. Furthermore, the number of LECs contributing
to a specific process increases rapidly, which renders one-loop calculations
already challenging and deteriorates the predictive power and the accuracy of
chiral effective field theories (χEFTs).
1.3. Physics of the η′ → ωγ decay
This section highlights the physics of the η′ → ωγ decay in terms of χEFTs as
well as previous measurements investigating this decay. The η′ is a pseudo-
scalar meson, JPC = 0−+, with a mass of mη′ = (957.78± 0.06)MeV [17]. The
ω is a vector meson, JPC = 1−−, with a mass of mω = (782.65± 0.12)MeV
[17]. Hence, η′ → ωγ belongs to the group of so-called pseudoscalar-vector-
gamma (PV γ) decays. As a two body process, the only physically interesting
11
1. Introduction
quantity of this decay is the branching fraction BR(η′ → ωγ) = Γ/Γtot, where
Γ is the partial width for this particular decay and Γtot = (0.197± 0.009)MeV
[17] the total width of the η′ meson.
As the mass of the η′ meson does not vanish in the chiral limit since it
cannot be identified as a Goldstone boson, it could be treated just as any other
massive degree of freedom, such as the vector mesons, within conventional
χEFTs. However, it is instructive to regard the η′ meson in terms of the
U(1)A anomaly in the so-called large-Nc limit, where QCD is generalized to an
SU(Nc) gauge theory [25]. Hence, 1/Nc is treated as another small expansion
parameter δ similar to the Goldstone boson momentum. As it ca√n be argued
from renormalization group theory, the coupling g behaves as 1/ Nc, which
makes the anomaly in equation (1.19) disappear in the large-Nc limit. Thus,
in large-Nc chiral perturbation theory (LNcChPT), the η′ meson is interpreted
as a ninth Goldstone boson in the limit Nc → ∞. This is implemented by
amending equation (1.22) as follows,
∑8 ∑8
ϕ = ϕaλa = √ϕaλa + λ⎛ 0
η1
a=0 a=1
⎜ ⎞⎜π0 + √1 η + 2
√ √
3 8 3η1 2π
+ √ 2K+⎜ ⎟ (1.24)√= ⎝ 2π− 0 1 2 √−π + √ η8 + η1 2K0 ⎟⎟ ,√ − √3 3 √ ⎠2K 2K̄0√ −√
2 2
3η8 + 3η1
where λ0 = 2/31. Since Trλ0 ̸= 0, the chiral symmetry in (1.20) is promoted
to U(3)R ×U(3)L, as the unitarian Goldstone fields in equation (1.21) do not
have a unit determinant anymore, detU = exp(iϕ0/F0Trλ0) ≠ 1.
The physically observed pseudo-scalars π0, η and η′ all possess the same
quantum numbers, such as vanishing strangeness, as depicted in figure 1.1.
Already the simple question how those mesons are composed in terms of their
quark flavor contents uū, dd̄, ss̄ is non-trivial, as in this case QCD induces
transitions between quarks of different flavors via annihilations to gluons [26].
In particular, the so-called mixing of the η and η′ states as a linear combination
from the flavor singlet η1 and octet η8, see equation (1.24), has been investigated
since the late 1970s using a parametrization with a single mixing angle θP .
However, phenomenology yielded largely inconsistent values for θP ranging
from −10° to −20°. This has been resolved around the year 2000 as rigorous
considerations in LNcChPT [26] showed that a parametrization using two
mixing angles is more appropriate. Nevertheless, the correct implementation
of η-η′ mixing beyond leading order is a subject of current research, see for
example [27], and the phenomenon involves answering fundamental questions
12
1.3. Physics of the η′ → ωγ decay
concerning explicit and spontaneous symmetry breaking in QCD and the
non-perturbative nature of the U(1)A anomaly.
The vector meson ω is usually implemented as a four-vector V µ to con-
veniently formulate a Lorentz-invariant effective Lagrangian in the sense of
Weinberg’s “theorem”. However, within the Hamiltonian formalism, introduc-
ing four fields V µ and canonically conjugated momenta to describe a massive
spin-1 particle with 2S + 1 = 3 degrees of freedom leads to the appearance of
so-called primary constraints during canonical quantization, from which the
velocities V̇ are not solvable to construct the conjugated momenta. This is
resolved by the physical requirement that such constraints shall be conserved
in time, which in general leads to additionally consistency equations involving
the LECs. This improves the predictive power of χEFTs and relations known
from phenomenology can be shown rigorously [28]. Employing the same con-
straint analysis to the usually favored description of massive vector mesons as
antisymmetric tensors representing 6 degrees of freedom is a topic of current
research, see for example [9].
In summary, PV γ interactions such as the η′ → ωγ decay provide a challeng-
ing subject for effective field theories, probing the correct implementation and
understanding of explicitly and spontaneously broken symmetries as well as the
proper treatment of massive vector particles in terms of necessary constraints.
Due to the large number of LECs, many different hadrons and their decay
channels need to be studied experimentally, and this thesis contributes to this
endeavor in chapter 4 with the analysis of the relative branching fraction of
the η′ → ωγ decay. For example, in [29] a LNcChPT including vector mesons
is constructed and applied to explain the phenomenology. Depending on which
experimental values are used to determine the LECs, other values can be
predicted and thus serve as a test of this model. In particular, the value for
the decay width extracted from fit reads
Γ(η′ → ωγ) = (7.4± 1.0) keV , (1.25)
which is in reasonable agreement with the experimental value of (6.2± 1.1) keV.
The current global fit for the relative partial decay width is [17]
Γ(η′ → ωγ)/Γtot = (2.62± 0.13)× 10−2 , (1.26)
which is dominated by the most recent measurement from the BESIII collabo-
ration [30] given as
BR(η′ → ωγ) = (2.55± 0.03stat ± 0.16 )× 10−2syst . (1.27)
The BESIII collaboration uses the electron-positron collider BEPCII in Beijing
to resonantly produce a huge amount of J/ψ mesons within the BESIII detector
13
1. Introduction
system. The radiative decay J/ψ → η′γ serves as a source of about 6.8× 106
η′ mesons, giving a signal yield of 33.2× 103 events. As further discussed in
chapter 4, the A2 collaboration produced an equally large sample of η′ mesons
and thus the A2 measurement can serve as a valuable cross-check for the global
fit in equation (1.26).
14
2. Experimental setup
This chapter describes the apparatus needed to carry out experiments with
energy-tagged photons. It focuses on the mechanical and technical aspects
of the components and the currently deployed read-out system, including the
improvements for the measurement campaign from July to December 2014.
Since the key objective of this campaign is to measure the η′ photo-production
at the high energy photon end of the specifically designed EPT, the campaign is
commonly referred to as “EPT 2014 measurements” or “η′ 2014 measurements”
in the following. Finally, this builds the foundations for the efforts described
in chapter 4.
The A2 detector system is located in the Tagger experimental hall at the
Institut für Kernphysik, Mainz, Germany. A schematic overview of the relevant
components along the electron and photon beam-line is shown in figure 2.1 on
the following page. The electron beam from the MAMI accelerator produces
bremsstrahlung photons on a radiator, which are tagged by magnetic analysis
and subsequent detection of the time-correlated electrons. Next, the photon
beam is collimated and impinges on the liquid hydrogen target. The reaction
products are subsequently detected in the CB and TAPS detector systems.
The right-handed Cartesian coordinate system in the lab frame originates
in the center-of-mass of the ideally positioned liquid hydrogen target cell
coinciding with the center-of-mass of the CB icosahedron. The z-axis is
pointing towards the ideal direction of flight of the photons, and the xy plane
is rotated such that the x-axis points to the left in the horizontal plane.
2.1. The electron accelerator MAMI
The MAMI facility provides a continuous-wave electron beam with energies of
up to 1604MeV and unpolarized currents of up to 100µA [32].
Unpolarized electrons are conventionally extracted from a heated metal
wire using a Wehnelt cylinder. Next, a linear accelerator (LINAC) stage of
microwave cavities increases the electron energy to about 4MeV and thus
to 99% speed of light, which is required for the injection into the so-called
race track microtron (RTM) stages as shown in figure 2.2: Bending magnets
re-utilize a dedicated LINAC stage in multiple turns, until the accelerated
15
2. Experimental setup
Ion Chamber
mm Photon Beam Camera
Lead Glass Detector
13329 TAPS
Crystal Ball
11872 Target Cell
Target System
6880
Halo Collimator, d = 16mm
500
Pair Spectrometer
Concrete Wall
Cleaning Magnet, d = 10mm
4263 Photon Beam Stop, Pb, d = 15mm
3616
Main Collimator, d = 4mm
Pre Collimator, d = 10mm
Tagger Yoke, d = 40mm
1530 Tagger
Correction Magnet
EPT
0 Radiator
Beam Axis
Figure 2.1.: A2 experiment hall overview, adapted from [31] (not to scale).
The MAMI electron beam enters from the bottom and is converted
into a photon beam at Radiator 1. This secondary beam impinges
on the target after collimation and the mostly unscattered photons
finally reach the Ion Chamber.
16
2.1. The electron accelerator MAMI
Figure 2.2.: The RTM in the top panel consists of two bending magnets re-
utilizing the same linear accelerator multiple times. The HDSM
design in the bottom panel keeps the size of the magnets for higher
energies technically achievable. Adapted from [32, 33].
beam is extracted by a kicker magnet. This keeps the overall size and thus
construction costs reasonable while still providing excellent beam emittance
and stability. Using this construction principle, the first three RTM stages,
called MAMI-B, achieve 855MeV nominal energy, see figure 2.3.
The last and largest RTM stage of MAMI-B needs already magnetic fields
close to the ≈ 2T saturation field of the iron yokes and hence the energy can
only be increased by scaling up the physical dimensions allowing larger radii
of the electron flight paths. Furthermore, the relatively low energy gain per
turn is compromised by the increasing losses due to synchrotron radiation
of the bent electrons. Those considerations gave rise to the construction of
the HDSM [32], enabling nominal beam energies of up to 1508MeV. The key
17
2. Experimental setup
Figure 2.3.: A MAMI accelerator facility floorplan at the Institute für Kern-
physik in Mainz from [32]. Either the 855MeV MAMI-B beam or
the 1508MeV MAMI-C beam can be utilized by the experiments
A1 and A2. The MESA accelerator is currently under construction
at the former A4 experiment site.
design idea is to split both bending magnets into two separate parts and to
use two LINAC sections where one is operated with twice the standard MAMI
microwave frequency of 2.45GHz to achieve phase stability.
By pushing all stages and their auxiliary components of the accelerator
system to their operation limits, a maximum beam energy of 1604MeV for the
so-called MAMI-C stage, consisting of MAMI-B and the HDSM, is achieved,
with an energy stabilization of about 10 keV over a timespan of one week [32].
As the minimum photon energy to produce the η′ meson off the proton is
roughly 1450MeV, operating at the maximum instead of nominal beam energy
triples the theoretically accessible kinematic range for the photo-production of
η′ mesons.
18
2.2. The end-point tagger (EPT)
2.2. The end-point tagger (EPT)
As shown in figure 2.4, the MAMI electron beam impinges on a radiator, which
is a folded copper (Cu) foil with thicknesses of 5µm, 10µm or 15µm. About
0.1% of the electrons1 emit bremsstrahlung photons in the vicinity of a Cu
nucleus,
e− +Cu→ Cu + e− + γ ,
and since the recoil energy of the heavy Cu nucleus can be neglected, the
energy of the emitted photon is determined by
E = Ee−γ beam − e
−
Etagged . (2.1)
The chosen radiator thickness of 10µm provides a sufficient rate of brems-
strahlung photons with a negligible probability of multiple electron scattering
within the foil. The radiator can be set using a remotely controlled motor
and is removed completely from the electron beam-line during MAMI beam
optimization to prevent any radiation damage to the detector system.
The energy and angular dependence of the bremsstrahlung cross section is
approximated by [34–37]
dσ ∼ 1 dσ θ/Eγ , ∼ ,
dEγ dθ (θ2 − θ2c)2
respectively, with the critical angle θc ≈
−
me/E
e
beam, which is in the order of
mrad for typical MAMI beam energies. Since over 50% of the photons are
emitted within an deflection angle below θc, the notion “photon beam” is
indeed justified. Furthermore, the beam is collimated by lead pinholes with
a final diameter of 4mm to provide a well-defined photon beam spot on the
target, which is monitored by a luminescent screen in front of the ionization
chamber, see also figure 2.1.
The EPT determines the scattered electron energy −Eetagged in equation (2.1)
with a spectrometer magnet and 47 detectors close to its focal plane, see
figure 2.4. Each detector module consists of a 12.5mm wide and 8mm thick
scintillator piece, a light guide and a photomultiplier tube (PMT). This yields a
clean waveform with high signal to noise ratio for impinging electrons, which are
1The fraction can be estimated from d/X0, where d ≪ X0 is the foil thickness and
X0 ≈ 1.4 cm the radiation length of Cu.
19
2. Experimental setup
Dump
Glasgow-Mainz-Tagger
End Point Tagger
Detector
(47 Channels)
Electron Beam
Photon Beam
Correction
Radiator Magnet
Figure 2.4.: The EPT is installed before the Glasgow tagger and a correction
magnet to ensure the correct flight path for unscattered electrons
into the beam dump. It covers the low energetic end of the
scattered electrons and thus allows studying events with highest
photon energies, from [37].
clearly visible in integral measurements2 carried out for high voltage (HV) and
discriminator threshold tuning, see figure 2.5. The photon energy resolution of
σEγ ≈ 1.5MeV is dominated by the width of the detector elements. The energy
calibration for each detector element is based on the simulated flight path of
electrons with constant momentum through the measured magnetic field map
of the dipole [37]. The field strength is monitored during the experiment with
a Hall probe located between the pole shoes. In order to bend the unscattered
electrons into the beam dump with the help of the Glasgow-Mainz tagger,
a correction dipole with opposite field direction is installed after the EPT
magnet.
At the end of the photon beam-line, an ionization chamber is installed to
detect the flux of unscattered photons. Its ratio to the total rate of electrons
detected in the EPT, called the “LadderP2Ratio”, is an indication for the
alignment of the electron beam on the radiator. During beam position opti-
2The EPT integral measurements are carried out with LeCroy 1885F FASTBUS modules
using a Versa Module Europa bus (VMEbus) controller, which are only activated for
such measurements due to performance reasons. Their readout timing is only working
correctly if the whole FASTBUS crate is readout due to timing issues although only one
module is needed for the 47 EPT channels.
20
2.2. The end-point tagger (EPT)
Element 10 Element 10 with TDC hit requirement
106 10
6
105 Pedestal 105
104 10
4
3
103 10
Electrons Electrons
102 102
10 10
1 1
0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500
ADC Value ADC Value
Figure 2.5.: For all 47 EPT elements, the integral output of the analog signal
is shown as the raw ADC value. In the left upper panel, energy
depositions from electrons around 1500 ADC counts are clearly
separated from the pedestal needles at 400. The right upper panel
requires a TDC hit, which makes the configured CFD threshold
visible for each channel. It shows that the HV voltages and the
thresholds are tuned such that no electron hits are rejected but
pedestals properly suppressed, as it is exemplified for element 10
in the lower row.
21
CFD Threshold
2. Experimental setup
mization, the “LadderP2Ratio” is minimized in order to maximize the photon
flux under constant beam current. The MAMI beam current is monitored with
a Faraday cup installed in the beam dump.
2.3. The liquid hydrogen target system
The produced photons impinge on hydrogen molecules, interacting predomi-
nantly with the contained protons at typical energies of a few hundred MeV.
In order to increase the proton density and thus the luminosity by a factor
of 50, the gaseous hydrogen is liquefied by a compressor system from the
DAPHNE experiment [38] providing a stable temperature of 20K, which is
the condensation point of hydrogen at atmospheric pressure. The temperature
is stabilized by either adding liquefied hydrogen to the cell or heating the cell
electrically, which results in a typical pressure of gaseous phase in the target
cell of 1080mbar. This light excess pressure compared to atmosphere ensures
a reliable leak detection for safety reasons. The target apparatus is monitored
and controlled by a dedicated computer system [39].
The target cell in figure 2.6 is (10.0± 0.1) cm long and has a diameter of
4.0 cm under cold conditions [39]. The chosen length of the target is a trade-off
between a sufficient number of protons as interaction targets and the precise
knowledge of the vertex position. In order to keep the amount of other material
around the liquid hydrogen as low as possible but still achieve sufficient thermal
insulation, the inner target cell is made of 125µm thick Kapton foil, isolated by
eight layers of 8µm Mylar and 2µm aluminum compound foil and protected
by 1mm CFK tube. In addition, 25µm Kapton foil is attached to prevent ice
formation close to the target cell.
2.4. The Crystal Ball (CB) detector system
As shown in figure 2.7, the CB detector system consists of the electromagnetic
NaI calorimeter itself and two inner detectors, the particle identification
detector (PID) and two coaxial cylindrical multi-wire proportional chambers
(MWPCs). As test measurements in July 2014 have shown, the MWPCs could
not cope with the three times higher photon fluxes now available due to the
upgraded read-out system described in section 2.6, and hence, they are not
used but left installed during the EPT measurement campaign.
The PID is a barrel detector of 24 scintillators with 50mm length and
4mm thickness, each element covering 15° of azimuthal ϕ-angle. The detector
was constructed in 2007 and replaces the first version from 2004 [40–42]. It
22
2.4. The Crystal Ball (CB) detector system
Figure 2.6.: The liquid hydrogen target geometry with 10 cm long inner target
cell, adapted from [39, 40]. Its length is measured under cold
conditions with the photon beam as an x-ray source and Polaroids
as photo plates. It can be changed to 5 cm and 15 cm by different
entrance window adapters. The photo shows the target cell with
the beam exit window and the semi-transparent Kapton foil to
the right.
measures the small energy deposition ∆E of charged particles, such as protons
or electrons, and thus allows for the discrimination of different particle types
using the ∆E/E technique if the deposition can be successfully matched to a
cluster with energy E in the calorimeter.
The CB NaI calorimeter was constructed in the mid-1970s [43] and, after
being deployed at different experiments, moved to Mainz in 2003 [44]. The 672
truncated pyramid crystals are arranged in an icosahedron geometry divided in
two hemispheres separated by an equator gap of 10mm, as shown in figure 2.8.
They cover the full azimuthal angle and a polar angle of 22° ≲ θ ≲ 158°
corresponding to 94% of 4π sr solid angle in the lab frame. The crystals are
optically isolated from each other and thus the detector is ideally suited to
determine the location and energy of electromagnetic showers.
Since the scintillation light of NaI has a typical rise-time of 30 ns and is
converted to electrical signals with fast PMTs, an analog sum of all inputs can
be used to trigger the read-out, called the CB energy sum trigger. To this
23
2. Experimental setup
Photon Beam
Target
Crystal Ball
PID & MWPC
Vetos
PbWO4
TAPS
BaF2
Figure 2.7.: The A2 detector system. The CB apparatus consists of the in-
ner detectors surrounding the target, PID and MWPC, and NaI
calorimeter array, which consists of 672 NaI crystals (some not
drawn), excluding 720− 672 = 2× 24 crystal positions around the
entrance and exit of the photon beam. The TAPS apparatus in
forward direction consists of 384 BaF2 modules and 72 PbWO4
crystals close to the beam axis. In addition, 402 hexagonal plastic
scintillator “Vetos” are installed in front of the crystals.
24
2.4. The Crystal Ball (CB) detector system
y Major Triangle
x
z
Icosahedron
20
y Minor Triangle
x
z
80
y Crystals
x
Equator
z Tunnel Region
720
Figure 2.8.: CB icosahedron geometry. The twenty major triangles are divided
into four minor triangles, each consisting of 9 truncated pyramids
as crystal positions. On the right, one truncated pyramid crystal
including the attached PMT is shown, and a picture of the CB
detector as currently installed in Mainz, viewed from the down-
stream side of the photon beam, where TAPS is positioned during
experiment. See also figure 2.7.
25
2. Experimental setup
Figure 2.9.: The optically isolated BaF2 crystal is directly read-out by a PMT.
The Veto scintillator light is transferred via fibers to MCP PMTs.
From [40].
end, the HV of each PMT must be tuned to obtain a homogeneous trigger
response [45–47]. This calibration is carried out with a radioactive americium-
beryllium source emitting 4.438MeV photons, which corresponds to roughly
1% of typical energy depositions during beam times.
2.5. The two-arm photon spectrometer (TAPS)
Due to the fixed target geometry of the experiment, the final state particles are
scattered predominantly in the forward direction. Hence, a part of the modular
TAPS detector system [48, 49] is installed as a forward wall calorimeter to
cover the polar angle region of 4° ≲ θ ≲ 20°. The 384 hexagonally shaped
BaF2 detector modules, as shown in figure 2.9, are arranged in six sectors
around the beam axis. Additionally, in order to handle the higher particle
fluxes close to the beam axis, 72 PbWO4 crystals have been installed as a
replacement for the two inner BaF2 rings [50], as shown in figure 2.7.
In front of each BaF2 module (or a group of four PbWO4 crystals), a hexag-
onally shaped plastic scintillator with 5mm thickness is installed [51]. Those
402 so-called Veto elements measure the small energy loss of charged particles
and facilitate ∆E/E particle identification, similar to the PID elements in the
CB detector.
Since the distance of the TAPS front face from the target center is 145.7 cm
and the timing resolution is about 1 ns, the time-of-flight (ToF) distinguishes
photons and highly relativistic electrons from neutrons and protons. In addition,
the ratio of the slow and fast component of the BaF2 scintillation light varies
for hadronic and electromagnetic showers. Based on this effect, the pulse shape
analysis (PSA) technique is available for the identification of particles. As
26
2.6. Upgrade and improvements in October 2013
discussed in more detail in section 4.1, the scattered protons from η′ photo-
production at EPT incident photon energies have a maximum polar angle of
θmax ≈ 22°, which renders TAPS a well-suited proton detection device.
2.6. Upgrade and improvements in October 2013
This section describes the various improvements undertaken before the EPT
measurement campaign and discusses details of the DAQ related to those
efforts. Within the scope of this thesis, the stability and performance of the
DAQ has been improved significantly, rendering the subsequent beam-times
less error-prone and thus more efficient. Those efforts also contributed to the
hardware feasibility studies for new DAQ components presented in chapter 3,
as a sound examination of the status quo is a prerequisite both for potential
hardware replacements and incremental upgrades. In the following, the term
“performance” is used to describe the speed of the data acquisition, which is
quantified by the mean read-out time for typical events. Obviously, this depends
on the experimental conditions: For example, the higher the beam energy, the
more reaction products are scattered in forward direction leading to more data
to be read-out in the corresponding solid angle. In contrast, the term “stability”
is used to describe improvements for the maintainability and reliability of
the system. This is quantified by the percentage of provided beam-time
actually used to record data flawlessly. For example, up to 10% of the beam
time in October 2012 was exclusively used to restart the DAQ. The upgrade
took place from October 2013 until the beam time in December 2013 and
consists of several parts, which all together are necessary to achieve the desired
performance and stability improvement. Extensive technical documentation
of this upgrade is available as a DokuWiki [52], which has been specifically
commissioned for this upgrade and later expanded to a collaboration-wide
source of practical information.
Accompanying the move of the CB calorimeter to Mainz in 2003, a new
data acquisition was installed to digitize analog signals from the electron
tagger ladder, the CB calorimeter, the PID and the MWPCs. The COMPASS
experiment provided the majority of hardware components [53]. For example,
the COMPASS Accumulate Transfer and Cache Hardware (CATCH) with 9U
VMEbus form factor is used with F1 TDC Application-Specific Integrated
Circuit (ASIC) mezzanine cards to measure the timings of all detectors except
for the TAPS apparatus. A simplified overview of the DAQ components as
of 2014 is shown in figure 2.10. Usually, auxiliary analog circuits split the
signal path to measure the integral of signals in parallel to the timing. For
27
2. Experimental setup
vme-tagg-tdc-a/b
Tagger KPH VMECPU/VITEC
352
COMPASS CATCH TDC
EPT
47 vme-beampolmon
KPH VMECPU/VITEC
LeadGlass GSI VUPROM FPGA vme-exptrigger
1 KPH VMECPU/VITEC
vme-cb-adc-1a/1b/2a/2b GSI VUPROM FPGA
CB KPH VMECPU/VITEC
672 COMPASS iSADC IRQ/ACK/EvID
PID CAEN V792 QDC
24 vme-cb-tdc-a/b
MWPC1 KPH VMECPU/VITEC
232+69+77 COMPASS CATCH TDC
=378
MWPC2 vme-mwpc-adc-a/b
296+89+97 KPH VMECPU/VITEC
=482 COMPASS iSADC vme-taps-triggerKPH VMECPU/VITEC
GSI VUPROM FPGA
vme-taps-baf-a/b/c/d/e/f
TAPS BaF2 KPH VMECPU/VITEC
6x61=366 TAPS NTEC 4ch IRQ/ACK/EvID
TAPS Veto vme-taps-veto-ab/cd/ef
6x64=384 KPH VMECPU/VITECTAPS NTEC 8ch
TAPS PbWO4 vme-taps-pwo
6x12=72 KPH VMECPU/VITEC
CAEN V1190 TDC
CAEN V965 QDC
Figure 2.10.: A simplified layout of detector and associated DAQ components
as of 2014. On the left of the diagram, the detectors and their
physical number of channels are shown (for example, CB has
720 logical channels, but the beam entrance and exit region are
left out). Their connection to the VMEbus crates are shown
which usually handle the digitization of timings (TDC) and
integral measurements (ADC/QDC). Furthermore, the trigger
system, which is mainly based on VUPROM FPGA boards, is
displayed very simplistically in blue, handling the read-out with
interrupt (IRQ), acknowledge (ACK) and event number (EvID)
distribution.
28
2.6. Upgrade and improvements in October 2013
VME vme-cb-adc-1a/1b/2a/2bKPH VMECPU Ethernet
VITEC IRQ/EvIDACK
COMPASS GeSiCa TCS
300ns delayed output
CB AnalogSplitter COMPASS iSADC
P2P i2c
COMPASS iSADC optical720 ch 23x2x16 ch PM-02 Low threshold
discriminator
CB AnalogSum to TDC only vme-cb-adc-2bCAEN V792 PID Gate/via NIM Linear High threshold FastClear
FanIn/FanOut to CB Multiplicity
VME vme-cb-tdc-a/bKPH VMECPU Ethernet
NIM/CAMAC Cable VITEC
IRQ/EvID
ACK
PID 10x Amplifier/ Delay24 ch TCSSplit/Discriminator F1 COMPASS TCS
RefTDC F1 CATCH Rec-eiver
Trigger F1 9U
Charged F1
Cluster
only vme-cb-tdc-b
VME to i2c
VME vme-exptriggerKPH VMECPU Ethernet VME
vme-tagg-tdc-b
KPH VMECPU Ethernet
optional VITEC VITEC
CB Esum IRQ/EvIDACK
discrimi- VUPROM master COMPASS TCS sender
TCS
CB Esum PID Gate/ TCSnator FastClear Start/
L1 low Thr. VUPROM CBMult Stop
L2 high Thr.
CAMAC Controller
Figure 2.11.: Components of the COMPASS-based DAQ for the CB and PID
detectors. Blue indicates trigger components, green indicates
FEE components, red indicates TDC or ADC components. Most
parts are located in VMEbus crates, denoted with their corre-
sponding host names vme-* assigned to the KPH VMECPU, see
also section 2.6.1. The analog signals from CB are split, delayed
and discriminated with specialized hardware to serve the trigger
system with fast event information such as hit patterns and the
CB energy sum (Esum) trigger signal. The 24 PID channels
are handled with standard NIM and CAMAC parts. The 720
CB channels account for the full icosahedron geometry, of which
only 672 are in use due to beam entrance and exit holes. Due to
historical reasons, the COMPASS TCS sender is still located in
a tagger-related crate. Note that for simplicity, not all trigger
connections and level converters are shown and the MWPCs and
the tagger, which are also read-out by COMPASS CATCH and
iSADC hardware components, are omitted.
29
2. Experimental setup
raw TDC spectrum
~25mV 
≅ 10MeV
~40MHz
~40MHz
Figure 2.12.: The CB analog sum signal shows a humming structure of about
40MHz as measured directly with a oscilloscope (left panel). This
hum is also visible in the TDC raw spectrum of some channels
(right panel). Several mitigations, such as better shielding, have
been tried unsuccessfully. From [54].
example, the CB and MWPC signals are digitized with COMPASS sampling
ADC boards, called iSADC, in combination with GEM Silicon Control and
Acquisition (GeSiCa) VMEbus boards. This is depicted in more detail in
figure 2.11 for the current realization after the upgrade.
The COMPASS read-out is designed to work with the bunched structure
of particle beam spills lasting 5.1 s and repeating every 16.8 s [55], which is
not present in the A2 experiment using quasi-continuous photon beams. The
COMPASS TCS distributes corresponding “begin-of-spill” and “end-of-spill”
signals via serial optical connections to the CATCH and GeSiCa boards besides
the actual internal read-out trigger. The TCS controller itself is managed
by the A2 experiment trigger system, and the whole TCS subsystem is reset
by a stop and start sequence issued every 105 events, which corresponds to
roughly one minute at typical event rates. Furthermore, the various COMPASS
components such as the CATCH and GeSiCa modules need a specific sequence
of “begin-of-spill” and “end-of-spill” to properly initialize the FPGAs with the
corresponding firmwares and register settings. For example, the firmware of the
COMPASS iSADC modules is transmitted via optical links from the GeSiCa
module under the precondition that the COMPASS TCS sender indicates
an “end-of-spill”. Before the upgrade in 2014, the system was maintained by
simplistic shell scripts with long wait periods due to sequential processing and
lacking state validation, which summed up to restart times on the order of 10
minutes. The initialization of the TCS was carried out manually by experts
30
2.6. Upgrade and improvements in October 2013
120
100
80
60
40
20
0
61800 61900 62000 62100 62200
ξ / raw units
Figure 2.13.: The CATCH TDC raw value distribution is shown for the channel
measuring the trigger reference timing. The black arrow indicates
the wrap-around value of 62054. The fitted sine wave modulation
is close to the COMPASS TCS frequency of 38.88MHz using the
conversion factor of 0.1171 ns per raw unit.
with a high probability of intermittent mistakes and retries. Accordingly, the
procedures for properly handling the COMPASS system have been improved
and are now fully automated by a script called “AcquManager”, taking care
of many failure states and properly reporting them to the user. During the
development of dedicated read-out software for the GeSiCa system independent
of the standard Acqu DAQ software, a readout bug in the system was discovered
for high buffer occupancies in the GeSiCa module and was fixed in January 2014,
see [40] for a detailed investigation. Furthermore, the whole COMPASS system
is synchronized to a clock with a frequency of 38.88MHz, which is probably the
source of the still unresolved hum on the CB analog sum, deteriorating its use
as a trigger signal as shown in figure 2.12. Another strange behavior is observed
in the distribution of raw values read-out from the CATCH modules shown in
figure 2.13. Although the correct wrap-around value is 62054 [36, 53] leading
to double-peak free timing spectra, see also section 4.4 on page 73, larger
raw values up to 62112 are observed. Again, the aforementioned hum is seen
as a sine wave modulation yielding more evidence that the TCS clock is the
source. Those shortcomings of the experimental setup, in particular concerning
the COMPASS components, still exist as of now although mitigations on the
software and hardware level have been tried.
31
2. Experimental setup
Since the BaF2 scintillation light consists of a fast and slow component,
the New TAPS Electronics Card (NTEC) add-on has been developed to
digitize four BaF2 signals [56] as a mezzanine card for the CAEN V874A
VMEbus board. Besides the integration over a short and a long gate each
with a high- and low-sensitivity gain, a CFD for timing and two leading-edge
discriminators (LEdDs) are implemented, whose outputs are also provided to
the trigger system for multiplicity-based event discrimination. Moreover, a
simplified version of the NTEC add-on digitizes eight TAPS Veto signals. The
TAPS calorimeter was used at different experimental facilities with customized
geometrical configurations. Thus, TAPS had its own stand-alone DAQ until
2013, and the remaining Acqu DAQ was coupled to it. This “coupled mode”
was a permanent source of errors and decreased the efficiency of beam times
tremendously. For example, restarting the coupled DAQ required manually
executed commands taking up several minutes to complete with a considerable
chance of failure. This makes a unified and automated readout system highly
desirable. Nevertheless, since the TAPS HV is calibrated before every beam
time using minimum ionizing cosmic radiation to ensure homogeneous trigger
responses, at least a stand-alone run mode and analysis of calibration data is
required. The installation of an FPGA based trigger system in 2012 [40, 57]
played a pivotal role in order to properly integrate the TAPS system into the
remaining experimental apparatus, which was finally achieved in the 2013/2014
upgrade.
In principle, most of the signal digitization is done with a variety of VMEbus
modules, as shown in figures 2.10 and 2.11. The bus is controlled by a master
module running a 32-bit Linux-based system, which sends the acquired data as
Transmission Control Protocol (TCP) streams to the event merger. In order
to improve the performance without modifying the master module, the crucial
quantity to reduce is the number of VMEbus cycles needed to read out the
whole system. This has been achieved for the CB and tagger section of the DAQ
by splitting the backplane of each VMEbus crate into two parts, doubling
the number of VMEbus master modules. Besides several other technical
improvements to the DAQ, such as the introduction of Experimental Physics
and Industrial Control System (EPICS) and virtualization of crucial computer
systems, two key developments are presented in sections 2.6.1 and 2.6.2, which
improve the stability and the performance of the whole system, respectively.
Eventually, the whole DAQ is twice as fast after the upgrade, which is a
substantial contribution to the η′ measurement campaign leading to the analysis
presented in chapter 4.
32
2.6. Upgrade and improvements in October 2013
Figure 2.14.: An image of the VITEC PCB designed by Klaus Weindel, KPH
electronics workshop. The FPGA is realized as a commercially
available mezzanine card. The prominent hole in the PCB makes
the VITEC a perfect fit for the heat-sink of the “KPH VMECPU”,
a simple VMEbus master module. This frees a previously blocked
slot in densely packed VMEbus crates.
2.6.1. Streamlined VME readout scheme
Besides performance improvements, the upgrade also streamlined the overall
readout scheme of the DAQ as follows: Each VMEbus crate including TAPS
is controlled by the KPH VMECPU, which is a VMEbus master module
developed by the KPH electronics workshop, in conjunction with the KPH
VITEC module in figure 2.14, which is a multi-purpose input/output VMEbus
slave module.
The VITEC uses a complex programmable logic device (CPLD) to commu-
nicate over VMEbus and thus provides access to an FPGA handling the NIM
and Emitter-coupled logic (ECL) input/output connections. Both firmwares
for the VITEC have been developed in VHSIC hardware description language
(VHDL) as part of this thesis [58] including auxiliary programs and VHDL
simulation test benches rendering future modifications verifiable. Furthermore,
the outsourcing of the VMEbus communication to the CPLD enables the
programming of the FPGA with newly developed firmwares without risking
a cumbersome manual recovery via the Joint Test Action Group (JTAG)
standard pin header due to malfunctioning firmware, as it is the case for the
commonly used VUPROM VMEbus modules. The VITEC FPGA mainly
handles the NIM communication to the trigger system via the interrupt (IRQ),
acknowledge (ACK) and serial event number (EvID) NIM signals, see also
figure 2.10. It indicates a rising edge on the IRQ signal via a status register
33
2. Experimental setup
bit, which is constantly polled by the AcquDAQ instance over the VMEbus in-
terface to start the read-out of the attached modules. The AcquDAQ instance
acknowledges the IRQ signal to the trigger system by setting the ACK signal
high. During read-out, the event serial number is received from the trigger
system and stored by the VITEC. After all modules have been read-out by the
AcquDAQ instance, the ACK is set to low, the serial event number is attached
to the event and eventually transmitted to the AcquRoot event merger via
Ethernet. The correct behavior of the VITEC is thoroughly scrutinized with
the aforementioned test benches and described in detail in [52]. Moreover,
the VITEC features an additional Arduino-compatible microprocessor to inde-
pendently monitor the voltages supplied to the VMEbus modules, indicating
imminent crate power supply failures.
In total, 12 + 11 = 23 “KPH VMECPU and VITEC” compounds are
responsible for the complete read-out of the CB and TAPS system, respectively,
all containing a disk-less 32bit x86 single board computer (SBC) running an
identical Debian GNU/Linux system, see also figure 2.10. This homogeneous
computer infrastructure design enabled the development of the AcquManager
script, which reduces the whole DAQ restart time from about 10 minutes
to 5 seconds. Thus, the whole DAQ software is restarted completely before
each run to increase stability. Restarting a run internally via the Acqu
system without killing all processes is not properly distributed to all AcquDAQ
instances most likely due to an incorrect implementation of the inter-process
communication. This leads to inconsistent states and potential data corruption
such as unsynchronized periodic slow control reads, known as scaler reads, or
the loss of data from COMPASS components due to improper setup of the
TCS. Although several attempts to improve this internal restart behavior of
the DAQ have been made, its multi-threaded network-distributed master-slave
“design” likely requires a rewrite from scratch to realize a proper fix.
2.6.2. TAPS efficient readout scheme
As already mentioned, the TAPS detector was handled until 2013 as a stand-
alone system with its own data-acquisition software, including slow control
tasks, such as HV and threshold settings. Since the existing VMEbus mas-
ter modules were single-core computers, a performance gain was expected
by replacing them with dual-core CPUs. However, as dedicated tests and
measurements of the VMEbus readout cycle time with an oscilloscope have
revealed afterwards, the performance is solely limited by the VMEbus com-
munication cycle as shown in figure 2.15 and not by other factors, such as
the CPU processing power or the Ethernet network bandwidth. Thus, the
34
2.6. Upgrade and improvements in October 2013
Figure 2.15.: VME timing measurement during the polling of the VITEC
status registers. Channel 1 (yellow) shows the DTACK (data
acknowledge) signal, channel 2 (cyan) shows the AS (address
strobe) signal, channel 3 and 4 are irrelevant here. As indicated by
the a/b cursors, one read cycle of the status register takes 2.14µs.
During that cycle, DTACK and AS are both high for about 40%
of the cycle time, which means that the VMEbus master spends
a significant percentage with internal PCI communication during
one VMEbus cycle. The length of VMEbus cycle time is currently
the limiting factor for the DAQ performance.
previous employed TAPS DAQ is unexpectedly faster than the “upgraded”
system with dual-core KPH VMECPUs. In fact, the KPH VMECPU consists
of a single-board computer connected via the PCI 32 bit bus to a CPLD inter-
facing the VMEbus. The advantage of this approach is that inside the Linux
operating system, the VMEbus is directly accessible via memory access within
the PCI address space without any additional kernel driver module. However,
the CPLD does not support block address accesses to the VMEbus and thus
is rather slow in particular with NTEC modules as slaves. Furthermore, the
firmware for the CPLD is rather undocumented and written in the hardware
description language ABEL, hampering the reduction of the single address
VMEbus access cycle time of 2µs, of which at least 0.8µs are spent in the
35
2. Experimental setup
4 4
inputs inputs
NTEC 1 NTEC 2
VME bus
VME CPU Data
FPGA Serial bitpattern:Which modules 
Trigger have data? VITEC
Figure 2.16.: The elements of an efficient readout scheme for the TAPS data-
acquisition, called “SpeedTAPS”. The NTEC transmits its hit
pattern to the trigger system for multiplicity-based triggering.
This information is passed on to the read-out, skipping “empty”
modules and thus increasing speed.
PCI communication, as shown in figure 2.15.
Since the TAPS subsystem turned out to be the slowest part of the DAQ
under typical beam conditions, the so-called SpeedTAPS technique is crucial to
eventually gain a performance improvement from the whole upgrade. The basic
idea is that the trigger system already knows after about 100 ns the hit pattern
of each detector module, since the NTEC cards send their discriminated outputs
immediately to the corresponding FPGA trigger module. This information is
additionally transmitted to the KPH VMECPU as a serial bit pattern in order
to reduce the number of VMEbuss accesses when reading out the modules
sequentially, as depicted in figure 2.16. To this end, the FPGA firmware for
the TAPS trigger system is modified to send out the occupancy for each NTEC
module as a serial bit pattern to the VITEC via an additionally installed
signal cable. Furthermore, the VITEC firmware is modified to provide this bit
pattern to the Acqu DAQ instance, which accordingly skips the NTEC modules
indicated as empty. This reduces the mean number of necessary VMEbus
accesses significantly and thus the mean readout time of the TAPS system is
improved from 176µs to 56µs. The correctness of this readout scheme has
been tested in detail [52] yielding a negligible probability of less than 10−5
per event that some data is found in the NTEC although the corresponding
bit pattern indicated an empty module. This is attributed to an incorrectly
working NTEC board and is most pronounced in case of the 8 channel version
for the TAPS Veto signals.
36
3. Hardware upgrade design studies
The existing electronics for the tagger and CB apparatus were installed in 2004
and are mostly based on hardware from the COMPASS collaboration [53], as
presented in chapter 2. After over ten years in operation, a sufficient number
of spare modules is not available anymore and documentation or support for
those devices from the COMPASS collaboration becomes harder to obtain.
Furthermore, most of the modules need firmwares for which no source code is
directly available to the collaboration, which renders fixes or improvements
impossible. Thus, to ensure the maintainability for the next decade of the
whole DAQ system including TAPS, the replacement of existing hardware by
new components fulfilling the detector requirements has become mandatory.
One important prerequisite of the feasibility studies is that an extensive
custom electronics development is not feasible within the A2 collaboration, so
as in 2004, existing electronics from other experiments or institutions needed
to be triaged and tested. The initial search focused on a modular system with
well-developed software and firmware environments due to the experiences with
the existing system, which suffers from the complexity of manifold hardware
components and closed-source firmwares. Of course, the anticipated system
should at least meet the timing resolutions as well as linearity and dynamic
ranges for energy measurements as further discussed in section 3.1, such that
solely the physical properties of the detectors limit the achievable performance
for A2 experiments. Eventually, the TDC readout board revision 3 (TRB3)
platform fulfilled all those requirements as presented in section 3.2.
Within the scope of this thesis, the integration of the TRB3 platform into
the existing A2 DAQ system and tests of different read-out approaches mostly
targeted at the CB calorimeter were achieved, as presented in sections 3.3
and 3.4. In section 3.5, the future upgraded system is discussed including
possible alternatives and intermediate upgrade milestones.
3.1. Experimental requirements
In total, the current A2 detector system consists of roughly 3000 channels, from
which timing and integral information is digitized after typical read-out times
of 150µs, see also section 2.6. The analog signal properties of the detectors,
37
3. Hardware upgrade design studies
which crucially determine the choice of the FEE components, are summarized
in table 3.1.
For a simple hit detection, as it is required for example for the tagger, a
single-channel time resolution of about 1 ns is sufficient to properly correlate
events. For ToF measurements, which can help to identify nucleons, a timing
resolution of at least 100 ps in TAPS is desirable. The trigger signal serves
as the reference for all timing measurements and is usually inferred from the
analog CB sum using a low threshold close to the noise level to avoid a timing
shift depending on the amplitude, the so-called time-walk. Still, this reference
typically limits the achievable resolution but can be compensated by an off-line
calculation of timing differences between detectors, such that the implicit
trigger reference cancels. See chapter 4 for further discussion of the relevance
of timing resolutions with respect to analysis.
In case of the calorimeters CB and TAPS, a linear conversion of the scin-
tillation light output is of paramount importance to ensure a proper energy
measurement of the electromagnetic shower. Of course, the linearity should
cover the whole range of energy depositions, which is typically from about
1MeV up to 400MeV for a single crystal, which corresponds to a large dynamic
range of 400. For CB, the response of the integral digitization hardware has
been verified using a signal generator in figure 3.1. As the summation and
pedestal subtraction is carried out digitally over a 40MHz sampled waveform
using a properly configured integration gate derived from the trigger, the
non-linearity is exceptionally small. In comparison, the PID has a much lower
dynamic range of about 50 and thus an analog integration becomes more
feasible for this detector. For TAPS, the slow and fast component of the
BaF2 scintillation light is currently integrated over a short and long gate in
parallel using dedicated analog circuits, which can be exploited to differentiate
hadronic from electromagnetic showers.
In summary, modern readout hardware can easily cope with the experi-
mental requirements for timing and integral measurements. However, the
adaption of already available solutions to each of the detector requires detailed
investigations and careful planning.
3.2. The TRB3 platform
The TRB3 is a 4 + 1 FPGA multi-purpose digital electronics PCB, which was
originally developed by the GSI Helmholtzzentrum für Schwerionenforschung
GmbH (GSI) in Darmstadt for the high-acceptance dielectron spectrometer
(HADES) collaboration [59]. Via additional mezzanine cards, so-called add-
38
3.2. The TRB3 platform
Detector/Scintillator Channels trise/ns tfall/ns Pile-up/‰
Tagger/EPT, Organic 352/47 2 10 1
CB, NaI(Tl) 672 30 400 0.4
PID, Organic 24 2 10 0.01
TAPS, BaF2 366 2/620 20/2700 3
TAPS Veto, Organic 384 2 10 0.01
TAPS, PbWO4 72 6 30 0.03
Table 3.1.: Signal properties of the main A2 detectors. The typical signal
shapes are characterized by their rise- and fall-times, and usually
determined by the scintilla(ting material.)The Poisson-distributed
pile-up probability 1− exp −r(trise+ tfall) was calculated for event
rates r of 1 kHz and 100 kHz for usual detectors and tagger, re-
spectively. The MWPCs are omitted here, as their suitability for
high rate experiments is questionable. Anyhow, they have similar
properties as the TAPS Veto detectors.
Current Hardware: Sampling ADC
5000 3
2.5
4000
2
3000
1.5
2000
1
1000
0.5
0 0
0 1000 2000 3000 4000
Total Charge / pC
Figure 3.1.: In the left panel, a single channel CB analog signal generated by a
random cosmic event is measured at the non-delayed TDC output
of the analog splitter. With 100 ns/div, the typical rise- and fall-
time of 30 ns and 400 ns is determined. Measuring parasitically
using a high-impedance probe is difficult due to the omnipresent
hum at the CB frame, see also section 2.6. The right panel shows
a signal generator test measurement of the raw ADC output value
using triangularly shaped pulses with different amplitudes, see
also equation (3.1) on page 46. The relative precision is given by
RMS over the mean.
39
ADC Raw Value
Relative Precision / %
3. Hardware upgrade design studies
Figure 3.2.: An image of the TRB3 PCB. The central FPGA is connected to the
eight on-board SFPs, and the four peripheral FPGAs communicate
with customizable add-on boards via high-density connectors.
on boards, the four peripheral FPGAs are connected to various front-end
electronics boards, see figure 3.2. The central FPGA acts as a data concentrator
and transmits the event data stream via standard Gigabit Ethernet connection.
The TRB3 user community has substantially grown beyond HADES and the
board is for example one crucial component of the readout system envisaged
for the anti-proton annihilations at Darmstadt (PANDA) experiment. It ships
with extensive documentation [60] and was tested in several beam-times and
larger setups with various front-ends [61–63].
More complex TRB3-based DAQ systems are realized by connecting multiple
TRB3s with optical serial links either via the on-board SFP transceivers or
via hub add-on boards providing six additional SFPs. Each FPGA is uniquely
identified via hard-coded 64 bit provided by the attached one-wire temperature
sensor. Using this identification, the so-called TrbNet models the FPGAs
as logical endpoints within a network hierarchy. TrbNet provides convenient
distribution of different trigger types, the transport of acquired data from the
FPGAs and access to registers for monitoring, slow control and debugging
[64–66]. It is implemented as well-structured VHDL entities and enables
40
3.2. The TRB3 platform
external users, such as the A2 collaboration, to develop customized firmwares
efficiently [61].
To access the TrbNet, one TRB3 is connected to a off-the-shelf computer via
standard Gigabit Ethernet. The Internet Protocol (IP) configuration of the
TRB3 is setup by Dynamic Host Configuration Protocol (DHCP) and accessed
via already provided TrbNet low-level user tools, providing basic register access
and in-field firmware programming. The read-out data is concentrated into
one Uniform Datagram Protocol (UDP) packet per event with a maximum size
of 64 kB. Furthermore, the TRB3 ships with a Central Trigger System (CTS)
component implemented on the central FPGA, which controls the triggered
read-out of all front-ends and can be conveniently configured via a responsive
web-based graphical user interface (GUI) [67]. This makes the TRB3 suitable
for table-top experiments such as front-end test environments as well as for
large-scale production detector systems.
Typically, the peripheral FPGAs are used as TDCs for discriminated digital
signals, as the acronym TRB3 already indicates. The TDCs are realized using
the tapped delay-line method [68], which exploits the physical propagation
time of the electrical signals inside the FPGA. Up to 64 + 1 TDC channels
are implemented with channel-to-channel resolutions in the order of 10 ps [69].
This is√two orders of magnitude better than the coarse counting resolution
of 5 ns/ 12 ≈ 1.4 ns RMS using a simple 200MHz digital clock counter. The
currently provided firmware is adaptable to different user requirements, such as
leading and trailing edge measurements in one channel or internal stretching of
very short signals, and thus ready-to-use for many applications [70]. However,
the asynchronous delay-lines are realized as digital adder carry-chains inside
FPGA slices and hence need a temperature-dependent calibration, which
assigns to each segment of the delay line a physical propagation time. To
obtain this calibration, each TDC channel needs to be fed with uncorrelated
signals with respect to the coarse counting clock. Otherwise, the likelihood
that the incoming hit stops in a certain delay bin is not uniformly distributed,
which spoils the statistical treatment of this problem. If those uncorrelated
hits are not provided directly by the attached detector system, which is in
particular the case for reference timings needed to synchronize channels across
FPGAs, the insertion of hits from an uncorrelated clock source is required.
This is already realized by artificial TDC calibration events within the TRB3
CTS.
The last component of the TRB3 platform is the versatile event builder called
Data-Acquisition Backbone Core (DABC) [71–74] amended by the flexible
ROOT-based analysis framework Go4 [75]. DABC merges the data streams
from multiple input sources, such as TRB3s or EPICS slow control, into one
41
3. Hardware upgrade design studies
HADES list mode data (HLD) stream [76, 77], which is eventually written
to disk or transported to on-line processing Go4 instances. Additionally, it
provides low-level analysis routines such as the TDC delay-line calibration.
Within the scope of this thesis, a simple stand-alone unpacker has been
developed [78] using the conventional HADES event builder “hadaq” but
was later replaced by the DABC/Go4 system. Furthermore, specific analysis
components for the TRB3 ADC add-on presented in section 3.4 have been
integrated into the so-called Stream library as part of the Go4 framework.
To integrate a TRB3 subsystem into the AcquRoot-based A2 DAQ as shown
figure 3.3, two goals were successfully achieved: First, the experiment reference
timing and a 16 bit serial ID provided by the A2 trigger system [40] as NIM
signals are fed into the TRB3 event stream. This led to the development of an
additional module for the TRB3 CTS, which is already merged into the TRB3
VHDL source repository. Second, the TRB3 UDP packets are processed by a
customized AcquDAQ instance with TRB3 software modules and subsequently
transmitted to the A2 event merger. The necessary modifications to the A2
Acqu ecosystem are available in the “trb” branch of the author’s repository
[79]. Other possible integration schemes will be discussed in section 3.5.
3.3. Charge-to-time conversion front-end PaDiWa
AMPS
Since the TRB3 is equipped with a mature TDC firmware for the peripheral
FPGAs, it appears convenient to convert any relevant detector information,
such as integrals or timings, into logical signals which are then digitized by the
TDC. The PANDA DIRC WASA (PaDiWa) front-end family was developed
by GSI following the COME&KISS concept [80], which promotes the usage of
readily available commercial elements (COME), such as FPGAs, and keeping
the remaining parts simple and sound, or stupid (KISS). For example, the
LVDS input buffers of a Lattice MachXO FPGA are mis-used as a leading-
edge discriminator as follows: The (possibly amplified) analog input Vin is
applied to the positive input of the differential buffer and a variable threshold
voltage Vthr generated by the FPGA with PWM to the corresponding negative
input. If the difference Vthr − Vin reaches the transition region of the input
buffer, the digital output signal becomes metastable. The resulting noise
causes hit rates in the order of 10MHz in the corresponding TDC channel.
Assuming that no detector hits arrive and thus Vin stays at the constant
baseline voltage, the threshold reference value V refthr to which the input signals
are relatively discriminated is thus determined by searching the maximum
42
3.3. Charge-to-time conversion front-end PaDiWa AMPS
NIM Crate Experiment TRB3Trigger
A2 Trigger Central FPGANIM2LVDS
A2 Trigger Central
Event ID Module TriggerSystem
Crystal Ball PaDiWa Front-End Peripheral FPGA
Analog/Splitter 16ch Leading Edge 64ch single edge TDC
300ns delayed Discriminator 32ch rising/falling edge
a2trb (desktop machine)
Event Merger AcquDAQ
AcquRoot TDAQ_TRB3 UDP PacketTTRB3module Fan-out
Online Display
Disk HADES DAQ
Figure 3.3.: TRB3 DAQ integration as used for test measurements, here shown
for a PaDiWa board attached to the CB analog-splitter, see sec-
tion 3.3 and figure 2.11 on page 29. The A2 trigger system provides
the reference timing and the Event ID for each event. The signal
data flow, as shown by red arrows, is eventually sent via network
to the AcquRoot event merger.
43
3. Hardware upgrade design studies
 100000
 10000
LVDS Input Buffer
V  1000in + to TDC  100
_
Vthr  10
100n  1
10k 10k  0.1PWM from FPGA
 0.01
100n 1u  2845  2850  2855  2860  2865  2870
Threshold Voltage / mV
Figure 3.4.: The left panel shows how the FPGA LVDS input buffer is used
as a discriminator for the signal Vin. The threshold voltage Vthr is
generated by the FPGA as well using a low-pass filtered PWM
signal. The right panel shows a scanning measurement of the TDC
hit rate for different settings of Vthr. The maximum hit rate is
found at Vthr ≈ 2858mV, which is then used as the reference V refthr .
TDC hit rate with respect to Vthr. This is depicted in figure 3.4. Since the
exact value of V refthr depends on the FPGA input buffer and the input baseline
voltage, this procedure is automated by auxiliary scripts. Temperature drifts
of those relative thresholds can be reduced to negligible extent within the
FPGA firmware. For example, time-over-threshold (ToT) measurements vary
with roughly 10 ps/K after compensation [81], which is on the order of the
timing resolution and thus negligible with respect to ToT lengths of about
10 ns. Typically, the 16 channel PaDiWa leading edge discriminator achieves
channel-to-channel timing resolutions of 23 ps RMS in conjunction with TRB3
TDCs [82], which is a remarkable achievement regarding the “unspecified use”
of FPGA resources.
Due to the good performance and cost-effectiveness of the PaDiWa discrim-
inator board, an 8 channel integrator board PaDiWa AMPS was developed
by Wolfgang Koenig, GSI, for the HADES electromagnetic calorimeter using
the COME&KISS concept [83–85]. It is based on a modified Wilkinson ADC
circuit with active discharge to achieve high hit rate capability. The functional
principle is also discussed in [86] as dual-slope integration. Similar to Wilkin-
son’s original idea, the charge information of the input signal is converted
into a time interval by using an integration capacitor, which is subsequently
measured by the TRB3 TDC. The leading edge timing of the input signal is
obtained similarly to the PaDiWa discriminator board. Again, the Lattice
MachXO FPGA discriminates the slow and fast output signals from the
44
TDC Hit Rate / kHz
3.3. Charge-to-time conversion front-end PaDiWa AMPS
FAST
IN
SLOW
DISCHARGE
FEE FPGA
Integration
capacitor
Figure 3.5.: PaDiWa AMPS building blocks, adapted from [83], and the FEE
schematic developed by Wolfgang Koenig, GSI, as implemented
in LTSpice. The integration time is mainly determined by the
indicated capacitor C262. The two TDC channels to measure the
fast and slow signal timings are implemented on the peripheral
TRB3 FPGA.
45
3. Hardware upgrade design studies
analog circuit, and generates an asynchronously delayed discharge signal
from fast, as shown in figure 3.5.
Since the integration capacitor1 is discharged with a constant current, the
ToT of the slow output is proportional to the input charge. However, as
the leading edge of slow arrives slightly earlier for higher input amplitudes,
an effect commonly referred to as time-walk, the ToT linearity is improved
by measuring the leading edge of the fast signal as well. Furthermore, an
active discharge is generated by the FPGA from an asynchronously delayed
fast by charging an external capacitor and discriminating its voltage via
an input buffer with constant reference voltage. The length of the delay is
adjusted by the drive strength of the output pin, which can be specified during
firmware building. Due to this discharge feedback from the fast, V refthr is
first determined for slow while fast is disabled and, after setting the relative
threshold for slow, V refthr is determined for fast and its relative threshold can
be set.
The PaDiWa AMPS FEE is designed for input signals with 10%-90% rise-
and fall-times of roughly 5 ns and 15 ns, respectively. The voltage range of
the input signal is designed as 25mV to 5000mV. The corresponding input
charges reads, using the approximation of a triangular pulse shape with voltage
amplitude∫A,
= = A 1 5 ns + 15 nsQ Idt 50 90% 10% 2 = 0.25 pC/mV ·A , (3.1)Ω −
with the input termination of 50W. Thus, the dynamic range is designed
as 6.25 pC to 1250 pC. This design was successfully tested with a lead glass
prototype of the HADES ECAL detector [83, 85] and different PMT types at
the A2 photon beam line.
Within the scope of this thesis, a LTspice IV [87] simulation was developed
[79] and validated using a signal generator test setup, see figure 3.6. Typical
timings and amplitudes were reproduced with 10% accuracy, supposedly
limited by nominal value variations of certain components, such as capacitors,
and the increased PCB temperature of about 50 ◦C during test. This served as
a model to explore the possible modifications needed for the signal properties
of CB NaI crystals, which are characterized by typical 10%-90% rise- and fall-
times of 30 ns and 400 ns, respectively, and thus an order of magnitude slower
than suitable pulses for the current PaDiWa AMPS design. Furthermore, the
dynamic range of the current A2 readout system based on a 40MHz sampling
ADC is roughly twice as large with an excellent linearity due to the different
1C262 in figure 3.5.
46
3.3. Charge-to-time conversion front-end PaDiWa AMPS
IN FAST
Ampl. 2V
SLOW lope
!
inea
r S
L
Figure 3.6.: PaDiWa AMPS LTspice simulation verification. The photography
on top shows the 8-channel PCB under test including custom
modification to tap different analog signal lines. The bottom panel
shows a screen-shot from the oscilloscope with simulated signals
scaled in xy according to the input signal only. The discharge
is simulated as too long since the slow signal is estimated too
high. The distortions are caused by the stray capacitance of the
attached oscilloscope probe if the discharge signal is measured.
Horizontal scale is 20 ns/div, vertical scales differ for each signal.
47
15ns Fall
e
5ns Ris
3. Hardware upgrade design studies
350 3.5 350
Fast Threshold: 25 mV Fast Threshold: 25 mV
300 Slow Threshold: 25 mV 3 300 Slow Threshold: 25 mV 10
250 2.5 250 8
200 2 200
6
Exp: f(x) = 33.0 + x*0.187
150 1.5 150 Sim: f(x) = 31.8 + x*0.195
f(x) = 33.0 + x*0.187 4
100 1 100
50 0.5 50 2
0
0 200 400 600 800 1000 1200 1400 1600 0 00 200 400 600 800 1000 1200 1400 1600 0
Total Charge / pC Total Charge / pC
Figure 3.7.: The PaDiWa AMPS circuit time interval output against the total
input charge. The rise- and fall-times were varied from 5ns to
14 ns and from 10 ns to 25 ns, respectively, and the amplitude
from 0.1V to 3.5V. For each measurement, the mean of the
total charge according to equation (3.1) on page 46 and the RMS
over the mean as the relative precision are shown in the left
panel. Those measurements are then compared to the LTspice
simulations in the right panel. Furthermore, a linear fit is shown to
asses the non-linearity of the charge measurement. Compared to
the measurement of the existing system in figure 3.1, the linearity
is insufficient.
measurement technique. Figure 3.7 shows that without major modifications of
the analog circuit design, the linearity and the dynamic range of the current
system as given in section 3.1 cannot be achieved. Moreover, a new sampling
ADC add-on became available at the same time which conceptually does not
suffer from such non-linearities, as shown in section 3.4. Thus, the PaDiWa
AMPS was discarded as a possible upgrade option for the CB calorimeter.
Nevertheless, it is still an attractive component for other parts of the A2
detector system, as further explained in section 3.5.
3.4. Sampling ADC firmware development and
measurements
In 2014, the GSI electronics workshop designed a 48 channel sampling ADC add-
on on behalf of a Portuguese group for the readout of resistive plate chambers
(RPCs) [88, 89]. Concerning the firmware, this required a configurable finite
impulse response filter with baseline subtraction and triggered readout. The
add-on is based on 12 quad-channel AD9219 integrated circuits (ICs) with 10 bit
resolution and up to 65MHz sampling rate. To simplify firmware development,
48
ToT Slow + Delta to leading fast
Relative Precision / %
ToT Slow + Delta to leading fast
Relative Difference to Simulation / %
3.4. Sampling ADC firmware development and measurements
the sampling rate was set to 40MHz since for this choice the double-data-rate
(DDR) serializer-deserializer (SERDES) output matches the 100MHz system-
wide TrbNet clock avoiding clock domain crossing (CDC) issues. This can be
seen as follows: At 40MHz sampling rate, the AD9219 outputs 4 channel bit
streams (DCO) and 1 common frame bit stream (FCO) with a DDR rate of
200MHz. Those (4 + 1) · 2 · 200 = 2000Mbit/s are output by the SERDES
as 20 bit parallel at 100MHz, which matches the standard TrbNet system
clock domain. If there is a clock mismatch, additional FPGA resources such
as first-in first-out buffers (FIFOs) are typically required to transfer parallel
buses from one clock domain to the other. This usually results in a complete
redesign of the firmware if CDCs have not been adequately anticipated during
development.
Initially, the write-only Serial Peripheral Interface (SPI) communication
to the ADC and clock distribution ICs was successfully established to setup
the correct phase alignments using the test pattern mode of the ADC. To
this end, the auxiliary MachXO FPGA was programmed as a SPI multiplexer
and scripts to automate the startup have been developed within the scope of
this thesis. Subsequently, the work focused on the development of a feature
extraction firmware as additional VHDL entities, providing timing and integral
information. First, modifications to the existing firmware were made in order
to test if a timing accuracy of a few hundred picoseconds can be achieved
with a sampling period of 25 ns. Although the digital constant fraction dis-
criminator technique with linear interpolation is already employed successfully
in many read-out systems, see for example [90], it was unclear if the 2 or 3
digitized samples of the 30 ns CB signal leading edge are sufficient to achieve a
satisfactory timing resolution, assuming a minimum specified sampling period
of Tsampling = (65MHz)−1 ≈ 15 ns.
Signal generator tests of the modified firmware eventually showed a sufficient
channel-to-channel resolution of about 300 ps RMS and motivated within the
scope of this thesis the development of a fully customizable feature extrac-
tion firmware for the ADC add-on, see figure 3.8. The key component is a
free-running digital CFD extracting the timing information of signals above
threshold. The various TrbNet slow control registers, such as the constant
fraction given by the two multipliers or the delay in number of samples, are
modeled in extensible markup language (XML) and are conveniently config-
ured via an interface inside a web-browser. However, the FPGA firmware
does not calculate the linear interpolation but rather sends the sample be-
fore and after the detected zero-crossing of the cfd signal to the unpacker,
which subsequently calculates the fine timing by linear interpolation. This
circumvents the demanding implementation of pipelined non-integer arith-
49
3. Hardware upgrade design studies
Integral Delay Integrator
Input CFD Delay MULT IntegralSum
10bit 15bit signed 16bit signed
unsigned
16bit signed ZeroX detection,
Threshold Bit ADD Coarse counter,
Generator 11bit signed, 1bit threshold Write to RAM
Subtraction, MULT -1 15bit signed
Polarity Inverter 10bit unsigned, 1bit threshold RAM 32bitEpoch Counter,
Baseline Configurable Trigger Trigger Trb  Integral Sum,Delay ReadoutAverager Delay Net BeforeZeroX, AfterZeroX
Figure 3.8.: The TRB3 ADC feature extraction firmware receives the 10 bit
ADC samples from the SERDES and removes the offset with a
digital baseline follower. Next, the signals are split, one path is
delayed and then both are multiplied and subtracted from each
other to obtain the cfd signal. If a zero-crossing is detected,
an event consisting of the cfd sample before and after the zero-
crossing, the integral and the epoch counter is queued into the
buffer and passed to TrbNet if a readout trigger was received.
metics in an FPGA. With the addition of a coarse counter, this approach
already provides a channel-to-channel timing measurement with sub-sampling
resolution of about 1 ns≪ 15 ns = Tsampling within the same phase-locked loop
(PLL) clock domain, for example one TRB3. Moreover, a baseline follower
constantly averages over the delayed input samples unless the input is not
above a user-configured threshold. This average is subsequently subtracted
from the input values in order to make the threshold relative to the input
baseline.
At this stage of the project, systematic test measurements with a signal
generator revealed a double-peak structure in the relative timings between
two channels with fsampling = 64MHz sampling frequency and trise = 30ns
rise-time of the input signal, as shown in the upper panel of figure 3.9. This
double-peak was most pronounced if the delay between the two identical input
signals was a half-integer multiple of the sampling period and vanished for
full-integer multiples. This effect is explained qualitatively with the Nyquist
criterion, limiting the maximum resolvable sinusoidal frequency component
to fsampling/2. Apparently, the criterion is not met for the input signal with
frequency components of roughly t−1rise ≈ 33MHz. The double-peak structure
was subsequently confirmed by simulations taking into account the jitter
between the sampling clock and the input signal besides the digitization noise.
This led to the choice of fsampling = 80MHz for further measurements, which
50
3.4. Sampling ADC firmware development and measurements
Figure 3.9.: The measured timing difference ∆t between two ADC channels is
shown for three different delays set by a signal generator (ampli-
tude, rise- and fall-time chosen to match CB signal shape). In the
upper panel, the two undistorted Gaussian peaks with σ ≈ 0.3 ns
are separated by T −1 −1sampling = fsampling = (64MHz) ≈ 16 ns delay
difference. In between those two undistorted peak, with about
8 ns ≈ Tsampling/2 change in delay, a double-peak structure is
observed which spoils a proper timing measurement for typical
CB signals. In the lower panel, the same measurement is re-
peated with a different firmware running at T −1sampling = fsampling =
(80MHz)−1 = 12.5 ns, where no double-peak structure is present.
51
3. Hardware upgrade design studies
shows no double-peak, see the lower panel of figure 3.9. This setting for the
sampling frequency is above the AD9219 maximum specification of 65MHz but
fulfills the Nyquist criterion and additionally simplifies static timing analysis
issues due to CDC in the SERDES.
To measure timings relative to an external trigger as required by the A2
detector system, its phase to the TRB3 clock is measured by a TDC in the
central FPGA, which has been already implemented for the PaDiWa (AMPS)
tests in section 3.3. The synchronous trigger is then sent to the peripheral
FPGA, where it is synchronized to the ADC sampling frequency clock. Again,
its phase is measured by a TDC in the peripheral FPGA. This procedure is
depicted in figure 3.10.
The finally developed firmware including a 1-channel TDC required carefully
chosen placement constraints and occupied already 60% of the available FPGA
resources. Furthermore, 3 of 12 ADC ICs could not be used at all, since some
of the SERDES pins were deprecated in Lattice software revisions newer than
2.1 due to noise issues, which has not been foreseen during the PCB design of
the TRB3, and the necessary TDC implementation is incompatible with the
Lattice software revision 2.1. To overcome this limitation of 36 usable ADC
channels per add-on, the so-called TRB3sc could be used, see section 3.5.
Eventually, a TRB3 setup with one ADC add-on connected to an off-the-shelf
personal computer has been tested under beam time conditions during the
Compton production run in June 2015. To carry-out a non-invasive parallel
measurement during beam time, one half of a 32 channel CB analog splitter is
modified by the KPH electronics workshop. The 16 differential inputs, directly
connected to the 124W transmission lines of the CB PMTs, are tapped and
provided as suitable differential outputs to the TRB3 ADC add-on board.
Due the aforementioned TRB3 PCB design bug, only 36 channels on the
ADC add-on are usable, which finally results in 12 available channels for this
measurement. All those 12 channels are configured identically and the data
from the TRB3 is not directly merged into the Acqu DAQ to avoid affecting
the normal data-taking.
Since the measurement is carried out in parallel with the existing Acqu DAQ,
the timing and integral information from both DAQs is compared event-by-
event using the event serial number. To this end, the 12 logical channels under
test are mapped to Acqu’s ADC and TDC numbering scheme using cosmic
events for low hit rates and comparing hit outputs manually, see table 3.2.
Using this fixed mapping, the data from typical beam time conditions with
about 1.5 kHz event rate are analyzed. Under those conditions, the read-out of
the TRB3 has worked flawlessly for over 6 hours with average read-out times
of 10µs per event, which is 10 times faster than the average read-out time of
52
3.4. Sampling ADC firmware development and measurements
TRG_ASY
T
SIGNAL
CLK_SYS
φ
CLK_ADC
TRG_SYS δ1
TRG_DLY ε θ
TRG_ADC δ2
Figure 3.10.: TRB3 ADC timing measurement T ′ = T − ϵ = δ1 + δ2 + θ of
SIGNAL to an external asynchronous trigger TRG_ASY. The system
clock and the ADC clock domain are denoted by CLK_SYS and
CLK_ADC, respectively, whose phase ϕ is fixed by a PLL. TRG_ASY
is synchronized as TRG_SYS, then propagated to the peripheral
FPGA as TRG_DLY, and again synchronized as TRG_ADC. The
necessary phases δ1 and δ2 measured by TDCs in the CTS and
in the peripheral ADC firmware, respectively. θ is determined by
interpolation. Since the propagation delay ϵ from the central to
the peripheral FPGA is unknown but constant, measuring T ′ is
equivalent to T up to an offset, which can be accounted for by
calibration.
TRB3 Acqu CB Element
Logical Input ADC TDC
0 – 3 8 – 11 3379 – 3376 2404 – 2407 372 – 375
4 – 7 24 – 27 3371 – 3368 2412 – 2415 380 – 383
8 – 11 28 – 31 3375 – 3372 2408 – 2411 376 – 379
Table 3.2.: TRB3 ADC Acqu channel mapping manually determined from
cosmics data via event-by-event correlation. The Acqu ADC and
TDC numbers are the channels in raw “Mk2” data format, the CB
element number refers to the standard numbering scheme of logical
channels.
53
3. Hardware upgrade design studies
the Acqu system. Thus, since adding more add-on boards to the TRB3 system
does not increase the read-out time significantly due to its parallelized event
building concept, the expected performance of a TRB3-based system is an
order of magnitude better than the current DAQ. Using the experience from
the signal generator tests, the constant fraction is set to 2/3 and the delay
to 2 samples. The integration window is 60 samples, which corresponds to
750 ns at 12.5 ns sampling period. The input threshold is reduced from the
rather conservative 15 ADC units, corresponding to roughly 30mV, to 3 and
5 units, corresponding to 6mV and 10mV, respectively, after a feedback-lock
issue in the baseline follower has been fixed and its average length was set to
214 ≈ 16000 input samples.
The promising results are shown for one selected channel in figure 3.11. For
each event, the timing and integral information from the Acqu and the TRB3
system is available and shown as correlation plots. The timing resolution is
apparently determined by the analog signal quality, since additional measure-
ments with a signal generator and typical pulse shapes showed resolutions
of 200 ps RMS for the TRB3 setup. The COMPASS F1 TDC ASICs of the
existing system have a fixed bin width of 117.1 ps, yielding potential timing
resolutions well below 100 ps under ideal conditions with sufficiently fast lead-
ing edges of the analog signal. This measurement here showed single channel
timing resolutions of 4 ns RMS for both systems, see figure 3.12. This is signif-
icantly worse than the expected rule-of-thumb resolution of trise/100 = 300 ps
but still sufficient to correlate the Poisson-distributed events with an average
event distance of 100µs. Concerning the integral measurements, the perfor-
mance of the existing system based on 40MHz sampling ADCs has been nicely
reproduced as expected. The negligible deviation from a perfect event-by-event
correlation of the two systems for the integral measurements has two causes:
First, the threshold settings were hard to match exactly, which determine what
actually is recorded as a timing and/or an integral measurement according to
the two systems. For example, the Acqu system discards the triggered integral
measurement if the pedestal subtracted integration is less than 15 raw units,
which corresponds to an energy of 1MeV, and a basically un-triggered timing
measurement is recorded if the leading-edge discrimination threshold of 25mV
is passed, whereas the free-running TRB3 system stores a combined integral
and timing measurement in its event buffer if the leading edge crosses the
configured threshold. Second, the read-out for the integral values is explicitly
triggered in the Acqu system but self-triggered in the TRB3 system, which
can lead to multiple integral values in the TRB3 without corresponding values
from the Acqu system. Similar results were obtained for the other 11 channels,
but are not shown here for brevity. Further steps in the development for the
54
3.4. Sampling ADC firmware development and measurements
Figure 3.11.: The top row shows the timing versus their integral measured
by the existing Acqu system and the TRB3 system, respectively.
Since the Acqu system has a LEdD, a shift towards later timings
for lower integrals is observed, the so-called time-walk. This effect
is not present for the CFD based TRB3 system. The bottom
row shows the timing and integral event-by-event correlation,
respectively. As expected, the timing correlation is distorted due
to time-walk. See text for discussion of deviations from perfect
correlation for the integral measurement.
55
3. Hardware upgrade design studies
Figure 3.12.: The TRB3 timing hits as a projection from figure 3.11. The shown
Gaussian plus constant fit obtained a resolution of σ ≈ 4 ns. The
peak distortion can probably attributed to the non-ideal analog
signal quality. Note that typical analysis timing resolution would
be better as they are usually taken from properly reconstructed
events.
sampling ADC firmware are discussed in section 3.5.
3.5. Summary and outlook
The test beam time in June 2015 has successfully shown that the ADC add-on
is well-suited for an upgrade of the CB calorimeter readout, in contrast to
the PaDiWa AMPS FEE. Many technical issues have been resolved, a highly
configurable and flexible firmware has been designed and a complete software
tool-chain is available to investigate the TRB3 ADC add-on as well as the
PaDiWa discriminator boards. Furthermore, based on the LTspice simulations,
the adaptations for PaDiWa AMPS to suit A2 detectors can be easily tested.
In the following, reasonable follow-up work based on the already achieved
feasibility studies is presented. Possible alternatives are also highlighted,
which are complementary to the currently available solutions. Due to lack of
manpower, the issues mentioned in the following have not been resolved to
date and thus statements should be taken with a grain of salt, as hardware
development efforts are particularly good for a surprise, as shown in figure 3.9
on page 51.
The TRB3 has been successfully evaluated as a future-proof platform for
56
3.5. Summary and outlook
Detector FEE TRB3 firmware
CB Splitter/ADC ADC feature extraction
PID PaDiWa AMPS TDC
MWPCs PaDiWa AMPS TDC
Tagger PaDiWa discriminator TDC
TAPS Improved VME?
Table 3.3.: The possible TRB3 upgrade options for different parts of the A2
detector system. For all detectors except TAPS, the TRB3 platform
already provides ready-to-use solutions.
the A2 experiment. As summarized in table 3.3, many already developed
components from the TRB3 community can be directly deployed at the various
detectors, leaving only TAPS as the major challenge. For TAPS, the already
installed NTEC modules are actually well-fitted for the BaF2 crystals including
the Vetos, whereas the read-out for the PbWO4 is still an ad-hoc solution based
on CAEN VMEbus modules, limiting their current usefulness in subsequent
analysis. Since the currently deployed VMEbus master module developed
by KPH supports only single address access reads but not the faster block
transfer modes, a custom developed VMEbus master module with an FPGA
connected directly to all VMEbus signals could achieve an optimal control
over all timings and thus maximum read-out performance. Furthermore, the
FPGA could run VMEbus machine code to execute loops and conditional reads
or writes to directly build data packets of each event. Such a development
could also profit from the TRB3 VHDL code base, for example by the Gigabit
Ethernet components providing a minimalistic DHCP client implementation.
However, a reasonable upgrade project plan should considerably take into
account the limited manpower for such an undertaking. One could be tempted
to upgrade only parts of the system, but this might quickly lead to the
undesirable situation of having to maintain a inhomogeneous system consisting
of Acqu and TRB3 parts coupled to each other. Unfortunately, the current
Acqu system exhibits a rather monolithic design and, additionally, takes
over a lot of slow control tasks, such as threshold settings, which must be
separated more cleanly before a proper integration of the TRB3 can be initiated.
Otherwise, the problems solved with the streamlined upgrade in October 2013,
as explained in section 2.6, will most likely appear again, eventually leading to
extended beam-time losses and increased maintenance requirements, as there
is no expert person knowing all parts of a certainly more complicated coupled
57
3. Hardware upgrade design studies
system with sufficient detail. One primary goal should be to replace the
existing COMPASS components, affecting the CB, PID, Tagger and MWPC
detectors. This would remove the remaining hassles of the rather complicated
and unreliable initialization of the COMPASS TCS optical trigger distribution
system. Moreover, if the read-out was changed from the current strongly
coupled AcquDAQ/AcquRoot with manual handshake TCP streams to a
system simply transmitting UDP packets for each interrupt signal, this could
ease incremental upgrades of the system.
The development for the ADC add-on has concentrated on the a highly
configurable firmware, which serves as a proof-of-principle under the specific
circumstances at the CB calorimeter. However, deploying the current firmware
as-is with a sufficient number of TRB3s as an replacement for the existing
COMPASS GeSiCa system would be premature. For example, the time
measurement showed a so-far unexplained glitch of the epoch counter, which
has been fixed later in the analysis by manually adding one sampling period
depending on δ2 defined in figure 3.10. Additionally, the SPI communication
and the related automatic phase adjustment of the serial LVDS transmission
should be implemented directly in the peripheral FPGA, which is a prerequisite
for seamless operation after power-loss or reboot of the DAQ. An alternative
approach for the timing measurement sends the external trigger asynchronously
to the peripheral FPGA and measures its phase with a TDC running at the
ADC sampling clock. However, this requires larger modifications to the
currently available TDC design, in particular a longer delay chain, which needs
careful placement inside the FPGA and might even be impossible to realize
due to size constraints.
Over the last years of A2-focused hardware development, the TRB3 commu-
nity provided valuable support in bug-fixing and helpful auxiliary components.
For example, a wrong supply voltage for the ADC ICs has been identified
recently. This aspect should not be underestimated in a collaboration suffering
from lack of manpower for such tasks. In particular, the so-called TRB3sc,
a crate-compatible single-FPGA version of the TRB3, has been developed
supporting existing add-ons. This board should be preferred over the TRB3
especially for the ADC add-on in order to leverage all 48 channels.
In conclusion, a successful upgrade is still a long-term challenge taking
into account the constraints given by the planned beam-times and existing
hardware. Within the scope of this thesis, the momentum of the presented
proof-of-principle developments have not finally led to relevant changes in
the current DAQ, although they are certainly needed for a reliable and high-
performance system prepared for challenges of the next decade.
58
4. Analysis of the η′ → ωγ
branching fraction
This chapter presents the analysis of the branching fraction of the η′ → ωγ
decay relative to the reference channel η′ → γγ. The analyzed dataset has
been taken with the A2 experimental setup as described in chapter 2 from
end of July 2014 until end of December 2014. As this dataset is also used in
[91–94], common efforts such as the reconstruction and calibration presented
in sections 4.3 and 4.4 are shared among those theses.
The branching fraction of the PV γ decay η′ → ωγ serves as an input and
verification for chiral effective field theories. As detailed in section 1.3, the
implementation of heavier degrees of freedom, such as the ω vector meson,
and the mixing of the singlet and octet states η1 and η8 into the physical
states η and η′ are covered by this decay. In particular, the understanding of
such non-perturbative effects on the level of a few percent is a topic of current
research, which motivates the analysis of η′ → ωγ and other related decays
such as ω → ηγ [91] or η′ → ηπ0π0 [95] with similar or better precision.
4.1. Introduction to photo-production experiments
The photon beam generated by electrons radiating bremsstrahlung impinges
on the liquid hydrogen target and produces strongly interacting particles,
whose subsequent decays are analyzed with the A2 detector system. The
total photo-production cross section off the proton is depicted in figure 4.1,
including the contribution of relevant single meson channels. As shown, the
EPT covers photon energies Eγ ideally suited to study the η′ meson at its
production threshold, given by
threshold η′ ′ ′= mη (mη + 2mp)Eγ 2 ≈ 1447MeV , (4.1)mp
where mη′ ≈ 958MeV and mp ≈ 938MeV are the rest mass of the η′ and
proton, respectively. The η′ production threshold is close to but still sufficiently
below the MAMI C maximum electron beam energy of 1604MeV.
59
4. Analysis of the η′ → ωγ branching fraction
total
102
π0
10 η
ω
1 η'
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
Eγ [GeV]
Figure 4.1.: The total photo-production cross-section off the proton is shown
including some single meson production channels, from [96]. The
data points from previous experiments, carried out mostly at A2 in
Mainz and CB/ELSA in Bonn, are amended by model predictions
shown in color. The solid red vertical lines indicate the photon
energy range covered by the EPT, whereas the blue dashed lines
show the η′ production from threshold to maximum MAMI C
electron energy.
60
σ [µbarn]
4.1. Introduction to photo-production experiments
In general, the photo-production of the η′ meson off the proton is described
by the reaction
γp→ η′p→ Xp , (4.2)
where X denotes an arbitrary decay of the η′, for example X = 2γ. The initial
state four-momentum of the reaction is known by detecting the bremsstrahlung-
emitting electron in time coincidence with the detected final state parti-
cles, assuming the target proton is at rest.1 The statistical treatment of
those “prompt” electrons opposed to randomly detected electrons is the well-
established “prompt-random” subtraction technique of photon-tagging [97].
To this end, each det⎧ected electron with timing t in the EPT is assigned aweight, ⎨⎩1 if t ∈ [−3 ns, 3 ns]w = − 6 ns , (4.3)2·(50 ns−5 ns) if |t| ∈ [5 ns, 50 ns]
or ignored if it is outside of any timing window, as depicted in figure 4.2. The
width of the prompt, where w = 1, and the two random timing windows,
where w < 0, are chosen such in equation (4.3) to include the full prompt
peak and to make the statistical error due to the random event subtraction
negligible while maintaining an acceptable analysis performance of a few
hundred events per second. In each event, the analysis is carried out for each
tagger hit and subsequent quantities are then weighted with the weight w
yielding prompt-random subtracted results. As the statistical errors are smaller
the narrower the prompt window is chosen, it is beneficial to improve the
timing resolution of the detected EPT electrons, which are implicitly measured
relative to the global trigger timing derived from the CB analog sum signal,
see also figure 2.11 on page 29. To this end, the trigger timing information for
each event is recovered by the energy-weighted sum over reconstructed cluster
timings in CB as follows: ∑∑ Ecl= CB i tclt̄ iCB cl , (4.4)
CBEi
where Ecl denotes the total energy of cluster i and tcli i the corresponding
timing given by the highest energy crystal. Eventually, the electron timing
t in equation (4.3) is improved by subtracting the trigger timing given by
equation (4.4) as the implicitly involved TDC read-out reference timing cancels,
t− t̄ ′CB = (t − tTDC ref.)− (t̄′CB − tTDC ref.) . (4.5)
1This assumption is well-justified, as at T ≈ 20K the mean kinetic energy of the proton is
negligible, kBT ≈ 1× 10−3 eV ≪ 1MeV.
61
4. Analysis of the η′ → ωγ branching fraction
40000
30000
σ ≈ 2.4 ns
20000
10000
0
−60 −40 −20 0 20 40 60
t / ns
Figure 4.2.: The timing of the hits detected in the EPT shows a coincidence
peak after an offset calibration as they are measured relative to
the trigger timing, as shown in the left column. As shown in the
right column, the timing resolution σ is improved significantly
by subtracting the energy-weighted timing of CB clusters given
by equation (4.4). The prompt and random intervals used in
equation (4.3) are also shown in the bottom right panel.
62
4.1. Introduction to photo-production experiments
The analysis of the η′ → ωγ decay is carried out relatively to the η′ → γγ
decay as a reference channel, which reduces the influence of systematics
related to the production of the η′. Alternatively, the photon flux and thus the
luminosity can be determined via a so-called tagging efficiency measurement2 to
achieve an absolute number of produced η′ mesons using the known production
cross-section and hence eliminate the need for a reference channel [92]. However,
as this requires a careful understanding of the systematics of an absolute
measurement, the first approach with a reference channel is chosen for this
thesis.
The branching fraction of the η′ → ωγ decay is given as
′
BR(η′ → ωγ) = BR(η′ → #(η → ωγ)γγ) · #(η′ → γγ)
′ ′ (4.6)
= BR(η′ → ) · N(η → ωγ) · ε(η → γγ)γγ
N( ,η′ → γγ) · ε(η′ → ωγ)
where N denotes the number of the reconstructed events associated with the
channel and ε the corresponding reconstruction efficiency of the whole analysis
chain determined by Monte Carlo (MC) detector simulation. The branching
fraction of the η′ → γγ decay is used as a reference input and is given as [17]
BR(η′ → γγ) = (2.20± 0.08)× 10−2 . (4.7)
This decay channel of the η′ is chosen since it has a comparatively large and
well-known branching fraction and its final state consists of photons only,
which nicely fits to the capabilities of the calorimeters CB and TAPS. The
alternative channel η′ → 2π0η → 6γ offers a three times larger total branching
fraction, but is more difficult to analyze due to the higher multiplicity in the
final state, such that the reconstruction efficiency does not compensate the
larger branching fraction.
Furthermore, the polar angle θ of the scattered proton in equation (4.2) is
limited kinematically to (θ ≲ 20°, as shown in figure 4.3 owing to)the relation
1 ( )(√ )cos θ = m22 η′ + 2 Eγ +mp m2 + p2p −mp , (4.8)Eγp
where mη′ ≈ 958MeV is the rest mass of the η′, Eγ = 1420MeV . . . 1580MeV
is the incident photon energy and mp ≈ 938MeV, p, θ are the rest mass,
2The term “efficiency” is commonly used in A2 but misleading, as it is actually the probability
that an electron hit in the EPT generated a photon impinging the target by passing the
photon beam collimation, which does not depend on the EPT electron detection efficiency.
63
4. Analysis of the η′ → ωγ branching fraction
900
20
800
700
15
600
500
10
400
300
5 200
100
0 0
0 100 200 300 400 500 600
Ekin / MeV
Figure 4.3.: The kinetic energy against the polar angle θ of the scattered
proton is shown for incident photon energies between 1447MeV
(production threshold) and 1580MeV (EPT highest photon en-
ergy), generated from γp → η′p according to phase space. The
maximum polar angle θmax of the scattered proton for η′ meson
production is roughly 20°. See also equation (4.8).
momentum and angle of the proton, respectively. This makes TAPS an ideal
proton detection device for η′ production regarding its particle identification
techniques such as ToF or PSA, see section 2.5.
A high luminosity, defined as the product of photon flux times the target cross
section area density, is required to compensate for the low photo-production
cross-section of the η′ mesons near threshold, see figure 4.1. Owing to the
substantial improvements to the DAQ as described in section 2.6, an unprece-
dented high electron beam current of 60 nA and thus photon flux on the liquid
hydrogen target has been achieved at acceptable DAQ live-times, see table 4.1
for an overview and [92] for a detailed investigation of the luminosity. In
comparison to a pilot EPT beam-time in 2012, the beam current is three
t∑imes larger. The trigger condition requires a total energy deposition in CB of′
CBE ≳ 550MeV, which has been optimized for η decay channels.
4.2. Software environment
An easily usable and well-tested software environment is a crucial component
for any successful analysis. Historically, the A2 collaboration entirely relied on
the so-called Acqu framework, taking care of the whole experiment software
64
θ / °
4.2. Software environment
Beam current 60 nA
Luminosity 5.9/(µb s)
Radiator thickness 10µm
Collimator 4mm
Target length 10 cm
Tagger rate 0.8MHz per-channel
Trigger condition ∑CBE ≳ 550MeV
Trigger rate 2.5 kHz
DAQ live-time ≈ 60%
Used detectors CB, PID, TAPS, EPT
Table 4.1.: Nominal beam time conditions during the EPT production runs.
They have been optimized during a test beam time in July 2014 to
record as many η′ events as possible under the given constraints of
the system, which is eventually the maximum rate of 1MHz per
EPT detector element. The maximum beam current the MWPCs
could stand is 20 nA, despite substantial Ethanol doping decreasing
its detection efficiency to hardly acceptable levels below 80%.
tasks from data acquisition to physics analysis. Its origins can be traced back
to the early 1990s and was later based on the common analysis framework
ROOT [98]. For many years, the analysis part of the Acqu framework has been
inhomogeneously distributed among the users, leading to tedious discussions
on technical issues and the re-implementation of identical functionality at
different places within the collaboration. At the beginning of this thesis, an
attempt [99] to synchronize those development efforts and to quickly share
fixes and improvements was initiated using the version control system git [100].
In particular, each beam time needs slightly adapted setup files reflecting
configuration changes in the DAQ and detector setup, some of them only
known to a few experts of the system. Furthermore, deploying and debugging
the Acqu framework has been improved by introducing a cmake-based [101]
build system and thus enabling support for Qt Creator [102] as the preferred
integrated development environment (IDE), which is an excellent tool for C++,
even for non-GUI projects despite its name. Moreover, after basic analysis
steps have been carried out for the η′ beam time data, a modern clustering
algorithm has been developed and subsequently tested on MC and data input.
The key improvement is the topological aggregation of energy depositions with
an arbitrarily large number of crystals and the subsequent search for local
energy maxima, exploiting the natural segmentation of the calorimeter, see
65
4. Analysis of the η′ → ωγ branching fraction
section 4.3 for details. Although this algorithm performs better [103] than
several old algorithms, which for example aggregated only the energy of the
nearest neighbors, the corresponding patch to the Acqu framework was not
accepted within the collaboration employing a single clustering algorithm due
to concerns about backwards compatibility of energy calibration parameters
and reproducibility of previous results.
The Acqu framework is supplemented by the CaLib framework [104, 105]
taking care of the various calibration tasks, for example time offsets or energy
gains for the calorimeters. However, improvements of this system always require
consistent changes in its stand-alone part and the corresponding Acqu part,
which led to the integration into the Acqu framework in 2013. Furthermore,
the calibration coefficients are stored in a MySQL database, whose design
did not allow calibration coefficients to change run-by-run or reverting to a
previous iteration without tediously restoring backups of the whole database,
possibly affecting all beam-times.
In 2013, the GoAT framework [106] was developed to mitigate shortcomings
of the Acqu framework for typical physics analyses, such as the incomplete
filtering capabilities to improve performance and the unstable and confusing
application programming interface (API). To this end, files in ROOT’s TTree
format are dumped from Acqu which contain events after the clustering
algorithm and calibration has been applied, as well as information about the
experimental setup to unpack the input data. Subsequently, those “GoAT
trees” are processed with particle identification and filtering techniques for
rapid development of physics analyses.
Eventually, after a few years of working with this complex tool-chain con-
sisting of Acqu, CaLib and GoAT, the Ant analysis framework [107] was
developed without any dependency on those existing frameworks within the
scope of this thesis. Many already available code parts, such as the clustering
algorithm, are re-used or suitably adapted. Moreover, techniques from modern
C++11 software development are enforced, such as test-driven development and
continuous integration [108], and documentation efforts are undertaken. The
implementation of all components required for a complete analysis was rapidly
achieved including the reconstruction of events from various data sources,
as shown in figure 4.4. In particular, the proper integration of the ROOT
framework within modern wrappers is crucial to prevent memory leaks or poor
input/output performance. For example, the Acqu framework suffers from the
3The multi-threading in Acqu is only required if run in data-acquisition mode merging
input from several sources, but still 4 threads are spawned if “off-line” analysis is carried
out in Acqu. Ant, as a pure analysis framework, is deliberately designed single-threaded
to avoid an overly complex design.
66
4.2. Software environment
AntReader PhysicsManager
AcquRaw Unpacker HistogramsA2Geant Unpacker TEvent Physicspreferred Plotter
ReadOnly 
optional WriteFlag  treeEvents
treeEvents SlowControl
Reconstruct Manager
GoatReader
PlutoReader
Figure 4.4.: The Ant analysis framework processing is shown as a flow chart.
Data is processed from different sources, for example raw data in
“Acqu Mk1/Mk2 format” or GEANT detector simulation output in
ROOT’s TTree format including true information from the event
generator Pluto. The PhysicsManager takes care of processing
the events including buffering for proper slow control information.
Finally, the data flow can be re-used with “saved” events flagged
by physics classes.
design decision that every class derives from ROOT’s TObject class and does
not properly take care of data encapsulation inside the multi-threaded envi-
ronment.3 Moreover, the calibration routines from CaLib are re-implemented
in Ant and subsequently improved including a convenient GUI for the fitting
of calibration spectra, see section 4.4. For example, the database is realized
as git-tracked folder structure, where each iteration is represented as a set of
files, which renders database changes into standard file operations. Addition-
ally, each calibration iteration is properly documented by a corresponding git
commit message.4
The reconstruction within the Ant framework has been successfully com-
pared event-by-event against standard Acqu/GoAT system. The challenging
implementation of the kinematic fitter has been carried out with the help of a
modern C++11 wrapper [109, 110] around the well-tested APLCON Fortran
code [111], which provides general routines for χ2 minimization under con-
straints treating measured and unmeasured variables identically. Additionally,
the GEANT-based detector simulation code a2geant [112] and the MC event
generator Pluto [113] are supported with corresponding readers, see figure 4.4.
In particular, a mixture of the main photo-production channels and their decays
4Note that each iteration of a time-dependent energy calibration, as described in section 4.4,
has a size of around 50MB compressed on disk, resulting in databases of a few GB in size.
67
4. Analysis of the η′ → ωγ branching fraction
has been developed as an extensible database containing realistic cross-sections
and branching fractions, the so-called Pluto MC cocktail [92]. This allows
for a quick and thorough check of background channels for any user-defined
analysis, although the cocktail does not model differential cross-sections but
assumes flat angular distributions instead. The Ant framework supports these
detailed MC studies by providing various tools to manage a possibly large
number of relevant backgrounds.
4.3. Event reconstruction
Within the Ant framework, the reconstruction of input into a representation
suitable for physics analysis takes place in several stages, which are described
in the context of the A2 experimental setup, although Ant uses concepts which
are applicable beyond the scope of A2.
Unpacking This stage extracts the raw information from the input file into de-
tector hits using the provided mapping from channel numbers as realized
in the experiment to logical channels realizing an abstract representation
of the detectors5. Furthermore, this stage figures out as much informa-
tion as possible about the input file automatically, runs sanity checks
and tries to handle incorrectly recorded raw data files.
Hit mapping As most detectors provide energy and timing information for
each element, this stage groups this information according to logical
channels. Furthermore, it decodes the raw information into physically
meaningful values, such as the timing information of the CATCH TDC
multiple hit buffer. The resulting object is called a cluster hit. At this
stage, the tagger detector is treated separately and adds its information
as so-called tagger hits to the event.
Clustering The cluster hits are aggregated into so-called clusters in this stage.
This process is trivial for the PID detector, as every cluster hit is
transformed into one cluster, but more involved for the electromagnetic
showers detected in the calorimeters CB and TAPS, as described in more
detail below.
Candidate matching A so-called candidate consists of one or more clusters,
and the candidate matching stage builds those from the provided clusters.
5This mapping renders re-cabling detector elements, which would change its channel number
used in the input file, transparent to subsequent analysis components using solely logical
channel numbers.
68
4.3. Event reconstruction
For example, the PID clusters are matched to clusters in CB and the
candidate is assigned a veto energy6 determined from the PID. Further-
more, some clusters may be ignored and not turned into a candidate,
for example unmatched PID clusters or calorimeter clusters below a
user-defined threshold.
While the event is being reconstructed, it can be modified and observed at any
intermediate stage using so-called hooks. For example, the conversion for the
CATCH TDC needs to find a trigger reference timing for hit synchronization
and calibration modules convert detector raw data into timings and energies.
Furthermore, during the decoding of the event stream, the reconstruction may
update the parameters of the calibration modules depending on the uniquely
assigned identification number of each event. This flexible approach makes
so-called time-dependent calibrations feasible, as detailed in section 4.4.
Clustering algorithm
A crucial part of the event reconstruction is the clustering for the calorimeters
CB and TAPS. The goal is to recover the energy and position information of the
incident initial particle which generated the recorded electro-magnetic shower
typically spanning more than one crystal element of the clustering detector.
To this end, the energy information of neighboring elements is aggregated and
an average position is calculated. However, as higher energetic particles create
laterally larger clusters, separate showers are more likely to merge into one.
Furthermore, some scattering reactions inside the scintillation material of the
detector create energy depositions sufficiently far away from the remaining
shower leading to so-called split-off clusters. Both phenomena are handled
by an appropriately designed algorithm, whose capability to do so is however
limited by the ignorance of the underlying physics of the complete event.
As already mentioned, joint analysis efforts in A2 suffer from the use of many
different clustering algorithms, each resulting in its own energy calibration, as
discussed below. Thus, the clustering algorithm implemented in Ant provides
a general solution with a minimum number of input parameters. It is inspired
by concepts presented in [114, 115], but in particular the details of cluster
splitting are novel. In principle, the algorithm consists of three phases:
Phase 1 Gather clusters by neighboring relation
Phase 2 Search local maxima inside cluster, called bumps
Phase 3 Split clusters according to stabilized bumps
6The term “veto energy” originates from the usage of the deposited ∆E PID energy to
discriminate, or “veto”, charged particles, such as protons or electrons, from photons.
69
4. Analysis of the η′ → ωγ branching fraction
The first phase is rather greedy because the neighbor relation is typically
defined as sharing the same corner and not only the same edge. This already
mitigates the generation of split-off clusters but inevitably deteriorates the
capability to separate two close particle depositions, possibly only apart by
one crystal and sharing the same corner. The greediness is compensated by
the second and third phase.
The second phase consists of the following steps, applied to each aggregated
cluster from the first phase consisting of N single crystal energy depositions
denoted Ei, i = 1, . . . , N .
1. Find seeds for local energy maxima by a robust gradient voting algorithm.
At each crystal, a vote is initially placed. If one of its neighboring crystals
has a higher energy, the vote is moved to that crystal, otherwise the vote
counts for the current crystal. If only one crystal obtained all votes, the
cluster is left unchanged and returned as a whole.
2. At each seed crystal from the previous step, a so-called bump with
position b⃗k is defined, where k counts the bumps. Each bump has the
energy ∑N
Ek kbump = wi Ei (4.9)
i=1
with the weights calculated as
( ⏐⏐ ⏐
k r⃗ − b⃗ ⏐)wi = 1 i kEi exp −2.5 , (4.10)Nk rM
where rM is the material-depe∑ndent Molière radius, r⃗i the position ofcrystal i and Nk is such that iwki = 1 for each bump k individually.
The exponential decay factor of 2.5, essentially rescaling the parameter
rM in equation (4.10), is suitably chosen while varying the factor shows
no dramatic influence on the performance of the clustering algorithm
[103].
3. Using the weights from the previous step, the bump position is recalcu-
lated according to [116] as follows
∑
ωki i r⃗ib⃗k = ∑ (4.11)
i ω
k
i
70
4.3. Event reconstruction
with the weights7 ( ( )
ωk = max 0, 4.0 + ln wkE /Ek
)
i i i bump . (4.12)
The max(. . .) statement in equation (4.12) assigns crystals with partial
energies wkE below e−4.0i i ≈ 1.8% of Ekbump a weight of 0, which improves
the position average in equation (4.11) by ignoring crystals with low
energy. As wki are normalized to each bump individually according to
equation (4.10), the sum of all bump energies is not equal to the total
cluster energy. The “energy conservation” is eventually taken care of in
the bump cluster building phase, as discussed below.
Step 3 is carried out iteratively until the bump positions b⃗k are do not change
anymore or, in rare cases, a maximum number of iterations is reached. In this
case of no convergence, the leftover unstable bumps are discarded. If no stable
bumps are found at all, again a rare case, then the cluster is returned as is,
which ensures that no energy information is discarded by the algorithm. If
two or more bumps with the same crystal of largest weight wi=imaxk are found
in one iteration, which is an overlap situation, then the corresponding bumps
are merged by averaging over their weights element-wise.
The third and last phase uses the stabilized bumps to split the given
cluster. To this end, each bump k iteratively builds a partial cluster with
Eksplit starting at the crystal8 i
i=i
max of its largest weight w maxk . One iteration
step subsequently adds the energy of the neighboring crystals to Eksplit. Once
a crystal at position r⃗j would be claimed by two or more bumps in the same
iteration step, the energy of that crystal is shared among the clusters. To this
end, a preliminary position ˜⃗bk analogously to equation (4.11) of each bump
claiming the crystal is calculate(d first with(weights ))
ω̃k k ki = max 0, 4.0 + ln Ei /Esplit , (4.13)
where Ei are the crystal energies previously assigned to the claiming bump
k and Eksplit is the sum of those energies.9 Next, the percentage energy of a
participating bump k at crystal j is ca
1 (lcu⏐lated as⏐ )
pkj =
˜⃗
Eksplit exp −⏐r⃗j − b ⏐k /rM , (4.14)Nj
7Note the different notation, ωki versus wki .
8By virtue of equations (4.10) and (4.12), this is the crystal element closest to the stabilized
bump position b⃗k.
9Note that the number of those energies Ei and thus Eksplit cannot be zero, as at least the
starting crystal is uniquely assigned to a non-overlapping bump at the beginning of the
phase.
71
4. Analysis of the η′ → ωγ branching fraction
1 6
200
180
0.8 4
160
0 Candidates 2 140
0.6
1 Candidate 120
0
2 Candidates 100
0.4
3 Candidates 80−2
60
0.2 −4 40
20
0 −6
10 20 30 40 50 0 500 1000 1500
0
∆α / ° Ekintrue / MeV
1.3 1.3 160
1.2 250 1.2 140
120
1.1 200 1.1
100
1 150 1 80
0.9 0.9 60100
40
0.8 50 0.8
20
0.7 0 0.7 0
20 40 60 80 100 120 140 160 20 40 60 80 100 120 140 160
θtrue / ° θtrue / °
Figure 4.5.: Reconstructed properties of two spherically uniformly generated
photons with an opening angle ∆α from 0° to 50° and uniformly
distributed kinetic energies from 0MeV to 1600MeV are shown.
Ideally, the number of reconstructed candidates in CB should be
2, which is predominantly the case for ∆α ≳ 20° as shown on the
top left. For the critical region 15° < ∆α < 20°, the difference of
the opening angle of the reconstructed candidates, ∆αrec, to true
opening angle ∆αtrue = ∆α is shown in the top right panel. For
the same ∆α region, the cluster energy of the higher energetic
(bottom left) and lower energetic (bottom right) reconstructed
candidate relative to the true energy information is shown, which
should ideally be 1, as a function of the true polar angle θ. See
also section 4.4 discussing single photon energy scales in more
detail.
72
E  / E Fraction of totalrec true
E ∆αrec / Etrue rec - ∆αtrue / °
4.4. Event calibration and quality checks
where Nj such that
∑
k p
k
j = 1. This normalization ensures “energy conser-
vation” in a sense that the total available energy defined as the sum of all
input crystal energies is equal to the sum of cluster energies. In summary,
the aggregated cluster from the first phase is split according to the stabilized
bumps representing local energy maxima. Note that the number of crystals
assigned to each cluster is not conserved, as crystals may be shared among
partial clusters.
A good indicator for the performance of the clustering algorithm is the
opening angle of two photons which are still reconstructed as two clusters.
This is conveniently studied with the GEANT4-based MC detector simulation
using suitably generated photons with well-known energies and relative angles,
as shown in figure 4.5 and also carried out in [103]. The smallest angle at which
two cluster events dominate is found to be around 15°, which is about two
times the average angular distance of two crystals in CB as naively expected.
In summary, the analysis of high beam energy data such as the EPT runs
in 2014 benefits significantly from this improved clustering algorithm, as the
two-photon invariant mass spectra show unprecedented narrow peak widths
and proper alignment after careful calibration, see section 4.4. Furthermore,
the algorithm needs only a small and well-motivated set of parameters without
beam-time specific tuning, which makes it a first step towards a collaboration-
wide common calibration routine.
4.4. Event calibration and quality checks
In general, calibration procedures adjust parameters to account for inho-
mogeneities of the experimental setup and thus serve as an input for the
successful reconstruction of an event, as explained in section 4.3. There are
various sources for those inhomogeneities, such as different cable lengths re-
sulting in shifted positions of time coincidence peaks or varying conversion
gains of PMTs, possibly caused by unstable HV supplies or temperature drifts,
resulting in different scales for an energy determination. In order to obtain
suitably calibrated events, various methods with complex interdependencies
are employed, as shown in figure 4.6. The different calibration modules as
implemented in Ant are explained in the following with a focus on the energy
calibration of the CB calorimeter.
The timings of the detector channels are typically measured relative to a
experiment-wide distributed timing reference derived from the trigger signal.
The time offset calibrations, for example “PID Time” or “TAPS Time” in
figure 4.6, align the resulting coincident timing peak for each detector channel
73
4. Analysis of the η′ → ωγ branching fraction
PID Time CB Time TAPS Time
PID Energy TAPS Energy
Pedestals CB TimeWalk Pedestals
PID PhiAngle CB Energy TAPS Energy MC TAPS
RelativeGains RelativeGains Energy/
PID Energy Cluster
RelativeGains analogous to MC CB MC CB TAPSVeto Energy Cluster SmearingEnergy RelativeGains
Cluster RelativeGains Energy ThresholdsMC CB Cluster Cluster Correction
Smearing Correction
TAPSVeto Time
MC CB
MC CB Energy Energy TAPSVeto Energy
RelativeGains Thresholds Pedestals
Figure 4.6.: The various calibration modules and their dependencies are shown.
Arrows denote “depends on” in this chart. For example, to carry
out the “PID PhiAngle” calibration, the “PID Energy Pedestals”
and the “PID Time” calibrations must be carried out first. Gray
items or arrows denote minor importance or dependence, respec-
tively. See text for further details, in particular regarding the
dependency loop for MC-driven energy calibrations.
at position zero, which simplifies the application of timing windows to suppress
random hits. The conversion of a raw timing measurement ξ into a physically
meaningful time t, by convention measured in ns, is calculated as
t = κ · ξ − toffseti i , (4.15)
where i denotes the per-channel dependence of the parameters. For the widely
used10 CATCH TDCs, the conversion factor κi ≡ κ is fixed to 0.1171 ns per raw
unit. The calibration module determines the coincident timing peak position
by a Gaussian fit and adjusts a previously set toffseti by a corresponding relative
amount. This calibration needs to be carried out only once and applies globally
to the whole beam-time and serves as an important data quality check as
described below.
10The CATCH TDC conversion implemented in Ant properly handles the overflow at the
magic number 62 054, see figure 2.13 on page 31.
74
4.4. Event calibration and quality checks
For TAPS timings, which are recorded with NTEC VMEbus modules as
shown in figure 2.10 on page 28, the TDC measurements are stopped instead
of being started by the trigger reference timing. This is accounted for by using
negative conversion factors κi ≡ κ of −0.1 ns per raw unit in equation (4.15).11
This proper treatment is crucial if TAPS timings are subtracted from CB
timings, which is typically the case to improve ToF measurements.12
The “PID PhiAngle” module determines the alignment of the PID elements
with respect to the CB elements by ignoring the candidate matching and
instead investigating events with exactly one CB and exactly one PID cluster.
They exhibit a correlation peak in the azimuthal angle ϕ, as the PID is
constructed as a detector with cylindrical symmetry. One global rotation
angle around the z-axis is determined as the y-intercept parameter from a
linear fit to all ϕi correlations per PID element i. In contrast, the CaLib/Acqu
framework uses element-wise ϕi angles for candidate matching, which may be
inconsistent with the geometrical constraints of the PID detector.13
The CB timings are corrected for their dependence on the input signal
amplitude originating from the LEdD, similarly to [104, 117], for example.
For the high-energy and high-rate EPT beam-times, it is crucial to properly
account for multiple TDC hits per event and to use a logarithm of uncalibrated
energies Eraw in raw ADC units, that is before conversion to the MeV scale,
as shown in figure 4.7. The logarithm avoids an incorrect extrapolation of
the fit function to higher energies. Choosing raw energies as a measure of the
input amplitude renders the time-walk correction independent of the energy
gain calibration discussed later. The amplitude dependence is sufficiently well
described by14 ( )
∆t(x) = p0 + p1(x− p2) + p3 exp −p4(x− p2)− p5 ln(x− p2) , (4.16)
where x = log10(Eraw) and pi, i = 1, . . . , 5, are fit parameters. The two-
dimensional histogram of multiple TDC hits versus log10(Eraw), as depicted in
figure 4.7, is projected for each bin at position xi and subsequently fitted with
11By virtue of a dedicated measurement, the TAPS TDC conversion factor is determined for
each channel individually. However, the deviation from −0.1 ns per raw unit is negligible
and currently not included in the calibration database.
12It is also common practice in A2 to improve TAPS timings by subtracting tagger timings,
which, however, leads to difficulties with respect to prompt-random subtraction.
13For an unknown reason, the PID are flipped around the z-axis in the A2 detector simulation
geometry. The CaLib/Acqu framework accounts for this by using decreasing instead of
increasing ϕi parameters. Ant fixes this already during the unpacking stage.
14To improve the numerical stability of the fit optimization, the factor 1/(x− p2) is written
as exp(− ln(x− p2)).
75
4. Analysis of the η′ → ωγ branching fraction
200
100
150
50
100
0 50
0
1.5 2 2.5 3 3.5
log (E )
10 raw
8000 σ = 1.97 ns
7000 µ = -0.34 ns
6000
5000
4000
3000
2000
1000
0
−10 −5 0 5 10
tCB / ns
Figure 4.7.: The CB time-walk calibration removes the dependence of the
timing on the signal amplitude (top left, with Eraw in ADC raw
units) and leads to an Gaussian-shaped timing reference (bottom
left) as defined in equation (4.4). After correction, the CB cluster
hit timings (top right) show similar behavior as TAPS timings
(bottom right) using a hardware CFD.
76
Time / ns
4.4. Event calibration and quality checks
24 4 1010
22 10
3
20 8
18 103
16
102
14 6
12 102
10 4
8 10
6 10
4 2
2
0 10 50 100 150 200 250 300 0 − − 140 20 0 20 40
EPID / raw units tPID / ns
Figure 4.8.: The PID pedestal peaks for each channel are shown on the left
and determined by fitting channel-wise projections, compare also
figure 2.5 on page 21. On the right, events containing a proton are
selected using a kinematic fit and the energy (roughly calibrated)
and timing response is shown. The proton detection efficiency is
significantly reduced if the timing window is narrower than −25 ns
to 40 ns.
a Gaussian to obtain the peak position as the mean value yi. The parameters
pi in equation (4.16) are then fitted to the points (xi, yi) after the removal of
outliers. After the application of equation (4.16), CB timings are discarded
outside a window of −25 ns to 25 ns. The proper implementation of this
correction requires no additional CB leading-edge adjustment in contrast to
[104] and derived timings such as the CB reference timing t̄CB in equation (4.4)
stay aligned close to zero, again shown in figure 4.7.
In order to infer an energy information from an analog detector signal, the
DAQ hardware carries out an integration over time of the input waveform. The
result is provided as a digital raw value ξ, similar to a timing measurement. The
single element energy E, by convention measured in MeV, is then determined
as ( )
E = gi ξ − ξpedi , (4.17)
where gi is usually called (energy) gain15 for channel i and ξpedi is the energy
offset or pedestal.
15In Ant, the gain g = ηg̃ is implemented as a product of a unit-less relative factor η and a
usually constant conversion factor g̃. Hence the notation “RelativeGains”.
77
PID Channel
EPID / MeV
4. Analysis of the η′ → ωγ branching fraction
Pedestals are defined as the result of the measurement when no signal is
present at the integrating ADC and thus the integration is carried out over the
constant voltage baseline with a fixed integration gate length.16 This should
always result in the same raw value and thus a very pronounced peak in the
ADC spectrum, see figure 4.8 for an example. Again, the position of this peak
is determined by a fit and stored as ξpedi with all other fit parameters for usage
during reconstruction in the database.
The PID energy, denoted as “PID Energy RelativeGains” in figure 4.6, is
calibrated such that neutral states can be clearly distinguished from charged
particles given the rather broad pedestal peak of the PID analog signal integra-
tion. The PID timing window is chosen rather wide, as shown in figure 4.8, as
some timings of identified proton candidates are seen about 25 ns later. Details
of the PID energy calibration using the typical curved shape of the proton
PID energy deposition17 ∆E when plotted against the matched CB energy E
are given in [93], as it is not crucial for the analysis presented later.
The energy gain calibration of the calorimeters CB and TAPS, denoted as
“CB/TAPS Energy RelativeGains” in figure 4.6, uses the ubiquitous decay of
the neutral pion into two photons with opening angle α and energies Eγ1 and
Eγ2 , whose corresponding invar√iant mass is given by
mγγ = 2Eγ1Eγ2(1− cosα) . (4.18)
As CB covers most of the solid angle, the whole procedure including the cluster
energy correction as described in the following is carried out first for CB by
using photons reconstructed in CB only. Subsequently, the procedure is applied
to TAPS by using one candidate from CB and one from TAPS as the photon
pair in equation (4.18), which improves the signal-to-background ratio in the
invariant mass spectra for TAPS elements considerably. In general, the gains
gi in equation (4.17) of the two central elements in the corresponding clusters
are tuned relatively such that the invariant mass peak mpeak, as shown in
figure 4.9, matches the nominal value (for the pion mass mπ0 = 134.98MeV,
→ + m
)
g g g k π
0
i i i − 1 , (4.19)
mpeak
where the factor k is chosen as k = 1 to increase convergence speed or
k = 0.5 < 1 to suppress oscillations originating from the azimuthal correlation
16During the EPT beam-times the conventional photon-beam has been used instead of a
random pulser to generate triggers for read-out. However, most of the time no signal is
present and the pedestals are assumed to be undisturbed by additional noise or cross-talk
by this non-optimal procedure.
17The PID energy measurement is multiplied by sin θ to compensate for the flight length
depending on the polar angle θ measured with CB.
78
4.4. Event calibration and quality checks
Figure 4.9.: The Ant-calib fit GUI for one channel in time-dependent cal-
ibration of CB relative gains. The π0 peak position mpeak is
determined using a Gaussian and separately controllable polyno-
mial fit function of order 2. The fit is interactively controlled,
for example moving the vertical blue line labeled with “x0” di-
rectly influences the mean position of the Gaussian signal function
(shown in red) and thus mpeak. Additionally, automatic fitting is
supported in order to manage the about 104 separate fits for each
time-dependent iteration.
79
4. Analysis of the η′ → ωγ branching fraction
of elements, in particular prominent in TAPS. Since mγγ in equation (4.18) is
calculated from two clusters with central crystals i and j ̸= i corresponding to
two different gains gi and gj , the procedure must be carried out iteratively and
converges after typically 10 iterations. It is first applied across some sufficiently
large subset of a beam-time,18 which averages over time-dependent gain drifts
and is thus called time-independent in the following. The dependence depicted
in figure 4.6 on the veto information, such as “PID Energy RelativeGains”,
stems from the discrimination of charged particles requiring no ∆E deposition
in matched veto elements. However, as the π0 invariant mass peak is clearly
dominated by neutral photons, this dependence is assumed to be weak. In
TAPS, the inner and outer elements do not show a discernible π0 peak due
to shower leakage and are thus flagged as “NoCalibFill”, meaning that their
gains are determined by an average of their neighbors. Furthermore, the
inner PbWO4 crystals are only calibrated with default gains for the whole
beam-time, thus flagged as “NoCalibUseDefault”, due to hardly identifiable
π0 peaks. The status of detector elements is shown in figure 4.14.
After the time-independent calibration has converged sufficiently, the energy
gains are tuned separately for each run, or “slice” in Ant terminology19, and
thus the time-dependence of the π0 peak position is compensated. Since one
slice does not provide enough statistics to ensure a stable determination of
the peak position over background, a Savitzky-Golay [118, 119] bin-by-bin
averaging20 along the slices is employed before the fit. The window size is chosen
as 10 and 30 slices for CB and TAPS21, respectively, and the polynomial order
for the Savitzky-Golay filter is set to 4. After each time-dependent iteration,
an additional averaging of the gains is performed with a width of 20 slices for
CB and 30 slices for TAPS, both with polynomial order 6. It accounts for slow
drifts of the gains on the time-scale of hours, while minimizing the influence
of additional noise due to the fitting procedure. This compromise between
smoothing and drift response is tested in detail using a MC toy simulation
of the calibration tool-chain in figure 4.10 by mimicking a typical input of
invariant mass spectra, see figure 4.9 for an example, with a priori known peak
positions.
18A random but constant subset of the beam-time is chosen to carry out those iterations.
19Ant supports arbitrary slicing of beam-time data according to unique event numbers,
which define validity ranges for arbitrary calibration data, but choosing a run-by-run
segmentation is convenient.
20Different run lengths are respected by scaling with the number of events in each run.
21For the PbWO4 crystals in TAPS, the default calibration gain determined from the full
beam-time is used, as the π0 peak position cannot be determined reliably due to low
statistics and high background.
80
4.4. Event calibration and quality checks
Figure 4.10.: MC toy model study for time-dependent energy calibration with
different smoothing options. For all CB channels, invariant
mass spectra with π0 peaks at µi are identically generated for
each slice i (counting from 0), mimicking a typical background
shape and statistics, see for example figure 4.9. At slice i = 10,
the peak position µi is quickly changed and at slice i = 30 a
slower but larger change in µi is induced, which corresponds to
changes on the time scale of hours. Fitted π0 peak positions
are subsequently determined with the standard Ant calibration
tool-chain with different bin-by-bin averaging settings. For the
case “No Average”, the spread of the π0 peaks for each slice
is largest, but the systematic deviation of the mean from the
true π0 position vanishes as expected. Using a moving average
window, the spread is reduced significantly, but the recovery of
time-varying position is completely lost. A good compromise is
found for a Savitzky-Golay filter with polynomial order 4 and
width 10. See text for further details.
81
4. Analysis of the η′ → ωγ branching fraction
Figure 4.11.: The relative gains of all channels are shown over time on the top
(bottom) left for CB (TAPS). On the right, the corresponding
fitted π0 peak positions are shown. For TAPS, the visible horizon-
tal lines correspond to elements flagged as “NoCalibUseDefault”,
which are mostly PbWO4 crystals, see figure 4.14. Around Au-
gust 15, 2014, denoted as 08/15, the TAPS cooling fans stopped
working due to a blown fuse resulting in a decreased scintillation
light output. This is accounted for by a time-dependent increase
of gains by roughly 40% to keep the π0 peak positions stable
within less than 1%. A typical channel is shown as an overlay in
red.
82
4.4. Event calibration and quality checks
Data MC
Raw Hits MeV Hits 900
Nothing
800
Calibration +Thresholds
700 +Calibration
+Smearing
Thresholds 600 +Correction
MeV Hits 500
400
Clustering 300
MeV Clusters 200
100
Smearing 
0
100 110 120 130 140 150 160 170
Energy Correction IM(γCB,γCB) / MeV
Final Calo Cluster
Figure 4.12.: For calorimeters CB and TAPS, the final cluster energy is de-
termined similarly for data and MC input, as shown on the left.
Besides the application of software thresholds on MC, an addi-
tional smearing is applied to clusters to correct the imperfect
modeling of detector resolutions. The final energy correction
of cluster energies accounts for the loss of energy due to single
crystal thresholds, see text for further explanation. For each step,
the effect on the invariant mass of two photons reconstructed in
CB for generated 2π0 events is shown on the right.
83
4. Analysis of the η′ → ωγ branching fraction
8000
µ = 136.1 MeV
σ/µ = 8.7 %
6000 µ = 552.5 MeV
σ/µ = 3.9 %
4000
2000
0
0 100 200 300 400 500 600 700
IM / MeV
Figure 4.13.: Data events with two candidates in CB are selected from 4.6× 106
total in one run file and assumed to be photons, whose invariant
mass according to equation (4.18) is plotted (black line). The
π0 → 2γ and η → 2γ decays are visible with excellent resolution
and within 1% of the expected position, mπ0 ≈ 135.0MeV and
mη ≈ 547.9MeV [17]. Each signal peak is fitted with a Gaussian
function (green line) with mean µ and width σ and fourth-order
polynomial background (blue line).
Once the gains do not show relative fluctuations of more than ±0.5%, the
calibrated dataset is used to match the energy resolution of MC detector
simulation to data. To this end, the cluster energies are additionally smeared
on MC using a Gaussian distribution with (Ek, cos θ)-dependent widths on
the order of σ ≈ 8MeV, as shown in figure 4.12. This procedure is carried
out iteratively on the MC cocktail mimicking beam-time data [92] for CB
and then, after CB has been finished completely, for TAPS. The π0 peak
widths are used to tune the σ(Ekin, cos θ) parameters of the Gaussian smearing
dependent on the kinetic energy Ekin and the polar angle θ. Next, after the
detector simulation matches the experimental resolutions well enough, the
total cluster energies are corrected on data and MC for losses due to finite
single crystal thresholds, which are in the order of 1MeV. This correction
is determined with simulated single photons, where the initial energy Etrue
is known, and the cluster energy correction factor is given by the average
⟨Etrue/Erec⟩(Erec, n) dependent on the reconstructed energy Erec and the
22The corrections are determined for the October 2014 beam-time, and then identically
applied to the July/August and December beam-times. Minor differences in the experi-
mental setup, such as differently flagged elements in figure 4.14, are neglected.
84
4.4. Event calibration and quality checks
Name Period Total runs “Good” runs
July/August 2014-07-30 – 2014-08-22 832 635, 76%
October 2014-10-14 – 2014-11-03 819 640, 78%
December 2014-12-03 – 2014-12-22 790 665, 84%
Table 4.2.: The three data periods are usually referred to as the July/August,
October and December EPT beam times, respectively. After several
quality checks, only the “good” runs are subsequently analyzed,
see text.
cluster size n. This compensates for the skewed mass scale of low-energy single
photons, as the calorimeter is calibrated using two photon invariant masses
given by equation (4.18). Details of the additional MC smearing and the
single photon energy correction are given in [91].22 After those two corrections
are determined, a final energy gain calibration for data and MC is carried
out, see figure 4.12. This assumes that those data-driven corrections are not
strongly influencing the other calibrations and, thus, their dependence relation
is indicated as weak in figure 4.6.
The energy calibration gains for all beam-times is shown in figure 4.11, and
the resulting invariant mass spectrum of two candidates in CB, assumed to be
photons, is shown in figure 4.13. Thanks to the improved clustering algorithm,
no non-linear gain calibration, as proposed in [104, 120, 121], is necessary to
match the η to the nominal mass position within less than a percent. Still,
there is a systematic offset towards slightly higher peak positions compared
to the nominal masses, which could be related to either the different analysis
procedure,23 to the time-dependent smoothing or to the single photon energy
correction as discussed above. More detailed studies focusing on the photon
energy dependence of π0 peak position are carried out in [122], which finds a
few percent rise of the peak position with increasing photon energy.
Data quality checks are important to ensure a homogeneous measurement
and are carried out in parallel with calibration procedures, which involve rather
basic detector information. To this end, runs exhibiting strange or unexpected
behavior are discarded. The potential loss of statistics is typically compensated
by smaller systematic errors. Some examples for such experimental deficiencies
are given in the following.
23For example, the number of clusters in CB is fixed to 2 to reduce combinatorial background
in figure 4.11 whereas for the calibration all pairs of clusters in CB are taken into account
to obtain sufficient statistics in each detector channel.
85
4. Analysis of the η′ → ωγ branching fraction
• The DAQ is triggered from the analog sum of the signals in CB, the
so-called energy sum trigger, and has been set to roughly 550MeV. After
the July/August beam-time it has been discovered [123] that crystals
with element numbers 352 to 415 did not contribute to this sum due to
a bad electrical connection within the analog sum chain, which has been
fixed for the October and December beam-times. This trigger inefficiency
is reflected in the MC simulation by ignoring the corresponding elements
in the summation of the energy in CB.
• During the timing calibration, some of the runs exhibited sudden shifts
of the coincident peaks for detectors using CATCH TDCs. The data is
not easily recoverable as those shifts cannot be interpreted as single bit
flips in the binary representation of the raw value ξ in equation (4.15).
It is attributed to a still unresolved bug in the COMPASS read-out
system and has been mitigated during data taking by restarting the run
immediately if such a shift appeared. The affected runs are excluded
from the analysis and comprise the largest part of discarded runs in
table 4.2.
• The CB time-walk calibration tests if the timing and energy measurement
of elements are properly correlated. For some channels, only the TDC
measurement appeared to be broken. Those elements are not ignored
completely but flagged as “BadTDC”, such that energy measurements
larger than 7MeV are still taken into account during reconstruction,
ignoring timing information. On MC, such elements are treated as
normally working.
• During time-dependent calibration of the calorimeters, few channels are
found not working over the full beam-time or an automatic stable fit
becomes impossible and needs permanent user intervention, see figure 4.9.
Those elements are accordingly either flagged as “Broken”, if becoming
dead completely, or as “NoCalibFill” or “NoCalibUseDefault” otherwise.
The choice “NoCalibFill” excludes them from further energy gain tuning
and their gain is set to an average of the neighbors, relying on the
homogeneous detector response due to the separately carried out HV
tuning. The preferable choice “NoCalibUseDefault” uses the gain from
the time-independent calibration.
In total, the runs used for analysis are summarized in table 4.2, where also
the calibration efforts from [91, 92] for the October and December beam-times
are included. The status of CB and TAPS detector elements are given in
figure 4.14 and parameters relevant for reconstruction and calibration are listed
in table 4.3.
86
4.4. Event calibration and quality checks
July/August:
October:
December:
Figure 4.14.: Status of detector elements in CB and TAPS, shown for each of
the three beam time periods defined in table 4.2. Filled black
elements are flagged as “Broken” (dead elements), red means
“BadTDC” (no timing but energy information in figure 4.7), blue
means “NoCalibFill” (relative energy gain averaged from neigh-
bors) and green means “NoCalibUseDefault” (time-independent
gain used). See text for details.
87
4. Analysis of the η′ → ωγ branching fraction
Timing windows EPT −125 ns to 125 ns see eq. (4.3)
CBa −25 ns to 25 ns see eq. (4.7)
PID −25 ns to 40 ns see fig. 4.8
TAPS BaF2 −15 ns to 15 ns
TAPS PbWO4 −25 ns to 25 ns
TAPS Veto −12 ns to 12 ns
Thresholds CB MCb > 1.2MeV
TAPS MCb > 3.4MeV
PID Raw > 15 see fig. 4.8
TAPS BaF2 Raw > 5
CB Broken TDCc > 7MeV
CB Cluster > 12MeV
TAPS Cluster > 12MeV
aFor elements with working TDC and after time-walk correction.
bMimics the hardware thresholds for single elements on MC.
cOn Data, single crystal energy deposition reaching this threshold is not discarded
if marked as broken TDC in CB. Not mimicked on MC.
Table 4.3.: Overview of setup parameters relevant for event reconstruction and
calibration. Timing windows are chosen as tight as possible without
risking to cut into coincidence peaks taking into account slightly
drifting timing offsets. Thresholds are for example applied to mimic
data behavior on MC due to hardware thresholds originating from
discriminators, or to discard unphysical pedestal contributions. The
settings are identically specified in Ant for all EPT beam-times.
88
4.5. Kinematic fitting
700 102
IM fitted photons 
4000 600IM input photons
500
3000
400
10
2000 300
1000 200
100
8050 900 950 1000 1050 0 1
IM(γ ,γ ) / MeV 0 200 400 600 800 1000fitted proton
Ekin  / MeV
Figure 4.15.: The kinematic fitting procedure tremendously narrows the peak
width of the invariant mass of two photons generated from η′ →
γγ with EPT photon energies and reconstructed according to the
detector simulation. Similarly, shown on the right for direct 2π0
production events, the kinetic energy of the proton is restored
from punch-through by the kinematic fit.
4.5. Kinematic fitting
In comparison to typical analyses in A2 investigating π0 or η production
and their decays, the EPT beam-times targeted at η′ production require the
kinematic fitting technique to obtain a sufficient resolution in invariant mass
spectra, as exemplary shown in figure 4.15. To this end, for each electron hit
in the EPT TDCs corresponding to an incident photon energy Eγ , a kinematic
fit with the energy-momentum conservation constraint is carried out, imposing
⎛ ⎞µ ⎛ ⎞µ
⎜Eγ⎝⎜⎜ 0 ⎟⎟ ⎜⎜
mproton
⎠⎟ +⎜⎝ 0 ⎟⎟⎟⎠ ∑= pµ µ0 0 proton + p , µ = 0, 1, 2, 3 . (4.20)photons
Eγ 0
The initial state represents a photon traveling along the z-axis with energy
Eγ and a proton at rest. The parametrization of the final state proton and
the final state photons depends on the calorimeter as depicted in figure 4.16.
For CB, the quadruple (1/Ekin, θ, ϕ,R) is used, where R is the radius of the
cluster position in spherical coordinates including the shower depth s, so
89
proton
Ekin  / MeV
4. Analysis of the η′ → ωγ branching fraction
Figure 4.16.: The kinematic fitter uses four degrees of freedom to describe
each candidate depending if the electromagnetic shower is recon-
structed in either in CB or in TAPS to account for the spherical
and forward-wall geometry, respectively. The target length of
10 cm is not negligible compared to the inner radius of CB,
RCB = 25.4 cm (sketch not to scale). The distance of the front-
face of TAPS to the target center is zTAPS = 145.7 cm.
R = RCB + s. For √TAPS, the quadruple (1/Ekin, Rxy, ϕ, L) is used, where24
Rxy = L sin θ, L = x2 + y2 + L2z and Lz is the distance of the cluster from
the target center in z-direction including the shower depth. Choosing the
inverse kinetic energy 1/Ekin as a parameter avoids unphysical negative kinetic
energies during optimization.25 The shower depth s(Ekin) is determined from
GEANT-based single-particle simulations as a function of the cluster energy
Ekin [123] as used in [125–127]. This(parametrization allows for)a calculation
of the Lorentz four momenta pµ = E = Ekin +m, p⃗ = px⃗/ |x⃗| required for
the constraint in√equation (4.20) of a final state particle with rest mass m,
momentum p = E2 −m2 and cluster position x⃗. Taking into account a
production vertex at v⃗ = (0, 0, zv), where zv is an additional parameter in the
kinematic fit⎧, t(he cluster position is calculated f⎨ )
rom the parametrization as
⎩(R cosϕ sin θ,R sinϕ sin θ,R√cos θ ) for CB ,x⃗ = −v⃗ + (4.21)Rxy cosϕ,R 2xy sinϕ,Lz = L −Rxy for TAPS .
24The input cluster position x⃗ = (x, y, z = zTAPS) in TAPS is already corrected in x and y for
the shower depth skew due to the forward wall geometry [104, 124], see also figure 4.16.
25The uncertainty for the inverse kinetic σ(1/Ekin) energy is propagated from the given
uncertainty for Ekin as σ(1/Ekin) = σ(E 2kin)/Ekin.
90
4.5. Kinematic fitting
The proton kinetic energy in TAPS or CB is not correctly measured for
energies above 400MeV since the hadronic shower of the proton is not en-
tirely contained within the crystals, an effect called “punch-through”, see
also figure 4.15. Thus, the kinematic fit treats the proton kinetic energy as
unmeasured, that means it sets its uncertainty to σ = 0, and its initial value
Einitkin is set by means of the missing momentum √ ∑p⃗miss = (0, 0, Eγ)− photons p⃗
for the proton, see equation (4.20), so Einitkin = m2 + p⃗ 2p miss − mp with the
proton rest mass mp. This prevents the fit procedure from converging to an
unphysical local minimum.
Furthermore, the z position of the interaction varies between ±5 cm due to
the finite target length of 10 cm, which is not negligible compared to the inner
radius of CB, RCB = 25.4 cm.26 Taking this into account in the fitter improves
the invariant mass resolution as the systematic error in the determination
of the polar angle θ is compensated. The fitting procedure shows slightly
better convergence rate when the z-vertex position √at zv = 0 is assumed
as “measured” with an uncertainty of 3 cm ≈ 10 cm/ 12, in comparison to
choosing the z-vertex to be unmeasured.27
Determining the uncertainties for the proton and the photons in the two
calorimeters CB and TAPS, given the already discussed parametrization, is
far from being trivial. If one assumes a sufficient description of the detector
resolutions within the MC simulation, a single particle gun with subsequent
comparison to the generated information could potentially provide those
uncertainties. Even in this ideal situation, the non-Gaussian tail towards lower
energies of the measured kinetic energy distribution is difficult to account for,28
see also figure 4.5 on page 72. Within this thesis, a data-driven approach to
study and iteratively tune the uncertainties based on events identified as 2π0
production29 was developed. To this end, for each parameter denoted as x,
such as 1/Ekin for photons in CB or Rxy for protons in TAPS, the distribution
26The lateral extent of the photon beam spot with a diameter of roughly 1.3 cm is neglected.
27The more “natural” parametrization (Ekin, θ, ϕ) suffers from the projective geometry of
crystals in CB pointing towards the origin and not to the interaction vertex. Despite
correcting for this systematic error in θ(zv) with single photon detector simulations, this
simple parametrization remains inferior to the currently employed one for an unknown
reason, in particular for lower photon multiplicities such as 2 or 4.
28Additionally, the simulation needs to extract a shower depth, as the fourth parameter is a
measured input to the kinematic fitter. The shower depth is currently implemented as a
polynomial parametrization depending on the kinetic energy [123].
29According to equation (4.8) on page 63 with the replacement m 0η′ → mπ0 , single π
production does not cover the proton phase space sufficiently for EPT photon energies,
and 3π0 production suffers from a comparatively small cross-section. Thus, the choice of
2π0 represents a compromise between phase space coverage and statistics.
91
4. Analysis of the η′ → ωγ branching fraction
of the pull px defined as follows [111, 128] is investigated,
= √ xf − xipx , (4.22)
(σi )2x − (σfx)2
where xi and xf are the values of parameter x before and after the fit, re-
spectively, and ( i/fσx )2 are the corresponding squared uncertainties given as
the diagonal elements of the covariance matrix. The starting uncertainty
model, which only depends on the input cluster energy Ekin for photons and
is constant for protons, is taken from [123, 125]. For each iteration, the mean
value of the uncertainty ⟨σx⟩ is relatively increased (decreased) if the RMS
of the pull distribution30 is larger (smaller) than the target value of 1. The
mean value of the uncertainty ⟨σx⟩ is determined in bins of (Ekin, cos θ) for
photons, as shown figure 4.17 for CB, and in bins of (cos θ) for protons, as
their kinetic energy is unknown due to the punch-through effect. The bin
sizes are chosen small enough such that the average ⟨. . .⟩ is meaningful and
chosen large enough to avoid statistical fluctuations in the RMS determination,
which is additionally mitigated by a bi-cubic interpolation over the binning
and by the removal of fluctuating bins at the edge of the 2π0 production phase
space. For the parameters R in CB and L in TAPS, which depend on the
shower depth s as explained, the offset of the pull distribution with target
value 0 is ensured by adjusting the mean value ⟨s⟩ iteratively. Despite the
careful adjustment of additional MC smearing parameters as described in
section 4.4, the pull distributions for simulated input do not show unit RMS
and zero offset if the uncertainties determined from data are used. Thus, the
identical procedure is applied to determine a separate set of uncertainties for
MC input as shown in figure 4.18, again using the MC cocktail. The final
χ2-probability distribution returned by the kinematic fitter for protons and
photons in both calorimeters is shown in figure 4.19, which is expected to be
uniformly distributed. The technical implementation of this tuning in Ant
is similar to the iterative improvement of the additional MC smearing, as
mentioned in section 4.4.
Besides the four kinematic constraints in equation (4.20), which coin the
name 4C fit31, additional conditions on the final state particles can be imposed.
For example, if two photons with Lorentz vectors pµ1 = (E1, p⃗1) and p
µ
2 =
30Data is prompt-random subtracted by weighting it according to equation (4.3). The fit
probability must be larger than 1% to suppress background and the z-Vertex is set to
unmeasured to avoid skewing the uncertainties in θ.
31Although the proton kinetic energy and the z-Vertex are free parameters, the number of
constraints associated with Lagrange multipliers is used here.
92
4.5. Kinematic fitting
1000 1000 0.05
σ(E ) / MeV 45 σ(θ) / rad
kin 0.045
800 40 800
0.04
35
600 30 600
0.035
0.03
25
400 400
20 0.025
15 0.02
200 200
10 0.015
0 5 0 0.01−0.5 0 0.5 cos θ −0.5 0 0.5 cos θ
1000 0.08 1000 6
σ(φ) / rad σ(R) / cm 5.5
0.07
800 800 5
4.5
0.06
600 600 4
0.05 3.5
400 400 3
0.04
2.5
200 200 2
0.03
1.5
0 0.02 1− 00.5 0 0.5 cos θ −0.5 0 0.5 cos θ
Figure 4.17.: The final fitter uncertainties of the four parameters (Ekin, θ, ϕ,R)
are shown for photons reconstructed in CB, for measured data.
Regions with insufficient statistics are not filled and the rather
coarse binning is mitigated with a two-dimensional cubic inter-
polation over (Ekin, cos θ). Compare also figure 4.18 for MC.
93
Ekin / MeV Ekin / MeV
Ekin / MeV Ekin / MeV
4. Analysis of the η′ → ωγ branching fraction
1000 1000 0.05
σ(E ) / MeV 45 σ(θ) / rad
kin 0.045
800 40 800
0.04
35
600 0.03530 600
0.03
25
400 400
20 0.025
15 0.02
200 200
10 0.015
0 5 0 0.01−0.5 0 0.5 cos θ −0.5 0 0.5 cos θ
1000 0.08 1000 6
σ(φ) / rad σ(R) / cm 5.5
0.07
800 800 5
4.5
0.06
600 600 4
0.05 3.5
400 400 3
0.04
2.5
200 200 2
0.03
1.5
0 0.02 0 1−0.5 0 0.5 cos θ −0.5 0 0.5 cos θ
Figure 4.18.: The final fitter uncertainties are shown for photons reconstructed
in CB, for MC. See figure 4.17 on the previous page for data.
94
Ekin / MeV Ekin / MeV
Ekin / MeV Ekin / MeV
4.5. Kinematic fitting
×103
100
10000
CB Photon TAPS Photon
80
8000
60
6000
40 4000
20 2000
0 0
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
Probability p Probability p
10000 12000
CB Proton TAPS Proton
8000 10000
8000
6000
6000
4000
4000
2000
2000
0 0
0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1
Probability p Probability p
Figure 4.19.: For protons and photons reconstructed in CB and TAPS, the
kinematic fit probability is shown for data (red line) and MC
(blue line). If the uncertainties are correctly modeled to obtain
pull distributions with unit variance and zero mean, a uniform
distribution is expected for the probability, assuming the param-
eters have indeed Gaussian uncertainties. MC is scaled such to
have the same integral in 0.01 < p < 0.1. The rise towards lower
p is due to backgrounds not fulfilling the kinematic fit constraint.
95
4. Analysis of the η′ → ωγ branching fraction
µ = 136.0 MeV µ = 136.6 MeV
104 σ/µ = 11.3 % 104 σ/µ = 10.6 %
µ = 548.5 MeV
µ σ/µ = 3.3 % = 549.8 MeV
103 σ/µ = 5.9 % 103
µ = 960.0 MeV
σ/µ = 0.9 %
102 102
0 200 400 600 800 1000 0 200 400 600 800 1000
IM(2γ) / MeV IM(2γ) / MeV
µ = 785.0 MeV
σ/µ = 2.4 %
3000 3000
µ = 787.9 MeV
σ/µ = 5.1 %
2000 2000
1000 1000
0 0
600 700 800 900 1000 600 700 800 900 1000
IM(3γ) / MeV IM(3γ) / MeV
1000 1000
µ = 546.3 MeV
σ/µ = 3.3 %
800 µ = 543.7 MeV 800
σ/µ = 6.1 %
600 600
400 400
200 200
0 0
400 500 600 700 400 500 600 700
IM(6γ) / MeV IM(6γ) / MeV
Figure 4.20.: Prompt-random subtracted invariant mass plots on 7% of all
2014 EPT beam-time data. Left column before kinematic fit,
right after. Top row shows the 2γ decays of pseudo-scalars with
nominal masses mπ0 ≈ 135.0MeV, mη ≈ 547.9MeV, mη′ ≈
957.8MeV [17]. Middle shows the ω → π0γ → 3γ decay with
nominal mass mω ≈ 782.7MeV [17]. Bottom shows the η →
3π0 → 6γ decay. See also figure 4.13 on page 84.
96
4.6. Selection of η′ → γγ events
(E2, p⃗2), respectively, are required to originate from a π0 decay, the constraint
( 2 !p1 + p2) = (E1 − E2)2 − (p⃗ 21 − p⃗2) = m2π0 (4.23)
is added to the 4C fit, making it a 5C fit. As a specific reaction with decays of
intermediate particles can be represented as a tree, or directed acyclic graph, a
kinematic fit including n invariant mass constraints is called a (4+n)C tree fit
in the following. As there are typically additional photons not belonging to the
π0 in the example above, the fit is carried out for all possible permutations of all
leaf photons, as discussed in detail in section 4.7. This significantly increases the
computational cost of decay tree fitting compared to simple kinematic fitting.
Additionally, the optimization becomes harder as invariant mass constraints
such as equation (4.23) are non-linear in terms of the parametrization.
A comprehensive study of the kinematic fitter is depicted in figure 4.20. A
sufficiently large part of the EPT beam-time data is analyzed and invariant
masses of the photons for the event multiplicities 2 + 1, 3 + 1 and 6 + 1
are investigated. The proton is selected as the best kinematic fit out of all
candidate permutations, see section 4.6 for details. For example, events with
2 + 1 = 3 candidates have 2 photons and thus show the prominent 2γ decay
of pseudo-scalar neutral mesons, π0, η, η′ → 2γ. All fitted peak positions
are within less than 1% before and after the kinematic owing to the careful
calibration presented in section 4.4. As discussed in more detail in section 4.7,
the correct positions are important for the invariant mass constraints as given
in equation (4.23), where the nominal masses are used.
4.6. Selection of η′ → γγ events
As already outlined in section 4.1, the decay η′ → γγ is used as a reference
channel for the analysis of the η′ → ωγ channel. This section presents the
selection of η′ → γγ events and also covers the basic event selection common to
both decay channels. In principle, the analysis strategy identifies two photons
and one proton in the final state, and extracts the number of eventsN(η′ → γγ),
see equation (4.6) on page 63, by fitting the η′ peak in the invariant mass
spectrum of the two photons above possible background. Correspondingly, the
reconstruction efficiency ε(η′ → γγ) is determined by MC simulation as the
number of reconstructed events divided by the number of generated η′ → γγ
events. The latter is chosen sufficiently large to minimize the statistical
uncertainty of the efficiency, which is neglected in the following.
The kinematic fit, without any additional invariant mass constraints, serves
two purposes. First, it increases the resolution of the invariant mass peak
97
4. Analysis of the η′ → ωγ branching fraction
if not at least one candidate in TAPS then next
foreach tagger hit do
foreach candidate as proton do
use remaining candidates as photons if θ > 7°
if discarded energy more than 70MeV then next
if photon invariant mass less than 600MeV then next
if missing mass outside 350MeV proton window then next
run kinematic fit for γp→ p 2γ
if larger fit probablity found then
compute and store values, such as invariant mass of 2γ after
fit
if best fit probablity greater than 0.005 then
write out values to file
Figure 4.21.: Processing of an event consisting of candidates and tagger electron
hits for the reference channel η′ → γγ. Statements with trailing
“then next” are wide pre-filtering cuts to increase analysis speed
and limit output file sizes. The first statement accounts for the
proton of η′ production always being reconstructed in TAPS, see
figure 4.3.
significantly as shown in figure 4.15, and second it is used to identify the
proton. This choice of particle identification is robust against ∆E detector
inefficiencies, such as the PID, and badly modeled detector responses in MC,
which is in particular problematic for the TAPS Veto detector. Furthermore,
ToF and PSA in TAPS are also insufficiently modeled. The identification with
the kinematic fitter is accomplished by testing all candidates of an event as the
proton while the remaining candidates are interpreted as photons, comprising
a list of proton-photons combinations. At this step, the photons are sorted
by decreasing kinetic energy and only the first two are taken into account in
order to match the reference channel signature having two photons in the final
state. The kinetic energy of the remaining photons is summed up, which is
denoted as DiscardedEk, see also the summary in table 4.4. Eventually, the
kinematic fit is carried out for each of the proton-photons combination and the
one with the highest probability is selected. The complete procedure yielding
the output for the reference channel analysis is shown in figure 4.21.
As the η′ production close to threshold is significantly influenced by the
kinematic fit, it is important to model the production mechanism as well as
possible on MC to obtain a correct reconstruction efficiency. To this end, the
98
4.6. Selection of η′ → γγ events
DiscardedEk Sum of kinetic energy of discarded photons to obtain
desired multiplicity (2γ for reference, 4γ for signal)
KinFitProb Best kinematic fit probability over proton-photons com-
binations, see figures 4.21 and 4.27
CBSumVetoE Sum of veto energies for photons reconstructed in CB
AntiPi0FitProb Best tree fit probability for π0π0 background hypothesis
AntiEtaFitProb Best tree fit probability for π0η background hypothesis
TreeFitProb Best tree fit probability for η′ → ωγ hypothesis,
see text for specific invariant mass constraints
gNonPi0_1/2 Kinematic (Ekin, θ) cut on photons not originating from
π0 for η′ → ωγ hypothesis, variant 1/2 (see text)
IM_Pi0g[1] The higher invariant mass combination of the two bach-
elor photons with the fitted π0 four-vector (see text)
Table 4.4.: The various cut variables are summarized as used in sections 4.6
and 4.7. Variables below the separator are solely used in section 4.7
and explained there.
1580 600 1580 600
1560 500 1560 500
1540 400 1540 400
1520 1520
300 300
1500 1500
200 200
1480 1480
100 100
1460 1460
0 0
−1 −0.5 0 0.5 1 −1 −0.5 0 0.5 1
cos θη' cos θη'
Figure 4.22.: The MC generated events are uniformly distributed (left panel)
and then weighted to account for the (Eγ , cos θη′)-dependent
production of the η′ close to threshold (right panel). The shape
is taken from [127] as fitted Legendre polynomials [129]. The
integral in both plots equals the number of generated events,
9× 105.
99
Eγ / MeV
Eγ / MeV
4. Analysis of the η′ → ωγ branching fraction
efficiency corrected numbers for γp→ pη′ on the 2014 EPT beam-times from
[127] are fitted to Legendre polynomials [129]. The shape in (Eγ , cos θη′), where
Eγ is the incoming photon energy and θη′ is the η′ polar angle in the center-
of-mass frame, is reproduced by properly weighting with a two-dimensional
probability density function. Accordingly, the generated events are uniformly
distributed in (Eγ , cos θη′), see figure 4.22, and the weights are normalized such
that the total number of input events is conserved. The experiment trigger
is mimicked on MC generated events by choosing a Gaussian-distributed CB
energy sum threshold with µ = 540MeV and σ = 52MeV [123, 130], compare
also table 4.1. Those parameters do not influence the reconstruction efficiency
significantly since both the reactions η′ → γγ and η′ → ωγ deposit kinetic
energies well above the trigger threshold.32
In order to reduce background and obtain a clearly visible η′ peak in the
invariant mass spectrum, the discarded kinetic energy is required to vanish,
denoted as DiscardedEk=0, and the kinematic fit probability for the best
proton-photon combination must exceed 2%, denoted as KinFitProb>0.02.
The effect of those cuts on the full dataset is shown in figure 4.23 and compared
to the MC cocktail. Although the cocktail is based on known production cross-
sections and branching fractions of the decays [92], the two main background
channels, direct 2π0 and direct ηπ0 production, γp → pπ0π0 → p4γ and
γp → pπ0η → p4γ, respectively, are scaled by a factor of 20 to match the
signal-to-background ratio as given by data. Currently, the reason for this
large scaling factor is not known but hints at an insufficient understanding
of the cluster multiplicities or the kinematic fitter, as discussed further in
section 4.8.
The number of η′ → γγ events is determined by fitting the peak close to the
rest mass of the η′ in the invariant mass spectrum of two photons, denoted
as IM(2γ) or short IM if the photon multiplicity is obvious from the context.
The binned extended likelihood fits are carried out per EPT detector channel,
which corresponds to fixed incident photon energies Eγ . This enables modeling
of the phase-space background close to threshold by the ARGUS probability
density functi⎧on((PDF),⎨ )p ( ( ))x 1− (x/x0)2 exp χ 1− (x/x0)2 if 0 ≤ x ≤ x
f(x) = 0N ·⎩ , (4.24)0 otherwise
where χ < 0 and p = 1/2 control the shape, x0 is a cut-off parameter and
32The analog sum signal used to trigger the read-out is not directly measured in the
experimental setup, see figure 2.11 on page 29. This inhibits a more careful investigation
at this point.
100
4.6. Selection of η′ → γγ events
800×10
3
Data (2.47e+06) Data (3.61e+05)
Ref (5.4e+04) 12000 Ref (5.39e+04)
Sum_MC (5.24e+06) Sum_MC (1.13e+06)
600 Bkg_MC (5.19e+06) 10000 Bkg_MC (1.08e+06)
Bkg_2Pi0 (3.81e+06) Bkg_2Pi0 (8.73e+05)
Bkg_Pi0Eta_4g (8.24e+05) Bkg_Pi0Eta_4g (1.97e+05)
8000
400
6000
4000
200
2000
0 0
0 10 20 30 40 50 60 70 900 950 1000 1050
DiscardedEk / MeV IM / MeV
4000
Data (7.66e+05) Data (1.58e+05)
Ref (4.13e+04) Ref (4.12e+04)
60000 Sum_MC (4.6e+05) Sum_MC (1.25e+05)
Bkg_MC (4.18e+05) 3000 Bkg_MC (8.39e+04)
Bkg_2Pi0 (2.03e+05) Bkg_2Pi0 (5.42e+04)
Bkg_Pi0Eta_4g (1.13e+05) Bkg_Pi0Eta_4g (2.83e+04)
40000 DiscardedEk=0 DiscardedEk=0
2000
20000 1000
0 0
0 0.2 0.4 0.6 0.8 1 900 950 1000 1050
KinFitProb IM / MeV
Data (1.28e+05)
Ref (4.01e+04)
3000 Sum_MC (1.12e+05)
Bkg_MC (7.14e+04)
Bkg_2Pi0 (4.56e+04)
Bkg_Pi0Eta_4g (2.48e+04)
2000 DiscardedEk=0
KinFitProb>0.02
1000
0
900 950 1000 1050
IM / MeV
Figure 4.23.: The applied cuts are shown in each row for the reference channel
η′ → γγ. Below the legend, the cut conditions are specified
according to table 4.4. The sum of all MC channels (black
line Sum_MC) are scaled to match the data points in the bottom
row panel with the final cut choice applied. Ref denotes the
channel η′ → γγ, Bkg_2Pi0 the channel γp → pπ0π0 → p4γ
and Bkg_Pi0Eta_4g the channel γp → pπ0η → p4γ. Note the
implicitly applied cuts as described in figure 4.21.
101
4. Analysis of the η′ → ωγ branching fraction
∫
the normalization N ensures ∞−∞ f(x)dx = 1. Choosing p ̸= 1/2 generalizes
the originally proposed ARGUS PDF in [131], which is exploited later in
section 4.7. The parameter x0 is fi√xed during the fit to the maximum invariantmass given by
x0(Eγ) = m2p + 2mpEγ −mp , (4.25)
where mp ≈ 938MeV is the rest mass of the target proton. The signal shape
PDF to extract the number of η′ → γγ events is determined from MC33, shifted
with the parameter δ and convoluted with a Gaussian with width σ to account
for remaining differences between data and MC.34 The signal, background
and total PDFs are summed separately over the EPT channels. The result
for the chosen cut DiscardedEk=0, KinFitProb>0.02 is shown in figure 4.24
including the input MC signal shape and prompt-random subtracted data.
The corresponding fit parameters are shown in figure 4.25 and the fits per
EPT channel are given in appendix A.
The final result for the number η′ → γγ events corrected for reconstruction
efficiency reads
#(η′ → γγ) = N(η′ → γγ)/ε(η′ → γγ) = 112652± 976stat . (4.26)
This value is used as the reference for the η′ → ωγ branching ratio in sec-
tion 4.7, according to equation (4.6). The selected cut choice is studied in
figure 4.26. It shows that allowing surplus candidates in the events by non-
vanishing DiscardedEk or changing the kinematic fit probability cut does
not influence the resulting efficiency-corrected number of η′ → γγ events
significantly. Additional cuts, such as CBSumVetoE using the PID information
matched to CB clusters, have been studied to test the correctness of the MC
detector response. A similar quantity, the PIDSumE, which is the energy sum
of all PID elements ignoring CB cluster information, is not well-modeled in
MC. This is attributed to the non-optimal handling of the PID signals leading
to largely varying and broad pedestals, which are difficult to reproduce in the
detector simulation, see also figure 4.8 on page 77.
4.7. Selection of η′ → ωγ events
The experimental setup of A2, in particular the calorimeters, is ideally suited
for the detection of photons. Thus, the signal channel η′ → ωγ is investigated
33One third each of the 107 generated events is analyzed for the three beam-times to account
for possible changes in the experimental setup, such as ignored elements, see figure 4.14.
34The package RooFit 3.60 is used to carry out those fits [132].
102
4.7. Selection of η′ → ωγ events
45 14000 45
40 12012000 40
35 35 100
10000
30 30
80
25 8000 25
20 606000 20
15 15
4000 40
10 10
2000 20
5 5
0 0 0900 950 1000 1050 0 900 950 1000 1050
IM / MeV IM / MeV
N = 50381± 434 4000 N
3000 N/ε = 112652± 976
χ2  = 205/141≈ 1.45 N/ε
red
3000
2000
2000
1000
1000
0
900 950 1000 0 1450 1500 1550
IM / MeV Eγ / MeV
Figure 4.24.: The invariant mass of the kinematically fitted photons is used
to extract the number of measured η′ → γγ events N and the
efficiency-corrected value N/ε, as shown on the bottom right.
The fits are carried out for each EPT channel with the corre-
sponding MC signal shape, as given in the top row. The sum
of all fits is displayed in the bottom left panel. The cut choice
requires DiscardedEk=0 and KinFitProb>0.02, see figure 4.23.
The determined fit parameters are given in figure 4.25.
103
Events / ( 1 MeV ) EPT Channel
EPT Channel
4. Analysis of the η′ → ωγ branching fraction
6
2
4
1.5 2
0
1
−2
1450 1500 1550 1450 1500 1550
Eγ / MeV Eγ / MeV
8
0
6
−2
4
−4
2
−6
0
−8
1450 1500 1550 1450 1500 1550
Eγ / MeV Eγ / MeV
Figure 4.25.: Fit parameters including χ2 = χ2red /#(d.o.f.) for each tagger
channel corresponding to a certain incident photon energy range
Eγ . See text for details.
104
σsmearing / MeV χ
2
red
χ
ARGUS δData-MC / MeV
4.7. Selection of η′ → ωγ events
DiscardedEk=0, KinFitProb>0.1 DiscardedEk=0, KinFitProb>0.02
DiscardedEk=0, KinFitProb>0.2 DiscardedEk<20, KinFitProb>0.02
DiscardedEk=0, KinFitProb>0.02, CBSumVetoE=0 DiscardedEk<50, KinFitProb>0.02
Events DiscardedEk=0, KinFitProb>0.02, CBSumVetoE<0.2 DiscardedEk=0, KinFitProb>0.05
 4000
N/ε
 3000
 2000
N
 1000
 0
 1440  1470  1500  1530  1560  1590
Eγ / MeV
Figure 4.26.: For each cut choice color-coded by the legend on the top, the
number of η′ → γγ events N extracted from the fit and the
efficiency-corrected value N/ε are shown with 1σ error bands for
each EPT channel corresponding to the incident photon energy
Eγ . The cut variables are explained in table 4.4.
in the decay chain
η′ → ωγ → π0γγ → 4γ , (4.27)
where the expected candidate multiplicity is five including the proton. To
calculate the number of signal events N(η′ → ωγ) in equation (4.6), the known
branching fractions of the intermediate decays ω → π0γ and π0 → γγ are
used [17],
BR(ω → π0γ) = (8.28± 0.28)× 10−2 ,
(4.28)
BR(π0 → γγ) = (99.823± 0.034)× 10−2 ,
where the former contributes predominantly to the systematic uncertainty
of the final result. The primary analysis strategy to extract the number of
signal events is similar to section 4.6 as it searches for the η′ peak in the
invariant mass of the four photons, where two of them are subject to the π0
constraint. This invariant mass is denoted as IM(π0γγ). Due to the higher
photon multiplicity leading to larger background contributions and the at least
10 times lower number of expected signal events, the analysis contains various
cuts to increase the signal-to-background ratio, as explained in the following.
105
4. Analysis of the η′ → ωγ branching fraction
if not at least one candidate in TAPS then next
foreach tagger hit do
foreach candidate as proton do
use remaining candidates as photons if θ > 7°
if discarded energy more than 70MeV then next
if missing mass outside 350MeV proton window then next
store proton-photons combination
foreach proton-photons combination do
run kinematic fit for γp→ p 4γ
if best KinFit probability smaller than 0.005 then next
foreach proton-photons combination do
run 6C tree fit for γp→ pπ0π0 → p 4γ
if best AntiPi0Fit probability greater than 0.001 then next
foreach proton-photons combination do
run 6C tree fit for γp→ pπ0η → p 4γ
if best AntiEtaFit probability greater than 0.02 then next
foreach proton-photons combination do
run 5C tree fit for η′ → ωγ with π0 constraint
if larger TreeFit probablity found then
compute and store values, such as invariant mass of 4γ after
fit
foreach proton-photons combination do
run 6C tree fit for η′ → ωγ with π0, ω constraint
if larger TreeFit probablity found then
compute and store values, such as η′ bachelor photon energy
if at least one tree fit successful then
write out values to file
Figure 4.27.: Processing of an event consisting of candidates and tagger electron
hits for the signal channel η′ → ωγ. The various tree fits implicitly
permute all photons assigned to the leaves, but skip permutations
outside a window of 90MeV for π0 constraints and 200MeV for
η constraints to increase performance.
106
4.7. Selection of η′ → ωγ events
105 µ = 135.5 MeV 105 µ = 135.9 MeV
σ/µ = 8.3 % σ/µ = 7.8 %
µ = 550.1 MeV
µ = 551.5 MeV σ/µ = 2.9 %
104 σ/µ = 5.2 % 104
0 100 200 300 400 500 600 700 0 100 200 300 400 500 600 700
IM(2γ) / MeV IM(2γ) / MeV
Figure 4.28.: Prompt-random subtracted 2γ out of 4γ invariant mass com-
binations on data, where the proton is identified with the best
kinematic fit. Left panel shows before kinematic fit, right after
the fit. The subsequent tree fits require that the π0 and η peaks
are close to the nominal masses. See also figure 4.13 on page 84.
180 γ 800 180 800
160 η'γ 700 160 700
140 γ
ω 600
140
γ1  / γ2 600
η′ 120 120 π0 π0500 500
ω 100 100γ 0 400 400
γ π 80 80
300 300
γ γ 60 60
40 200 40 200
20 100 20 100
0 0 0 0
0 200 400 600 800 1000 0 200 400 600 800 1000
Ek / MeV Ek / MeV
Figure 4.29.: The phase space distribution in kinetic energy Ek and polar angle
θ of the final state photons for generated signal events is shown.
γX indicates the photon originating from the meson X = η′, ω, π0.
γη′ and γω are bachelor photons of the η′ and ω, respectively.
107
θ / °
θ / °
4. Analysis of the η′ → ωγ branching fraction
105 105
AntiPi0FitProb AntiEtaFitProb
104 104
103 103
Data (9.8e+06)
Sig (7.66e+03)
Data (9.25e+06)
Sum_MC (9.79e+06)
Sig (7.56e+03)
Bkg_MC (9.78e+06) Sum_MC (9.25e+06)
102 2Bkg_2Pi0 (2.14e+06) 10 Bkg_MC (9.24e+06)
Bkg_Pi0Eta_4g (1.03e+06) Bkg_2Pi0 (1.87e+06)
DiscardedEk=0 Bkg_Pi0Eta_4g (1.01e+06)
DiscardedEk=0
AntiPi0FitProb<10-5||nan
10 10
−15 −10 −5 −15 −10 −5
log  p log  p
10 10
Data (8.49e+06)
Sig (6.87e+03) Data (2.67e+05)
106 Sum_MC (8.43e+06) 5 Sig (5.6e+03)Bkg_MC (8.42e+06) 10
TreeFitProb Bkg_2Pi0 (1.81e+06) Sum_MC (1.84e+05)
Bkg_Pi0Eta_4g (5.26e+05) Bkg_MC (1.75e+05)
DiscardedEk=0
105 AntiPi0FitProb<10
-5||nan Bkg_2Pi0 (7.5e+04)
AntiEtaFitProb<10-4||nan Bkg_Pi0Eta_4g (4.17e+04)
104 DiscardedEk=0
AntiPi0FitProb<10-5||nan
AntiEtaFitProb<10-4||nan
104 TreeFitProb>0.1
103
103
102
102
0 0.2 0.4 0.6 0.8 1 920 940 960 980 1000 1020
p IM(π
0γγ) / MeV
Figure 4.30.: The probability distribution for the two background-suppression
fits and the 5C tree fit, constraining the π0, are shown. On
the bottom right, the resulting invariant mass spectrum after
applying all probability cuts is displayed. More cuts are obviously
needed to obtain a visible signal peak. The MC cocktail is scaled
by a factor of 7.8 to roughly match the black data points, see
also figure 4.23.
108
4.7. Selection of η′ → ωγ events
In order to discriminate direct 2π0 and direct ηπ0 production, which are the
dominant background contributions, the event is subjected to a 6C kinematic
fit with the invariant mass constraints matching those background channel hy-
potheses. As shown in figure 4.28, the invariant mass constraints can be applied
with the nominal masses without introducing a fit bias. The corresponding
best fit probabilities, denoted as AntiPi0FitProb and AntiEtaFitProb, are
required to be less than 10−5 and 10−4, respectively. The event is also accepted
if the fit has not converged, which is indicated by the trailing ||nan. The
signal decay tree, as depicted in figure 4.29, is primarily tested by requiring a
single π0 invariant mass constraint of two photon leaves as a 5C tree fit. As
an alternative signal identification, the ω invariant mass of three photons is
additionally constrained as a 6C tree fit. In addition to the proton selection,
the leaves are correspondingly permuted over the photons and the tree fit
with the highest probability is selected. The full analysis procedure is given
in figure 4.27. The 6C tree fit should be handled with care due to the com-
paratively large decay width of the ω of about Γω ≈ 8MeV [17] and is only
used to cross-check aspects of the analysis chain. The 5C tree fit suffers from
the remaining ambiguity of the bachelor photons not originating from the π0
decay. This is resolved by choosing the photon with the higher invariant mass
when added to the π0 four-vector, denoted as IM(π0γ), as the bachelor of
the ω, which is well-motivated by MC generated signal events, see figure 4.33.
The signal hypothesis is ensured by requiring the best fit probability to be
larger than 10%, denoted as TreeFitProb>0.1. Figure 4.30 shows that 2π0
and ηπ0 are significantly suppressed by the corresponding anti tree fits, and
the signal hypothesis shows a flat probability distribution for the MC signal
channel. Assuming a proper detector simulation and kinematic fit procedure,
the probability cuts can be optimized to increase the signal-to-background
ratio, but the discussed choice is sufficient to extract the result.
After those selection cuts related to kinematic fitting, which at least ensure
the proper assignment of photons to the π0 meson, additional kinematic cuts
regarding the η′ and ω bachelor photons not belonging to the π0 are employed.
The first variant, denoted as gNonPi0_1(, discards th)e event if the condition
Ek > 230MeV · 1− θ/160° (4.29)
is not fulfilled for both bachelor photons, where Ek and θ are their reconstructed
kinetic energy and polar angle, respectively. Similarly, the second variant
gNonPi0_2 is given by {
140MeV if θ < 22° (TAPS)
Ek > (4.30)60MeV otherwise (CB)
109
4. Analysis of the η′ → ωγ branching fraction
400 104
MC Signal
300
103
200
102
100
0
0 50 100 150
θ / °
Figure 4.31.: In the top row, the kinetic energy Ek and polar angle θ dis-
tribution of the two bachelor photons for prompt-random sub-
tracted data and MC signal η′ → ωγ is shown after applying the
AntiPi0/EtaFitProb and TreeFitProb cuts, see text. The bot-
tom row shows the same data histogram after the gNonPi0_1/2
cuts defined in equations (4.29) and (4.30), as indicated.
110
Ek / MeV
4.7. Selection of η′ → ωγ events
Data (1.42e+06)
Sig (5.11e+03)
6 Sum_MC (9.88e+05)10 Bkg_MC (9.83e+05)
Bkg_2Pi0 (2.72e+05)
Bkg_Pi0Eta_4g (1.63e+05)
Bkg_Pi0PiPPiM (1.1e+05)
DiscardedEk=0
105 AntiPi0FitProb<10-5||nan
AntiEtaFitProb<10-4||nan
TreeFitProb>0.1
gNonPi0_2
104
103
102
10
0 0.5 1 1.5 2
gNonPi0_CBSumVetoE / MeV
Figure 4.32.: Backgrounds such as γp→ pπ0π+π− is reduced by requiring the
sum of veto energies of the two bachelor photons, denoted as
gNonPi0_CBSumVetoE, to be less than 0.2MeV.
900 900
50
45000
40 40000
850 850
35000
30 30000
800 800 25000
20 20000
15000
750 10 750
10000
5000
0
700 700 0
920 940 960 980 1000 1020 920 940 960 980 1000 1020
IM(π0γγ) / MeV IM(π0γγ) / MeV
Figure 4.33.: Prompt-random subtracted data is shown on the left, and MC
signal on the right. The signal events are visible as a peak around
the nominal ω and η′ mass values for IM(π0γ) and IM(π0γγ),
respectively. Using the 5C tree fit constraining the π0 only, the
bachelor photon of the ω is selected as the one with the higher
invariant mass combination with the fitted π0 four-vector, here
denoted as IM(π0γ) or IM_Pi0g[1].
111
IM(π0γ) / MeV
IM(π0γ) / MeV
4. Analysis of the η′ → ωγ branching fraction
ε / % see
100 Generated events
45.9 Pre-processing of events figure 4.27
33.8 DiscardedEk=0 ⎫section 4.6
33.4 AntiPi0FitProb<10−5||nan ⎪⎬
30.9 AntiEtaFitProb<10−4||nan ⎪⎭figure 4.3028.2 TreeFitProb>0.1
28.0 gNonPi0_2 figure 4.31
23.3 CBSumVetoE_gNonPi0<0.2 figure 4.32
17.3 IM_Pi0g[1] figure 4.33
Table 4.5.: Overview of the cuts for the extraction of the η′ → ωγ signal
events, which are applied from top to bottom. In each row, the
reconstruction efficiency ε determined from generated MC signal
events is given after applying the corresponding cut. See also
table 4.4.
where the choice θ = 22 ◦C is the interface between the calorimeters CB and
TAPS, as indicated. Both variants are depicted in figure 4.31 and the second
variant representing a looser cut is selected henceforth.
Next, the sum of the matched PID energy information of the two bachelor
photons is required to be less than 0.2MeV, denoted as CBSumVetoE_gNonPi0<0.2,
which has been cross-checked for the reference channel in figure 4.26. This
primarily suppresses the background channel γp → π0π+π−, as shown in
figure 4.32. The last cut resolves the bachelor photon ambiguity in case of the
5C signal tree fit. It limits the higher photon invariant mass combination out
of the two bachelor photons to be within 40MeV of the ω rest mass,
762.65MeV ≤ IM(π0γ) ≤ 802.65MeV , (4.31)
which is denoted as IM_Pi0g[1] and depicted in figure 4.33.
All cuts, as given in table 4.5 including their impact on the reconstruction
efficiency, are applied to obtain the final spectrum of the invariant mass of
all four photons after the 5C kinematic fit constraining the π0, denoted as
IM(π0γγ). Different than the extraction η′ → γγ events in section 4.6, the
fit for the η′ → ωγ decay must be carried out on data summed over all EPT
channels, since the signal-to-background ratio is not sufficient for a reliable
fit in each single channel. In this case, a specific threshold cannot be used
similar to equation (4.25) and thus the generalized ARGUS background PDF
112
4.7. Selection of η′ → ωγ events
×103 300
N = 1334± 137
150 250 N/ε = 7714± 793
χ2  = 1.06
red
200 σ = 2.7 MeV
δ = 1.9 MeV
100
150
100
50
50
0 0
920 940 960 980 1000 1020 920 940 960 980 1000 1020
IM(π0γγ) / MeV IM (MeV)
Figure 4.34.: The MC signal shape on the left is fitted to prompt-random
subtracted data on the right, which is the sum over all EPT chan-
nels. The signal shape is weighted according to figure 4.22 and
additionally shifted and Gaussian-smeared with fit parameters δ
and σ, respectively. See text and also figure 4.24.
Parameter Fitted value
N 1334± 137
δData-MC (1.91± 0.34)MeV
σsmearing (2.74± 0.48)MeV
Nbkg 7940± 179
χARGUS −9.91± 3.1
pARGUS 2.37± 0.35
Table 4.6.: The fit parameters as determined in figure 4.34, using the MC
line shape shifted by δ and smeared by σ with a generalized AR-
GUS PDF as background. The cut-off parameters x0 is fixed to
1025MeV.
113
Events / ( 1 MeV )
4. Analysis of the η′ → ωγ branching fraction
Cut Variations
DiscardedEk = 0, < 20, < 50 MeV
AntiPi0FitProb < 10−7, < 10−5, < 10−3
AntiEtaFitProb < 10−6, < 10−4, < 10−2
TreeFitProb > 0.05, > 0.1, > 0.2
gNonPi0 Variant 1, 2 and
2 with half the limits in equation (4.30)
CBSumVetoE_gNonPi0 = 0, < 0.1, < 0.2, < 0.4 MeV
IM_Pi0g[1] Widths 30, 40, 50 MeV in equation (4.31)
Table 4.7.: The variations of the cut choice in table 4.5, marked bold, are
summarized to obtain figure 4.35, yielding in total 4 · 36 = 2916
permutations. See also table 4.4.
with p ̸= 1/2 in equation (4.24) is used to allow for a more flexible description
of the background shape. The final extended likelihood fit, again utilizing a
shifted and Gaussian-smeared MC signal line shape, is shown in figure 4.34
and the number of η′ → ωγ events in the decay chain (4.27) corrected for
reconstruction efficiency reads
#(η′ → ωγ) = N(η′ → ωγ)/ε(η′ → ωγ) = 7714± 793stat . (4.32)
The complete list of fit parameters is given in table 4.6 and the result is
discussed further in section 4.8. Similar to the shown main backgrounds, in
total 20 photo-production channels have been identified and tested if they
contribute significantly to this signal extraction using the MC cocktail. In
particular, peaking background contributions such as η′ → ηπ0π0 → 6γ have
been investigated as well as the interfering decay η′ → ρ0γ → π0γγ → 4γ. As
all those decays are present in the MC with their appropriate branching ratios,
it is found that all backgrounds are well under control or can be neglected.
This conclusion relies on the correctness of the MC detector simulation and the
correct modeling of the generated decays. This assumption is fundamentally
challenged by the results presented in section 4.8.
4.8. Results
Combining the findings from sections 4.6 and 4.7, the result according to
equation (4.6) for the relative branching fraction reads
BR(η′ → ωγ) = (1.82± 0.19 )× 10−2stat , (4.33)
114
4.8. Results
 4
Cut variations
Cut choice
 3.5 PDG 2016
BES III
 3
 2.5
 2
 1.5
 1 4  6  8  10  12  14  16  18  20
Relative Uncertainty / %
Figure 4.35.: The relative branching ratio BR(η′ → ωγ) is plotted for the cut
variations of the signal channel in table 4.7 while the reference
analysis is fixed to equation (4.26). The relative uncertainty
is solely determined from the fit, see figure 4.34. They are
compared to the PDG world average and the BESIII result, the
latter plotted with its dominating systematic uncertainty [17, 30].
More detailed figures are given in appendix B.
where the statistical uncertainty is propagated from the fit result in equa-
tion (4.32). A lower bound for the systematic uncertainty in equation (4.33)
reads 0.092× 10−2, which is the statistical uncertainty of the reference chan-
nel in equation (4.26), neglecting systematics as given by figure 4.26, and
the uncertainties of the branching ratios given in equations (4.7) and (4.28)
added in quadrature. The result is about 30% or 4.3σstat lower than and
thus inconsistent with the current world average and the latest measurement,
given in equations (1.26) and (1.27), respectively. To investigate this further,
the cut choice for the signal analysis is varied according to table 4.7 and the
obtained relative branching ratio with its statistical uncertainty is plotted in
figure 4.35. It shows that the efficiency correction does not compensate the
rather moderate changes in the choice of cuts. As shown in appendix B, no
single cut is solely responsible for the wide spread of values, but the cut on the
bachelor photon kinematics, gNonPi0, and with lesser extent the DiscardedEk
cut are more strongly partitioning the distribution. Eventually, a conservative
estimation of the relative systematic uncertainty is at least 100%, which is far
from rendering the presented result reliable.
115
Branching Ratio / %
4. Analysis of the η′ → ωγ branching fraction
Many parts of the analysis have been developed from scratch, such as the
clustering algorithm, the kinematic fitter and the calibration routines. To this
end, the GEANT4-based detector simulation as provided by the collaboration
is a crucial tool to debug and tune the reconstruction process. In particular,
the kinematic fitting procedure is sensitive to the correct implementation of the
uncertainty model, which is initially determined from single photon detector
simulation. It is surprising that investigating the kinematic fit procedure with
a comparatively simple 2π0 analysis, as discussed in section 4.5, requires the
introduction of separate uncertainty models for beam-time data and MC input,
compare figures 4.17 and 4.18. This either hints at an incorrectly modeled
detector simulation or at an error in the kinematic fitter implementation. Both
possibilities have been scrutinized, which again relies on MC simulation, and
although subtle errors have been found and fixed, some apparently remain
unresolved.
Despite those shortcomings, the whole extraction procedure is cross-checked
with the MC cocktail instead of data, which contains about one quarter of the
total number of η′ mesons and uses the branching fractions from [17] as input.
The result in this case reads
BR(η′ → ωγ) = (3.02± 0.23)× 10−2 , (4.34)
with statistical and systematical uncertainties added in quadrature, again the
systematical contribution should be regarded as a lower bound. Although
the backgrounds are typically underestimated in the cocktail and all angular
distributions are generated flat, this cross-check shows that the extraction
procedure can potentially yield competitive results and is consistent with the
input. The slight tendency to higher values is still to be investigated but does
not explain the systematically lower values determined on data.
Eventually, using the result from the reliable η′ → γγ analysis given in
equations (4.7) and (4.26), the total number of η′ mesons produced in the
EPT 2014 beam-time is calculated as
#(η′) = (5.12± 0.19)× 106 . (4.35)
This number is consistent with the cross-sections published in [127] taking
into account the more conservative selection of “good” run files given in
table 4.2. Furthermore, the reconstruction efficiency appears to be reasonably
well-modeled according to figure 4.26 despite the comparatively large additional
MC smearing of cluster energies as explained in section 4.4. This result is
encouraging and should be the basis of further work.
Although the treatment of data and MC input within Ant is kept as transpar-
ent as possible to analysis algorithm, it is suspected that not the reconstruction
116
4.8. Results
efficiency, as detailed in table 4.5, is the cause for the deviation, but rather
yet undiscovered mistake in the reconstruction of beam-time data leading to
too small number of signal events N in figure 4.34, somehow not appropriately
taken into account by ε. Many event-by-event comparisons, in particular
regarding the existing analysis code used in [125, 127], have been carried out
and no apparent differences are left uncorrected. However, this statement is
speculative and future work should concentrate on obtaining a better under-
standing of the detector system, including properly simulated energy- and
timing measurement resolutions.
117

5. Conclusion
The A2 collaboration probes the theory of the strong interaction in the low-
energy regime using its unique experimental setup for photo-production ex-
periments. Despite tremendous progress in the last decades, many challenging
questions remain in this field, for example how an effective description of QCD
can consistently be established in the energy regime below 1GeV, where the
conventional perturbative treatment with quarks and gluons as the degrees
of freedom fails. This thesis as part of a collaborative effort contributes to
this endeavor from an experimental point of view in various aspects. The data
acquisition has been improved, future hardware upgrade possibilities have been
assessed, a beam-time with unprecedented statistics has been carried out and
the PV γ decay η′ → ωγ has been analyzed. Future work is outlined for each
of those contributions in the following.
The detector system as used for the η′ production runs in 2014 consists
primarily of the CB calorimeter and the photon-tagging device EPT, ideally
suited to study the photo-production of η′ mesons close to threshold. As the
production cross-section off the proton is more than two orders of magnitude
lower than the total photo-production cross-section, the data-acquisition must
cope with high event rates while the detector system should provide complete
coverage of the solid angle in the center-of-mass frame. To this end, the
TAPS calorimeter is additionally installed as a forward-wall detector, which
coincidentally covers the complete proton polar angle for η′ production. The
two calorimeters are supplemented by particle identification detectors, but only
the barrel scintillator detector PID within CB has proven useful for analysis.
As the limiting factor for beam-times before 2013 was the performance and
reliability of the data acquisition system, bottlenecks and various shortcomings
have been removed within the scope of this thesis. The improvements include
the introduction of modern software engineering techniques such as a version
control system and a common documentation platform. These improvements
have proven crucial for the success of the EPT beam-time in the second half
of 2014 by increasing the recorded event rate by a factor of 3 and by enabling
rapid error detection during data-taking.
The hardware upgrade feasibility studies focus on the TRB3 multi-purpose
FPGA board, as it fulfills all requirements of future A2 experiments. The
119
5. Conclusion
applicability of this platform has been successfully shown in test measurements
and several conversion front-ends are shown to be suitable for the components
of the A2 detector system. The TRB3 collaboration, primarily consisting of
future experiments such as PANDA at the GSI in Darmstadt, provides support
to overcome the lack of manpower in A2 needed for a major overhaul of the
data acquisition system, which should be planned carefully to avoid creating
an overly complex system. Within the scope of this thesis, a feature extraction
firmware has been developed for the read-out of timing and energy information
with sufficient accuracy for the CB detector and front-end electronics for
other parts of the detector system have been evaluated. Improvements of
the development tool-chain and firmware have been shared among the TRB3
community during this work.
The subsequent analysis of the 2014 EPT beam-time data led to the devel-
opment of a new analysis framework, of which major parts have been designed
and implemented as part of this thesis. During this effort, many technical
improvements such as decent calibration and tuning tools have been provided
to the A2 collaboration. For example, a new clustering algorithm has been
successfully developed, which is a key component to provide calibrations as
a service to all collaboration members in the future. The initial goal of a
measurement of the relative branching fraction of the η′ → ωγ decay, which is
competitive with the current world data, has not been achieved. Nevertheless,
the new software framework enabled thorough tests of the various analysis
components and their systematic influence on the final result. Although an
acceptable agreement with already published results of the same dataset using
an independent analysis framework has been found for the η′ → γγ reference
channel, the more challenging extraction of η′ → ωγ events eventually re-
vealed major shortcomings of the current detector simulation resulting in huge
and not fully quantified systematic uncertainties. Despite tremendous effort
re-implementing and re-designing analysis concepts to make them generally
applicable, those shortcomings could not be resolved. The presented findings
serve as a starting point for future analysis efforts.
120
A. Supplementary figures for η′ → γγ
For each tagger channel corresponding to the given incoming photon energy
Eγ , the fit to the signal peak of the reference channel η′ → γγ is shown in the
following. N is the number of signal events, ε the reconstruction efficiency
determined from MC, δ the applied shift of the MC line shape in MeV, σ the
additional Gaussian detector resolution.
150 Eγ = 1446.7 MeV 150 Eγ = 1449.9 MeV 150 Eγ = 1453.2 MeV
N = 67± 21 N = 398± 28 N = 643± 35
N/ε = 215± 69 N/ε = 834± 58 N/ε = 1321± 72
χ2  = 0.88 χ2  = 1.37 χ2  = 1.36
red red red
100 σ = 1.4 MeV 100 σ = 0.3 MeV 100 σ = 0.0 MeV
δ = -1.6 MeV δ = -0.0 MeV δ = 0.4 MeV
50 50 50
0 900 950 1000 1050 0 900 950 1000 1050 0 900 950 1000 1050
IM (MeV) IM (MeV) IM (MeV)
150 Eγ = 1456.4 MeV 150 Eγ = 1459.7 MeV 150 Eγ = 1462.9 MeV
N = 849± 42 N = 842± 44 N = 924± 48
N/ε = 1739± 86 N/ε = 1720± 90 N/ε = 1889± 99
χ2  = 1.33 χ2  = 1.25 χ2  = 1.21
red red red
100 σ = 1.5 MeV 100 σ = 1.5 MeV 100 σ = 2.1 MeV
δ = 0.7 MeV δ = 0.9 MeV δ = 1.6 MeV
50 50 50
0 900 950 1000 1050 0 900 950 1000 1050 0 900 950 1000 1050
IM (MeV) IM (MeV) IM (MeV)
150 Eγ = 1466.1 MeV 150 Eγ = 1469.4 MeV 150 Eγ = 1472.6 MeV
N = 985± 53 N = 1042± 58 N = 1033± 62
N/ε = 2017± 108 N/ε = 2139± 119 N/ε = 2132± 128
χ2  = 1.96 χ2  = 1.11 χ2  = 1.01
red red red
100 σ = 2.4 MeV 100 σ = 2.6 MeV 100 σ = 2.4 MeV
δ = 1.8 MeV δ = 1.8 MeV δ = 2.0 MeV
50 50 50
0 900 950 1000 1050 0 900 950 1000 1050 0 900 950 1000 1050
IM (MeV) IM (MeV) IM (MeV)
121
Events / ( 1 MeV ) Events / ( 1 MeV ) Events / ( 1 MeV )
Events / ( 1 MeV ) Events / ( 1 MeV ) Events / ( 1 MeV )
Events / ( 1 MeV ) Events / ( 1 MeV ) Events / ( 1 MeV )
A. Supplementary figures for η′ → γγ
150 Eγ = 1475.8 MeV 150 Eγ = 1479.0 MeV 150 Eγ = 1482.3 MeV
N = 993± 67 N = 1154± 70 N = 1198± 76
N/ε = 2054± 138 N/ε = 2395± 145 N/ε = 2493± 159
χ2  = 1.24 χ2  = 1.47 χ2  = 1.29
red red red
100 σ = 1.9 MeV 100 σ = 2.7 MeV 100 σ = 3.2 MeV
δ = 2.2 MeV δ = 2.4 MeV δ = 2.7 MeV
50 50 50
0 900 950 1000 1050 0 900 950 1000 1050 0 900 950 1000 1050
IM (MeV) IM (MeV) IM (MeV)
150 Eγ = 1485.5 MeV 150 Eγ = 1488.7 MeV 150 Eγ = 1491.9 MeV
N = 1067± 70 N = 1147± 89 N = 1009± 65
N/ε = 2242± 147 N/ε = 2414± 188 N/ε = 2130± 138
χ2  = 0.94 χ2  = 1.05 χ2  = 1.42
red red red
100 σ = 2.1 MeV 100 σ = 3.3 MeV 100 σ = 1.7 MeV
δ = 2.8 MeV δ = 3.1 MeV δ = 2.8 MeV
50 50 50
0 900 950 1000 1050 0 900 950 1000 1050 0 900 950 1000 1050
IM (MeV) IM (MeV) IM (MeV)
150 Eγ = 1495.2 MeV 150 Eγ = 1498.4 MeV 150 Eγ = 1501.6 MeV
N = 1166± 72 N = 1342± 94 N = 1241± 75
N/ε = 2480± 153 N/ε = 2862± 200 N/ε = 2678± 162
χ2  = 0.85 χ2  = 1.08 χ2  = 0.93
red red red
100 σ = 2.6 MeV 100 σ = 3.7 MeV 100 σ = 2.7 MeV
δ = 3.2 MeV δ = 3.0 MeV δ = 3.1 MeV
50 50 50
0 900 950 1000 1050 0 900 950 1000 1050 0 900 950 1000 1050
IM (MeV) IM (MeV) IM (MeV)
150 Eγ = 1504.9 MeV 150 Eγ = 1508.1 MeV 150 Eγ = 1511.4 MeV
N = 1279± 77 N = 1426± 79 N = 1292± 70
N/ε = 2760± 167 N/ε = 3091± 171 N/ε = 2824± 153
χ2  = 1.06 χ2  = 1.27 χ2  = 2.29
red red red
100 σ = 3.6 MeV 100 σ = 4.1 MeV 100 σ = 3.2 MeV
δ = 3.7 MeV δ = 3.5 MeV δ = 3.0 MeV
50 50 50
0 900 950 1000 1050 0 900 950 1000 1050 0 900 950 1000 1050
IM (MeV) IM (MeV) IM (MeV)
122
Events / ( 1 MeV ) Events / ( 1 MeV ) Events / ( 1 MeV ) Events / ( 1 MeV )
Events / ( 1 MeV ) Events / ( 1 MeV ) Events / ( 1 MeV ) Events / ( 1 MeV )
Events / ( 1 MeV ) Events / ( 1 MeV ) Events / ( 1 MeV ) Events / ( 1 MeV )
150 Eγ = 1514.6 MeV 150 Eγ = 1517.9 MeV 150 Eγ = 1521.1 MeV
N = 1311± 72 N = 1291± 76 N = 1393± 71
N/ε = 2873± 159 N/ε = 2842± 168 N/ε = 3075± 158
χ2  = 1.00 χ2  = 1.00 χ2  = 1.37
red red red
100 σ = 3.6 MeV 100 σ = 4.2 MeV 100 σ = 4.2 MeV
δ = 3.9 MeV δ = 3.7 MeV δ = 3.9 MeV
50 50 50
0 900 950 1000 1050 0 900 950 1000 1050 0 900 950 1000 1050
IM (MeV) IM (MeV) IM (MeV)
150 Eγ = 1524.4 MeV 150 Eγ = 1527.7 MeV 150 Eγ = 1530.9 MeV
N = 1483± 78 N = 1404± 49 N = 1463± 70
N/ε = 3282± 173 N/ε = 3131± 110 N/ε = 3270± 157
χ2  = 1.24 χ2  = 0.93 χ2  = 0.89
red red red
100 σ = 4.8 MeV 100 σ = 3.2 MeV 100 σ = 4.3 MeV
δ = 3.6 MeV δ = 4.1 MeV δ = 4.9 MeV
50 50 50
0 900 950 1000 1050 0 900 950 1000 1050 0 900 950 1000 1050
IM (MeV) IM (MeV) IM (MeV)
150 Eγ = 1534.2 MeV 150 Eγ = 1537.4 MeV 150 Eγ = 1540.7 MeV
N = 1580± 68 N = 1499± 63 N = 1499± 66
N/ε = 3570± 155 N/ε = 3397± 144 N/ε = 3399± 150
χ2  = 1.33 χ2  = 1.38 χ2  = 1.27
red red red
100 σ = 4.9 MeV 100 σ = 3.7 MeV 100 σ = 4.4 MeV
δ = 4.3 MeV δ = 4.4 MeV δ = 4.0 MeV
50 50 50
0 900 950 1000 1050 0 900 950 1000 1050 0 900 950 1000 1050
IM (MeV) IM (MeV) IM (MeV)
150 Eγ = 1544.0 MeV 150 Eγ = 1547.2 MeV 150 Eγ = 1550.5 MeV
N = 1451± 109 N = 1671± 67 N = 1542± 64
N/ε = 3320± 250 N/ε = 3844± 155 N/ε = 3585± 150
χ2  = 1.49 χ2  = 1.28 χ2  = 1.58
red red red
100 σ = 2.7 MeV 100 σ = 5.6 MeV 100 σ = 5.1 MeV
δ = 3.7 MeV δ = 4.7 MeV δ = 4.9 MeV
50 50 50
0 900 950 1000 1050 0 900 950 1000 1050 0 900 950 1000 1050
IM (MeV) IM (MeV) IM (MeV)
123
Events / ( 1 MeV ) Events / ( 1 MeV ) Events / ( 1 MeV ) Events / ( 1 MeV )
Events / ( 1 MeV ) Events / ( 1 MeV ) Events / ( 1 MeV ) Events / ( 1 MeV )
Events / ( 1 MeV ) Events / ( 1 MeV ) Events / ( 1 MeV ) Events / ( 1 MeV )
A. Supplementary figures for η′ → γγ
150 Eγ = 1553.8 MeV 150 Eγ = 1557.1 MeV 150 Eγ = 1560.4 MeV
N = 1606± 65 N = 1479± 63 N = 1482± 28
N/ε = 3756± 153 N/ε = 3500± 151 N/ε = 3544± 69
χ2  = 0.98 χ2  = 1.07 χ2  = 1.57
red red red
100 σ = 6.1 MeV 100 σ = 5.2 MeV 100 σ = 5.3 MeV
δ = 4.2 MeV δ = 3.9 MeV δ = 4.2 MeV
50 50 50
0 900 950 1000 1050 0 900 950 1000 1050 0 900 950 1000 1050
IM (MeV) IM (MeV) IM (MeV)
150 Eγ = 1563.7 MeV 150 Eγ = 1567.1 MeV 150 Eγ = 1570.4 MeV
N = 1600± 76 N = 1456± 64 N = 1370± 64
N/ε = 3894± 185 N/ε = 3573± 158 N/ε = 3431± 160
χ2  = 0.85 χ2  = 1.34 χ2  = 0.96
red red red
100 σ = 7.4 MeV 100 σ = 6.8 MeV 100 σ = 7.1 MeV
δ = 4.4 MeV δ = 6.2 MeV δ = 5.6 MeV
50 50 50
0 900 950 1000 1050 0 900 950 1000 1050 0 900 950 1000 1050
IM (MeV) IM (MeV) IM (MeV)
150 Eγ = 1573.8 MeV 150 Eγ = 1577.3 MeV
N = 1377± 60 N = 1329± 107
N/ε = 3492± 154 N/ε = 3447± 279
χ2  = 1.01 χ2  = 0.95
red red
100 σ = 7.4 MeV 100 σ = 6.3 MeV
δ = 5.2 MeV δ = 5.4 MeV
50 50
0 900 950 1000 1050 0 900 950 1000 1050
IM (MeV) IM (MeV)
124
Events / ( 1 MeV ) Events / ( 1 MeV ) Events / ( 1 MeV )
Events / ( 1 MeV ) Events / ( 1 MeV ) Events / ( 1 MeV )
Events / ( 1 MeV ) Events / ( 1 MeV )
B. Supplementary figures for η′ → ωγ
Figure 4.35 on page 115 is shown for fixed cuts as specified in the legend, see
also table 4.7 on page 114.
 4  4
DiscardedEk=0
DiscardedEk<20 AntiPi0FitProb<10
-7
-5||nan
 3.5 DiscardedEk<50  3.5 AntiPi0FitProb<10 ||nanAntiPi0FitProb<10-3||nan
 3  3
 2.5  2.5
 2  2
 1.5  1.5
 1 4  6  8  10  12  14  16  18  20  1 4  6  8  10  12  14  16  18  20
Relative Uncertainty / % Relative Uncertainty / %
 4  4
AntiEtaFitProb<10-6 TreeFitProb>0.05
AntiEtaFitProb<10-4
||nan TreeFitProb>0.1
 3.5 AntiEtaFitProb<10-2
||nan
||nan  3.5 TreeFitProb>0.2
 3  3
 2.5  2.5
 2  2
 1.5  1.5
 1 4  6  8  10  12  14  16  18  20  1 4  6  8  10  12  14  16  18  20
Relative Uncertainty / % Relative Uncertainty / %
 4  4
gNonPi01 CBSumVetoE_gNonPi0=0gNonPi02 CBSumVetoE_gNonPi0<0.1 3.5 gNonPi03  3.5 CBSumVetoE_gNonPi0<0.2CBSumVetoE_gNonPi0<0.4
 3  3
 2.5  2.5
 2  2
 1.5  1.5
 1 4  6  8  10  12  14  16  18  20  1 4  6  8  10  12  14  16  18  20
Relative Uncertainty / % Relative Uncertainty / %
 4
IM_Pi0g[1] 30
IM_Pi0g[1] 40
 3.5 IM_Pi0g[1] 50
 3
 2.5
 2
 1.5
 1 4  6  8  10  12  14  16  18  20
Relative Uncertainty / %
125
Branching Ratio / % Branching Ratio / % Branching Ratio / % Branching Ratio / %
Branching Ratio / % Branching Ratio / % Branching Ratio / %

Glossary
PV γ pseudoscalar-vector-gamma.
χEFT chiral effective field theory.
ADC analog-to-digital converter.
API application programming interface.
ASIC Application-Specific Integrated Circuit.
CAMAC Computer Automated Measurement and Control.
CATCH COMPASS Accumulate Transfer and Cache Hardware.
CB Crystal Ball.
CDC clock domain crossing.
CFD constant fraction discriminator.
COMPASS Common Muon Proton Apparatus for Structure and Spectroscopy.
CPLD complex programmable logic device.
CTS Central Trigger System.
DABC Data-Acquisition Backbone Core.
DAQ data acquisition system.
DDR double-data-rate.
DHCP Dynamic Host Configuration Protocol.
ECL Emitter-coupled logic.
EPICS Experimental Physics and Industrial Control System.
EPT end-point tagger.
127
Glossary
FEE front-end electronics.
FIFO first-in first-out buffer.
FPGA field-programmable gate array.
GeSiCa GEM Silicon Control and Acquisition.
GSI GSI Helmholtzzentrum für Schwerionenforschung GmbH.
GUI graphical user interface.
HADES high-acceptance dielectron spectrometer.
HDSM harmonic double-sided microtron.
HLD HADES list mode data.
HV high voltage.
IC integrated circuit.
IDE integrated development environment.
IP Internet Protocol.
JTAG Joint Test Action Group.
LNcChPT large-Nc chiral perturbation theory.
LEC low-energy constant.
LEdD leading-edge discriminator.
LINAC linear accelerator.
LVDS low-voltage differential signal.
MAMI Mainzer Mikrotron.
MC Monte Carlo.
MCP microchannel plate.
MWPC multi-wire proportional chamber.
NIM Nuclear Instrumentation Module.
128
Glossary
NTEC New TAPS Electronics Card.
PaDiWa PANDA DIRC WASA.
PANDA anti-proton annihilations at Darmstadt.
PCB printed circuit board.
PCI Peripheral Component Interconnect.
PDF probability density function.
PID particle identification detector.
PLL phase-locked loop.
PMT photomultiplier tube.
PSA pulse shape analysis.
PWM pulse-width modulation.
QCD quantum chromodynamics.
QED quantum electrodynamics.
RMS root mean square.
RPC resistive plate chamber.
RTM race track microtron.
SBC single board computer.
SERDES serializer-deserializer.
SFP small form-factor pluggable transceiver.
SPI Serial Peripheral Interface.
TAPS Two-arm Photon Spectrometer.
TCP Transmission Control Protocol.
TCS trigger control system.
TDC time-to-digital converter.
129
Glossary
ToF time-of-flight.
ToT time-over-threshold.
TRB3 TDC readout board revision 3.
UDP Uniform Datagram Protocol.
VHDL VHSIC hardware description language.
VMEbus Versa Module Europa bus.
VUPROM VME Universal Processing Module.
XML extensible markup language.
130
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