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Authors: San José Pérez, Miguel Teseo
Title: The hadronic contribution to the running of the electromagnetic coupling and the electroweak mixing angle
Online publication date: 5-Aug-2022
Language: english
Abstract: The electromagnetic coupling and the electroweak mixing angle are two quantities used in precision SM tests and probes of new physics. However, their dependence on the energy suffers from uncertainties at low momenta, induced by hadronic effects. In this work, we study the latter in the space-like energy range 0-10 GeV squared, employing a lattice regularisation of isosymmetric QCD, which allows us to access the confining regime of the strong coupling constant. One may compute the hadronic contribution to the electromagnetic coupling and the electroweak mixing angle from vacuum polarisation functions. For the first case, we use two electromagnetic currents, while for the second, we require the mixing of an electromagnetic current with the vector component of a weak neutral current. We employ the time-momentum representation to compute both vacuum polarisation functions. We use a set of seventeen Monte Carlo simulations based on CLS ensembles with 2+1 flavours, order-a-improved Wilson fermion action and tree-level improved Lüscher-Weisz gauge action. The simulations include the charm quark at the quenched level, and we include both quark-connected and quark-disconnected diagrams. Our simulations possess pion masses that span from 420 MeV to 130 MeV, slightly below the physical pion mass, and include four different lattice spacings, 0.086 fm, 0.076 fm, 0.064 fm and 0.050 fm. This wide set allows us to combine extrapolating to the continuum limit and interpolating the physical pion and kaon masses in a single, correlated fit. Since improvement and renormalisation mix the various contributions to the vacuum polarisation function to order a, we rearrange the flavour components in a SU(3)-flavour basis. Autocorrelations in our two-point functions are studied and removed using a combination of binning and Ulli Wolff's Gamma-method, and we employ bootstrap sampling to carry the statistical uncertainty and data correlations through the entire analysis. The signal-to-noise ratio is improved using a bounding procedure, which we compare with the more straightforward single-exponential fit and find the former more reliable for our ensembles with lighter pion mass. We remove the lattice infrared cut-off ---the simulation spatial size--- adding the difference between finite and infinite volumes, which we estimate using two different methods, the so-called Hansen-Patella and Meyer-Lellouch-Lüscher procedures. We find both methods to give compatible results. Finally, we cross-check the finite-volume correction by comparing ensembles with the same simulation parameters but different volumes. We perform a correlated extrapolation to the physical point of the various components for a dense set of momenta and establish that below 7 GeV squared our fit functions describe the lattice artefacts correctly. We give the running with the energy of the electromagnetic coupling and the electroweak mixing angle using Padé approximants.
DDC: 530 Physik
530 Physics
Institution: Johannes Gutenberg-Universität Mainz
Department: FB 08 Physik, Mathematik u. Informatik
Place: Mainz
URN: urn:nbn:de:hebis:77-openscience-c530f847-d0ed-4b6e-86af-6df4895e112e6
Version: Original work
Publication type: Dissertation
License: In Copyright
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Extent: xi, 176, 2 Seiten, Diagramme
Appears in collections:JGU-Publikationen

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