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Authors: Risch, Andreas
Title: Isospin breaking effects in hadronic matrix elements on the lattice
Online publication date: 29-Sep-2021
Language: english
Abstract: In this thesis, we investigate the consequences of isospin symmetry breaking on hadronic matrix elements based on combined calculations in Quantum Chromodynamics (QCD) and Quantum Electrodynamics (QED). We employ the lattice regularisation for quantum field theories, which enables the access of both the perturbative and the non-perturbative regime of a coupling constant. The inclusion of isospin-breaking corrections in lattice QCD calculations is required to improve the theoretical prediction of hadronic contributions to high-precision observables, such as the muon anomalous magnetic moment $a_{\mu}$ and the running of the fine-structure constant $\alpha$, which are determined from correlation functions of electromagnetic currents. We relate QCD+QED to isosymmetric QCD via Monte Carlo reweighting and formulate a perturbative expansion of correlation functions around isosymmetric QCD. Expansion parameters are the differences of the bare quark masses and their isosymmetric counterparts, a shift of the inverse strong coupling and the electromagnetic coupling. Expectation values with respect to isosymmetric QCD are evaluated by means of Monte Carlo simulations based on gauge ensembles generated with a $N_{\mathrm{f}} = 2+1$ $O(a)$-improved Wilson fermion action and tree-level improved L{\"u}scher-Weisz gauge action. The handling of the manifest infrared divergence of non-compact lattice QED is addressed in this thesis. We regularise the divergence using the QED$_{\text{L}}$ prescription. We derive the lattice photon propagator for open and periodic temporal boundary conditions in Feynman and Coulomb gauge. The perturbative expansion is truncated at leading order, so that the electromagnetic coupling does not renormalise. Further expansion parameters are fixed via a hadronic renormalisation scheme based on masses of pseudo-scalar mesons. In our calculation, we only consider isospin breaking effects in the valence quark sector and focus on quark-connected contributions. We derive the axial and vector Ward identity for continuum QCD+QED. A conserved vector current is deduced from the vector Ward identity for the particular lattice regularisation of QCD+QED considered in this thesis. We determine the masses of pseudo-scalar octet mesons including leading isospin breaking corrections and describe the application of the procedure to baryon masses. We provide a detailed discussion of the renormalisation of the local vector current in QCD+QED taking operator mixing into account. We further determine the leading isospin breaking correction for the renormalised HVP function, which is related to the hadronic contribution of the running of the of the fine-structure constant $\alpha$ and the anomalous magnetic moment of leptons. The presented formalism is finally used to compute the hadronic vacuum polarisation contribution to the anomalous magnetic moment of the muon $a_{\mu}$ including leading isospin breaking corrections. The knowledge of a precise Standard Model prediction for the latter is of particular interest, as it offers a probe for new physics. The calculations are performed on three Monte Carlo ensembles with pion masses of $354$, $216$ and $282$ MeV and lattice spacings of $0.086$, $0.076$ and $0.064$ fm.
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-8fbd1791-84f0-455a-ae68-145c62c8d6098
Version: Original work
Publication type: Dissertation
License: In Copyright
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Extent: 262 Seiten
Appears in collections:JGU-Publikationen

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