The hadronic vacuum polarization contribution to (g−2)_µ from lattice QCD with coordinate-space methods
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Abstract
Precision calculations are nowadays of central interest for the physics community. They serve on one hand as a test of the standard model and on the other hand as a window into the search for new physics. The anomalous magnetic moment of the muon $a_\mu$ has represented a puzzle for many years now. At the 0.20 ppm level of accuracy, the experimental measurement is in strong tension with the theoretical prediction. On the theory side, the main source of uncertainty is due to hadronic contributions, which cannot be evaluated perturbatively. The hadronic vacuum polarization (HVP) is the largest such contributions. To obtain this quantity, there are two methods: The dispersive approach, which relies on experimental input from $e^+e^-$-scattering data and lattice QCD, as a framework to obtain hadronic observables from first principles. In recent years, the lattice community has made tremendous effort in order to reach sub-percent precision in the determination of the HVP contribution $\ahvp$.
In this thesis, we want to investigate a covariant coordinate-space (CCS) approach for the calculation of $\ahvp$, which has some advantages compared to the traditional time-momentum representation (TMR) used in the community.
We develop a method for estimating finite-size effects in this new method based on a field theory approach. We present a full lattice calculation of the quark-connected light and strange component to the intermediate distance window quantity at an unphysical pion mass of $m_\pi=350$ MeV. This calculation verifies the result obtained using the TMR method. We furthermore give a blueprint for computations of other observables in the CCS representation, especially with applications for very large lattices, which will become more relevant as computing resources become more powerful.
We then turn to the evaluation of isospin breaking corrections to $\ahvp$. These need to be included in order to match the accuracy of the experimental measurement. We propose a scheme for regularizing the effects from quantum electrodynamics (QED) by introducing a Pauli-Villars regulator in the photon propagator. We present a calculation of one UV-finite diagram that constitutes a major part of the QED corrections to $\ahvp$. This is performed on several ensembles with pion masses ranging from approximately $132$ MeV to $ 422$ MeV. We furthermore employ a calculation of the dominant charged pion and pseudoscalar meson contribution using an effective field theory approach to support the lattice calculation. We obtain a physical result for this partial contribution that can be seen as a benchmark quantity for the lattice calculation of QED corrections to the HVP contribution.