The isospin-violating part of the hadronic vacuum polarisation

TL;DR

This paper calculates the isospin-violating contribution to the hadronic vacuum polarization part of muon g-2 using lattice QCD, employing coordinate-space methods and a Pauli-Villars regulated photon propagator for crosschecks and continuum extrapolation.

Contribution

It introduces a lattice QCD calculation of isospin-violating HVP contributions with a novel regularization and crosscheck approach, improving the precision of muon g-2 predictions.

Findings

Results show minimal dependence on the regulator scale mbda.

Continuum extrapolation yields a reliable estimate of the isospin-violating HVP contribution.

Method allows for crosschecks between lattice and continuum calculations.

Abstract

We present our calculation of the isospin-violating part of the hadronic vacuum polarisation (HVP) contribution to muon $(g-2)$ in lattice QCD at the $SU(3)_{\mathrm{f}}$ symmetric point. The computation of the contributing fully connected diagrams with one internal photon as well as the computation of the only (mass) counterterm are shown. The latter is determined from the charged-neutral kaon mass splitting. We employ coordinate-space methods and a photon propagator which is regulated \`a la Pauli-Villars with a cutoff scale $\Lambda$ well below the lattice cutoff. This regularization makes it possible for us to do crosschecks of individual contributions with calculations in the continuum. Our continuum extrapolated results show little to no dependence on $\Lambda$. This makes our final limit $\Lambda \rightarrow \infty$ straightforward.