Update on the isospin breaking corrections to the HVP with C-periodic boundary conditions

TL;DR

This paper reports progress in calculating isospin-breaking corrections to the muon g-2 using lattice QCD+QED with C-periodic boundary conditions, comparing two computational methods to improve theoretical precision.

Contribution

It introduces the use of C-periodic boundary conditions in lattice QCD+QED simulations for isospin-breaking corrections and compares two different computational approaches.

Findings

Progress in computing IB corrections with two methods

Implementation of C-periodic boundary conditions preserves symmetries

Comparison of results at specific lattice parameters

Abstract

In the RC$^\star$ collaboration, we simulate lattice QCD+QED using $C-$periodic spatial boundary conditions to ensure that locality, gauge invariance, and translational invariance are preserved throughout the calculation. We present our progress in computing isospin-breaking (IB) corrections to the leading hadronic contribution to $(g-2)_\mu$. We compare two ways of including the IB corrections: the RM123 method and dynamical QCD+QED simulations, both with $C-$periodic boundary conditions. The two calculations are performed at $\beta=3.24$ with four flavours of $\mathcal{O}(a)-$improved Wilson fermions; the QCD ensemble features $SU(3)-$symmetric sea quarks plus charm, while down and strange quarks are degenerate in QCD+QED gauge ensembles.