Comparing RM123 and non-perturbative QCD+QED approaches to the HVP with C-periodic boundary conditions

TL;DR

This paper compares two approaches, RM123 and non-perturbative QCD+QED, for calculating isospin-breaking corrections to the HVP in muon g-2, highlighting their differences and implications.

Contribution

It provides a detailed comparison of RM123 and non-perturbative QCD+QED methods for isospin-breaking corrections in lattice QCD+QED calculations.

Findings

Simulating full QCD+QED reduces uncertainties at fixed statistics.

Both methods preserve locality, gauge invariance, and translational invariance with C-periodic boundary conditions.

Full QCD+QED simulations yield smaller uncertainties than perturbative approaches.

Abstract

Isospin-breaking corrections to the HVP are among the leading sources of uncertainty in the Standard Model prediction of the muon $g-2$. In recent work by the RC$^{\star}$ collaboration, we compute the intermediate window contribution for a flavour non-singlet current using two strategies to include isospin-breaking corrections: the RM123 approach and a fully non-perturbative dynamical QCD+QED simulation. In both computations, we use $C$-periodic spatial boundary conditions to ensure that locality, gauge invariance, and translational invariance are preserved throughout the calculation. At fixed lattice spacing and volume with $N_f =1+2+1$ dynamical fermions, and fully including sea-quark effects in both computations, we find that simulating the full QCD+QED distribution yields smaller uncertainties for a fixed statistics. We summarize the comparison of the two approaches and discuss the implications for future lattice QCD+QED computations.