Comparing QCD+QED via full simulation versus the RM123 method: U-spin window contribution to $a_\mu^{\mathrm{HVP}}$

TL;DR

This paper compares non-perturbative and perturbative methods for calculating electromagnetic corrections to hadronic vacuum polarization in lattice QCD+QED, aiming to improve precision in the muon g-2 prediction.

Contribution

It introduces a comparative analysis of full simulation versus the RM123 perturbative approach for QCD+QED contributions using C* boundary conditions.

Findings

Full QCD+QED simulation is advantageous for fixed sample sizes.

Comparison of methods shows consistent results within uncertainties.

Study sets groundwork for physical point QCD+QED calculations.

Abstract

Electromagnetic corrections to hadronic vacuum polarization contribute significantly to the uncertainty of the Standard Model prediction of the muon anomaly, which poses conceptual and numerical challenges for ab initio lattice determinations. In this study, we compute the non-singlet contribution from intermediate Euclidean current separations in quantum chromo- and electrodynamics (QCD+QED) using C* boundary conditions in two ways: either non-perturbatively by sampling the joint probability distribution directly or by perturbatively expanding from an isospin-symmetric theory. This allows us to compare the predictions and their uncertainties at a fixed lattice spacing and volume, including fully the sea quarks effects in both cases. Treating carefully the uncertainty due to tuning to the same renormalized theory with $N_{\mathrm{f}} = 1 + 2 + 1$ quarks, albeit with unphysical masses, we find it advantageous to simulate the full QCD+QED distribution given a fixed number of samples. This study lays the ground-work for further applications of C* boundary conditions to study QCD+QED at the physical point, essential for the next generation of precision tests of the Standard Model.