Efficiently unquenching QCD+QED at O($\alpha$)

TL;DR

This paper proposes an efficient method to include electromagnetic sea-quark interactions in QCD+QED calculations, improving the precision of iso-spin breaking corrections by analyzing stochastic estimator variances.

Contribution

It introduces a variance analysis approach to better estimate disconnected diagrams in QCD+QED, with preliminary numerical results on domain-wall fermion ensembles.

Findings

Variance reduction for stochastic estimators in specific flavor and space-time decompositions.

Preliminary numerical results demonstrating variance improvements.

Potential for more precise calculations of electromagnetic effects in hadronic physics.

Abstract

We outline a strategy to efficiently include the electromagnetic interactions of the sea quarks in QCD+QED. When computing iso-spin breaking corrections to hadronic quantities at leading order in the electromagnetic coupling, the sea-quark charges result in quark-line disconnected diagrams which are challenging to compute precisely. An analysis of the variance of stochastic estimators for the relevant traces of quark propagators helps us to improve the situation for certain flavour combinations and space-time decompositions. We present preliminary numerical results for the variances of the corresponding contributions using an ensemble of $N_\mathrm{f}=2+1$ domain-wall fermions generated by the RBC/UKQCD collaboration.