Isospin breaking corrections to the hadronic vacuum polarization with stochastic coordinate sampling

TL;DR

This paper discusses a novel stochastic coordinate sampling method to efficiently compute isospin breaking corrections to the hadronic vacuum polarization in lattice QCD, reducing computational costs and uncertainties.

Contribution

It introduces a stochastic coordinate sampling approach for calculating isospin breaking effects in the HVP contribution, improving efficiency and accuracy.

Findings

Successful implementation of stochastic coordinate sampling for Wick contractions.

Use of different QED formulations to estimate finite-volume effects.

Progress towards reducing uncertainties in HVP calculations.

Abstract

In the recent Muon g-2 Theory Initiative white paper update, the hadronic vacuum polarization (HVP) contribution -- which dominates the theoretical uncertainty -- is evaluated as an average of different lattice QCD calculations. Since lattice simulations are mostly carried out in isospin symmetric QCD, corrections due to the mass difference of the up and down quarks and the coupling to photons have to be accounted for. These isospin breaking effects are of order 1\% and can be treated as corrections to the result for the HVP contribution in isospin symmetric QCD. In the current estimate of the HVP contribution, these effects are a large source of uncertainty due to the extensive computational cost to compute all occurring Wick contractions and degrading signal-to-noise behaviour especially for quark disconnected diagrams. We present the current status of the calculation of isospin breaking corrections in the HVP contribution for the RBC/UKQCD collaborations. We use a dataset of propagators computed using stochastic coordinate sampling (SCS) to construct all necessary Wick contractions for the electromagnetic and strong isospin breaking effects. We employ different versions of QED on the lattice, such as QED$_L$, QED$_r$ and QED$_\infty$ to improve our estimate of finite-volume uncertainties.