On the application of Effective Field Theory to finite-volume effects in $a_\mu^{\rm HVP}$

TL;DR

This paper discusses how Effective Field Theory, specifically finite-volume chiral perturbation theory, can be used to accurately estimate and correct finite-volume effects in lattice calculations of the muon's anomalous magnetic moment contribution.

Contribution

It demonstrates that finite-volume corrections to $a_^{ m HVP}$ can be systematically calculated at any order in chiral perturbation theory once low-energy constants are known.

Findings

Finite-volume effects can be predicted at any order in chiral perturbation theory.

Finite-volume corrections depend on known low-energy constants.

Method enables sub-percent precision in lattice QCD calculations.

Abstract

One of the more important systematic effects affecting lattice computations of the hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon, $a_\mu^{\rm HVP}$, is the distortion due to a finite spatial volume. In order to reach sub-percent precision, these effects need to be reliably estimated and corrected for, and one of the methods that has been employed for doing this is finite-volume chiral perturbation theory. In this paper, we argue that finite-volume corrections to $a_\mu^{\rm HVP}$ can, in principle, be calculated at any given order in chiral perturbation theory. More precisely, once all low-energy constants needed to define the Effective Field Theory representation of $a_\mu^{\rm HVP}$ in infinite volume are known to a given order, also the finite-volume corrections can be predicted to that order in the chiral expansion.