Finite-volume effects in the muon anomalous magnetic moment on the lattice

TL;DR

This paper analyzes finite-volume effects in lattice QCD calculations of the hadronic vacuum polarization, highlighting their significance for accurately determining the muon anomalous magnetic moment at a few percent precision.

Contribution

It demonstrates that finite-volume effects are substantial even with large lattice volumes and provides a quantitative understanding using chiral perturbation theory and lattice data.

Findings

Finite-volume effects are significant at current lattice sizes.

Leading-order chiral perturbation theory accurately models finite-volume effects.

Finite-volume effects cannot be neglected for precise muon g-2 calculations.

Abstract

We investigate finite-volume effects in the hadronic vacuum polarization, with an eye toward the corresponding systematic error in the muon anomalous magnetic moment. We consider both recent lattice data as well as lowest-order, finite-volume chiral perturbation theory, in order to get a quantitative understanding. Even though leading-order chiral perturbation theory does not provide a good description of the hadronic vacuum polarization, it turns out that it gives a good representation of finite-volume effects. We find that finite-volume effects cannot be ignored when the aim is a few percent level accuracy for the leading-order hadronic contribution to the muon anomalous magnetic moment, even when using ensembles with $m_\pi L> 4$ and $m_\pi \sim 200$ MeV.