The muon anomalous magnetic moment with staggered fermions: is the lattice spacing small enough?

TL;DR

This study improves lattice QCD calculations of the muon anomalous magnetic moment using staggered fermions, emphasizing the need for finer lattice spacings below 0.06 fm to reduce systematic errors and enhance accuracy.

Contribution

It extends previous work by increasing statistics, adding new ensembles, and applying NNLO chiral perturbation theory to correct for systematic effects in lattice calculations.

Findings

Higher statistics reduce errors significantly.

NNLO corrections help address finite-volume and pion-mass effects.

Finer lattice spacings below 0.06 fm are essential for accuracy.

Abstract

We extend our previous work on the light-quark connected part, $a_\mu^{\rm HVP,lqc}$, of the leading order hadronic-vacuum-polarization (HVP) contribution to the muon anomalous magnetic moment $a_\mu$, using staggered fermions, in several directions. We have collected more statistics on ensembles with lattice spacings of $0.06$, $0.09$ and $0.12$ fm, and we added two new ensembles, both with lattice spacing $0.15$ fm, but with different volumes. The increased statistics allow us to reduce statistical errors on $a_\mu^{\rm HVP,lqc}$ and related window quantities significantly. We also calculate the current-current correlator from which $a_\mu^{\rm HVP,lqc}$ is obtained to next-to-next-to-leading order (NNLO) in staggered chiral perturbation theory, so that we can correct lattice values for $a_\mu^{\rm HVP,lqc}$ to NNLO for finite-volume, pion-mass mistuning and taste-breaking effects. We discuss the applicability of NNLO chiral perturbation theory to $a_\mu^{\rm HVP,lqc}$ and to the window quantities, emphasizing that it provides a systematic EFT approach to $a_\mu^{\rm HVP,lqc}$, but not to short- or intermediate-distance window quantities. This makes it difficult to assess systematic errors on the standard intermediate-distance window quantity that is now widely considered in the literature. In view of this, we investigate a longer-distance window, for which EFT methods should be more reliable. Our most important conclusion is that, especially for staggered fermions, new high-statistics computations at lattice spacings smaller than $0.06$ fm are indispensable.