Muon anomalous magnetic moment with staggered fermions: Is the lattice spacing small enough?

(Received 6 May 2022; accepted 25 August 2022; published 12 September 2022) We extend our previous work on the light-quark connected part, a(mu)(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 HVP'lqc and related window quantities significantly. We also calculate the current-current correlator from which a(mu)(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)(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)(HVP'lqc) and to the window quantities, emphasizing that it provides a systematic effective-field theory (EFT) approach to a(mu)(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. Our results are based on configurations provided by the MILC and also by the CalLat collaborations.

Automated summary

In this study, we extend previous work on the light-quark connected part of the muon anomalous magnetic moment using staggered fermions. By collecting more statistical data and adding new configurations, we are able to reduce errors and correct the results using chiral perturbation theory. We discuss the applicability of this theory to short- and intermediate-distance window quantities and emphasize the need for further high-statistics computations.