Consistency of hadronic vacuum polarization between lattice QCD and the R-ratio

Abstract

There are emerging tensions for theory results of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment both within recent lattice QCD calculations and between some lattice QCD calculations and R-ratio results. In this paper we work towards scrutinizing critical aspects of these calculations. We focus in particular on a precise calculation of Euclidean position-space windows defined by RBC/UKQCD that are ideal quantities for cross-checks within the lattice community and with R-ratio results. We perform a lattice QCD calculation using physical up, down, strange, and charm sea quark gauge ensembles generated in the staggered formalism by the MILC collaboration. We study the continuum limit using inverse lattice spacings from $a^{-1}\approx 1.6$ GeV to $3.5$ GeV, identical to recent studies by FNAL/HPQCD/MILC and Aubin et al. and similar to the recent study of BMW. Our calculation exhibits a tension for the particularly interesting window result of $a_\mu^{\rm ud, conn.,isospin, W}$ from $0.4$ fm to $1.0$ fm with previous results obtained with a different discretization of the vector current on the same gauge configurations. Our results may indicate a difficulty related to estimating uncertainties of the continuum extrapolation that deserves further attention. In this work we also provide results for $a_\mu^{\rm ud,conn.,isospin}$, $a_\mu^{\rm s,conn.,isospin}$, $a_\mu^{\rm SIB,conn.}$ for the total contribution and a large set of windows. For the total contribution, we find $a_\mu^{\rm HVP~LO}=714(27)(13) 10^{-10}$, $a_\mu^{\rm ud,conn.,isospin}=657(26)(12) 10^{-10}$, $a_\mu^{\rm s,conn.,isospin}=52.83(22)(65) 10^{-10}$, and $a_\mu^{\rm SIB,conn.}=9.0(0.8)(1.2) 10^{-10}$, where the first uncertainty is statistical and the second systematic. We also comment on finite-volume corrections for the strong-isospin-breaking corrections.