Hadronic vacuum polarization for the muon $g-2$ from lattice QCD: Complete short and intermediate windows

Abstract

We present complete results for the hadronic vacuum polarization (HVP) contribution to the muon anomalous magnetic moment $a_{\mu }$ in the short- and intermediate-distance window regions, which account for roughly 10% and 35% of the total HVP contribution to $a_{\mu }$, respectively. In particular, we perform lattice-QCD calculations for the isospin-symmetric connected and disconnected contributions, as well as corrections due to strong isospin-breaking. For the short-distance window observables, we investigate the so-called log-enhancement effects as well as the significant oscillations associated with staggered quarks in this region. For the dominant, isospin-symmetric light-quark connected contribution, we obtain $a_{\mu }^{ll,\mathrm{SD}}(conn.)=48.139(11{)}_{\mathrm{stat}}(91{)}_{\mathrm{syst}}[92{]}_{\mathrm{total}}\times 10^{-10}$ and $a_{\mu }^{ll,\mathrm{W}}(conn.)=206.90(14{)}_{\mathrm{stat}}(61{)}_{\mathrm{syst}}[63{]}_{\mathrm{total}}\times 10^{-10}$. We use Bayesian model averaging to fully estimate the covariance matrix between the individual contributions. Our determinations of the complete window contributions are $a_{\mu }^{\mathrm{SD}}=69.05(1{)}_{\mathrm{stat}}(21{)}_{\mathrm{syst}}[21{]}_{\mathrm{total}}\times 10^{-10}$ and $a_{\mu }^{\mathrm{W}}=236.45(17{)}_{\mathrm{stat}}(83{)}_{\mathrm{syst}}[85{]}_{\mathrm{total}}\times 10^{-10}$. This work is part of our ongoing effort to compute all contributions to HVP with an overall uncertainty at the few permille level.

Comments: v3: Updated to reflect published version, which includes minor updates to the prose in Section IV and a correction to the statistical error estimate of a^W_{\mu}. Final results unchanged