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 $a^{ll,\,{\mathrm{SD}}}_{\mu}(\mathrm{conn.}) = 48.139(11)_{\mathrm{stat}}(91)_{\mathrm{syst}}[92]_{\mathrm{total}} \times 10^{-10}$ and $a^{ll,\,{\mathrm{W}}}_{\mu}(\mathrm{conn.}) = 206.90(14)_{\mathrm{stat}}(61)_{\mathrm{syst}}[63]_{\mathrm{total}} \times 10^{-10}$. We use Bayesian model averaging to fully estimate the covariance matrix between the individual contributions. Our determinations of the complete window contributions are $a^{{\mathrm{SD}}}_{\mu} = 69.05(1)_{\mathrm{stat}}(21)_{\mathrm{syst}}[21]_{\mathrm{total}} \times 10^{-10}$ and $a^{{\mathrm{W}}}_{\mu} = 236.45(17)_{\mathrm{stat}}(83)_{\mathrm{syst}}[85]_{\mathrm{total}} \times 10^{-10}$. This work is part of our ongoing effort to compute all contributions to HVP with an overall uncertainty at the few permille level.