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

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 \(a^{ll,\,{\mathrm{SD}}}_{\mu}(\mathrm{conn.}) = 48.116(16)(94)[96] \times 10^{-10}\) and \(a^{ll,\,{\mathrm{W}}}_{\mu}(\mathrm{conn.}) = 207.06(17)(63)[66] \times 10^{-10}\). We use Bayesian model averaging combined with a global bootstrap to fully estimate the covariance matrix between the individual contributions. Our determinations of the complete window contributions are \(a^{{\mathrm{SD}}}_{\mu} = 69.01(2)(21)[21] \times 10^{-10}\) and \(a^{{\mathrm{W}}}_{\mu} = 236.57(20)(94)[96] \times 10^{-10}\). This work is part of our ongoing effort to compute all contributions to HVP with an overall uncertainty at the few permille level.