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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 $a_{\mu }^{ll,\mathrm{SD}}\left(\mathrm{conn}\right)=48.139\left(11{)}_{\mathrm{stat}}\right(91{)}_{\mathrm{syst}}[92{]}_{\text{total}}\times {10}^{-10}$and $a_{\mu }^{ll,\mathrm{W}}\left(\mathrm{conn}\right)=206.90\left(14{)}_{\mathrm{stat}}\right(61{)}_{\mathrm{syst}}[63{]}_{\text{total}}\times {10}^{-10}$. We use Bayesian model averaging to fully estimate the covariance matrix between the individual contributions. Our determinations of the complete window contributions are $a_{\mu }^{\mathrm{SD}}=69.05\left(1{)}_{\mathrm{stat}}\right(21{)}_{\mathrm{syst}}[21{]}_{\text{total}}\times {10}^{-10}$and $a_{\mu }^{\mathrm{W}}=236.45\left(17{)}_{\mathrm{stat}}\right(83{)}_{\mathrm{syst}}[85{]}_{\text{total}}\times {10}^{-10}$. This work is part of our ongoing effort to compute all contributions to HVP with an overall uncertainty at the few-permille level. Published by the American Physical Society2025 

We present results for B(s)- and D(s)-meson semileptonic decays from ongoing calculations by the Fermilab Lattice and MILC Collaborations. Our calculation employs the highly improved stag- gered quark (HISQ) action for both sea and valence quarks and includes several ensembles with physical-mass up, down, strange, and charm quarks and lattice spacings ranging from a ≈ 0.15 fm down to 0.06 fm. At most lattice spacings, an ensemble with physical-mass light quarks is included. The use of the highly improved action, combined with the MILC Collaboration’s gauge ensembles with lattice spacings down to a ≈ 0.042 fm, allows heavy valence quarks to be treated with the same discretization as the light and strange quarks. This unified treatment of the valence quarks allows (in some cases) for absolutely normalized currents, bypassing the need for perturbative matching, which has been a leading source of uncertainty in previous calculations of B-meson decay form factors by our collaboration. All preliminary form-factor results are blinded. 

e-Print: arXiv:1902.03808 [hep-lat]