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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.

We give an update on the status of the Fermilab Lattice-HPQCD-MILC calculation of the con- tribution to the muon’s anomolous magnetic moment from the light-quark, connected hadronic vacuum polarization. We present preliminary, blinded results in the intermediate window for this contribution a^ll_{\mu W}. The calculation is performed on Nf = 2 + 1 + 1 highly-improved staggered quark (HISQ) ensembles from the MILC collaboration with physical pion mass at four lattice spacings between 0.15 fm and 0.06 fm. We also present preliminary results for a study of the two- pion contributions to the vector-current correlation function performed on the 0.15 fm ensemble contribution, 𝑎𝑙𝑙 . The calculation is performed on the 0.15 fm ensemble where we see a factor of four improvement over traditional noise reduction techniques.

We report progress on calculating the contribution to the anomalous magnetic moment of the muon from the disconnected hadronic diagrams with light and strange quarks and the valence QED contribution to the connected diagrams. The lattice QCD calculations use the highly- improved staggered quark (HISQ) formulation. The gauge configurations were generated by the MILC Collaboration with four flavors of HISQ sea quarks with physical sea-quark masses.

We investigate the state-of-the-art Lanczos eigensolvers available in the Grid and QUDA libraries. They include Implicitly Restarted Lanczos, Thick-Restart Lanczos, and Block Lanczos. We measure and analyze their performance for the Highly Improved Staggered Quark (HISQ) Dirac operator. We also discuss optimization of Chebyshev acceleration.