Lattice QCD results for mesons containing b quarks from the HPQCD collaboration

I report on progress by the HPQCD Collaboration using radiatively-improved lattice NonRelativistic QCD and relativistic HISQ valence quarks on ensembles of gluon field configurations, generated by the MILC collaboration that now include u, d, s and c HISQ quarks in the sea, with the u/d quark masses going down to their physical value. I describe the background field approach for determining the one-loop radiative improvement to coefficients in the NRQCD action, and I present the most accurate results yet for a range of quantities, including: the hyperfine splittings Mϒ − Mηb and MBq*−MBq; fB, fBs and the leptonic decay constants fϒ(′); B-meson masses mBq for q = u/d, s, c; B−B¯ mixing; the b-quark mass mb; and the lattice calculation for the rare decays B0 → K*0 μ+ μ− and Bs → φμ+ μ−. I briefly discuss future prospects.