Phenomenology with Lattice NRQCD b Quarks

The HPQCD collaboration has used radiatively-improved NonRelativistic QCD (NRQCD) for $b$ quarks in bottomonium to determine the decay rate of $\Upsilon$ and $\Upsilon^\prime$ mesons to leptons in lattice QCD. Using time-moments of vector bottomonium current-current correlators, we are also able to determine the $b$ quark mass in the $\overline{\mathrm{MS}}$ scheme. We use the same NRQCD $b$ quarks and Highly Improved Staggered Quark (HISQ) light quarks -- with masses down to their physical values -- to give a complete picture of heavy-light meson decay constants including those for vector mesons. We also study the semileptonic $B\rightarrow\pi\ell\nu$ decay at zero recoil to show that lattice QCD is consistent with the soft pion theorem for this decay: $f_0(q^2_{\mathrm{max}})=f_B/f_\pi$ in the massless pion limit. Finally, we present preliminary results for the $B_c \rightarrow \eta_c \ell \nu$ semileptonic decay form factors. This is a showcase for the comparison of results for NRQCD $b$ quarks with those from HISQ $b$ quarks (both with HISQ $c$ quarks). We give the first 3-point results from our `heavy HISQ' programme, which will allow us to improve the normalisation of NRQCD-HISQ currents for other calculations.