$B_s\to K\ell \nu$ form factors from lattice QCD

Abstract

We report the first lattice QCD calculation of the form factors for the standard model tree-level decay $B_s\to K\ell \nu$. In combination with future measurement, this calculation will provide an alternative exclusive semileptonic determination of $|V_{ub}|$. We compare our results with previous model calculations, make predictions for differential decay rates and branching fractions, and predict the ratio of differential branching fractions between $B_s\to K\tau \nu$ and $B_s\to K\mu \nu$. We also present standard model predictions for differential decay rate forward-backward asymmetries, polarization fractions, and calculate potentially useful ratios of $B_s\to K$ form factors with those of the fictitious $B_s\to {\eta }_s$ decay. Our lattice simulations utilize NRQCD $b$ and HISQ light quarks on a subset of the MILC Collaboration's $2+1$ asqtad gauge configurations, including two lattice spacings and a range of light quark masses.

Comments: 24 pages, 21 figures; Ver. 2 matches published version