We report the first lattice QCD calculation of the form factors for the standard model tree-level decay $B_sto K ell u$. 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 $B_sto Ktau u$ and $B_sto Kmu u$. We also present standard model predictions for differential decay rate forward-backward asymmetries, polarization fractions, and calculate potentially useful ratios of $B_sto K$ form factors with those of the fictitious $B_stoeta_s$ decay. Our lattice simulations utilize NRQCD $b$ and HISQ light quarks on a subset of the MILC Collaborations $2+1$ asqtad gauge configurations, including two lattice spacings and a range of light quark masses.
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