$B_s\to K\ell \nu$ 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.

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

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• Flavor Anomalies in Heavy Quark Decays
• The Exclusive Vision of Rare $K$ and $B$ Decays and of the Quark Mixing in the Standard Model
• Precision calculations of $B_{d,s}\to \pi ,K$ decay form factors in soft-collinear effective theory
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• Exclusive semileptonic $B_s\to K\ell \nu$ decays on the lattice
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• Semileptonic and leptonic $B$ decays, circa 2016
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