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

TL;DR

This paper presents the first lattice QCD calculation of $B_s o K u$ form factors, providing theoretical predictions for decay rates and ratios to aid future experimental determinations of $|V_{ub}|$.

Contribution

It introduces the first lattice QCD computation of $B_s o K$ form factors, enabling improved exclusive semileptonic decay analysis and comparison with models.

Findings

Predicted differential decay rates and branching fractions.

Calculated ratios of $B_s o K$ form factors with $B_s o ext{eta}_s$.

Provided SM predictions for asymmetries and polarization fractions.

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.