New determination of $|V_{ub}/V_{cb}|$ from $B_s^0\to \{K^{-},D_s^{-}\}{\mu }^{+}\nu$

Abstract

We update the full set of ${\bar{B}}_s\to K$ form factors using light-cone sum rules with an on-shell kaon. Our approach determines the relevant sum rule parameters -- the duality thresholds -- from a Bayesian fit for the first time. Using a modified version of the Boyd-Grinstein-Lebed parametrisation, we combine our sum rule results at low momentum transfer $q^2$ with more precise lattice QCD results at large $q^2$. We obtain a consistent description of the form factors in the full $q^2$ range. Applying these results to a recent LHCb measurement of branching ratios for the decays $B_s^0\to \{K^{-},D_s^{-}\}{\mu }^{+}{\nu }_{\mu }$, we determine the ratio of Cabibbo-Kobayashi-Maskawa elements $${\left|\frac{V_{ub}}{V_{cb}}\right|}_{q^2<7{\text{GeV}}^2}=0.0681\pm 0.0040\text{and}{\left|\frac{V_{ub}}{V_{cb}}\right|}_{q^2>7{\text{GeV}}^2}=0.0801\pm 0.0047,$$ which are mutually compatible at the $1.9\sigma$ level. We further comment on the sensitivity to Beyond the Standard Model effects through measurements of the shape of $B_s^0\to K^{-}{\mu }^{+}{\nu }_{\mu }$ decays, in light of recent limits on such effects from other exclusive $b\to u\ell \nu$ processes.

Comments: 21 pages, 5 figures, 3 tables, and supplementary material