Form factor ratios for $B_s \rightarrow K \, \ell \, \nu$ and $B_s \rightarrow D_s \, \ell \, \nu$ semileptonic decays and $|V_{ub}/V_{cb}|$

TL;DR

This paper uses lattice QCD to calculate form factor ratios for specific $B_s$ meson decays, aiming to improve the extraction of $|V_{ub}/V_{cb}|$ and address existing tensions in CKM matrix measurements.

Contribution

It provides the first lattice QCD determination of the scalar and vector form factor ratios for $B_s ightarrow K \, \ell \, \nu$ and $B_s \rightarrow D_s \, \ell \, \nu$ decays, offering new insights for CKM matrix element extraction.

Findings

Calculated form factor ratios for the two decays.

Determined ratios of differential decay rates, asymmetries, and polarizations.

Results will aid future experimental analyses to extract $|V_{ub}/V_{cb}|$.

Abstract

We present a lattice quantum chromodynamics determination of the ratio of the scalar and vector form factors for two semileptonic decays of the $B_s$ meson: $B_s \rightarrow K \ell \nu$ and $B_s \rightarrow D_s \ell \nu$. In conjunction with future experimental data, our results for these correlated form factors will provide a new method to extract $|V_{ub}/V_{cb}|$, which may elucidate the current tension between exclusive and inclusive determinations of these Cabibbo-Kobayashi-Maskawa mixing matrix parameters. In addition to the form factor results, we determine the ratio of the differential decay rates, and forward-backward and polarization asymmetries, for the two decays.