Estimating Form Factors of $B_s\rightarrow D_s^{(*)}$ and their Applications to Semi-leptonic and Non-leptonic Decays

TL;DR

This paper estimates the form factors for $B_s$ to $D_s^{(*)}$ transitions using a Bethe-Salpeter approach and applies these to predict decay rates, CP asymmetries, and polarization fractions, aligning well with experimental data.

Contribution

It introduces a novel method based on the instantaneous Bethe-Salpeter equation to estimate form factors across the entire physical region for these decays.

Findings

Calculated decay rates agree with experimental data.

Longitudinal polarization fractions are approximately 0.8 for light meson decays.

Polarization fractions are around 0.5 for $D_q$ meson decays.

Abstract

$B_s^0\rightarrow D_s^{-}$ and $B_s^0\rightarrow D_s^{*-}$ weak transition form factors are estimated for the whole physical region with a method based on an instantaneous approximated Mandelstam formulation of transition matrix elements and the instantaneous Bethe-Salpeter equation. We apply the estimated form factors to branching ratios, CP asymmetries and polarization fractions of non-leptonic decays within the factorization approximation. And we study the non-factorizable effects and annihilation contributions with the perturbative QCD approach. The branching ratios of semi-leptonic $B_s^0\rightarrow D_s^{(*)-}l^+\nu_l$ decays are also evaluated. We show that the calculated decay rates agree well with the available experimental data. The longitudinal polarization fraction of $B_s\rightarrow D_s^*V(A)$ decays are $\sim0.8$ when $V(A)$ denotes a light meson, and are $\sim0.5$ when $V(A)$ denotes a $D_q$ ($q=d,s$) meson.