Weak decays of $B_s$ to $D_s$ based on the helicity analysis

TL;DR

This paper provides a detailed theoretical analysis of $B_s$ meson decays to $D_s$ mesons using helicity analysis, lattice QCD inputs, and form factors, predicting branching ratios and polarization observables in agreement with experimental data.

Contribution

It introduces a comprehensive helicity analysis combined with lattice QCD inputs for $B_s$ decays, offering new predictions for form factors, branching ratios, and polarization observables.

Findings

Calculated form factor at zero recoil: 0.67 ± 0.01

Predicted branching ratio ratios in agreement with LHCb

Provided detailed polarization observable predictions

Abstract

Employing dipole and exponential hadronic transition form factors and helicity analysis combined with the Lattice QCD input, we present a detailed study of the decays $B_s \to D_s^{(*)}\ell \nu_\ell$. $B_s \to D_s + P(V)$, where $P = \pi^+, K^+, D_s^+$ and $V = \rho^+, K^{*+}, D_s^{*+}$, are also investigated and their branching fractions are examined. At the large recoil point, we calculate $f_{ + ,0}^{{B_s} \to {D_s}}(0) = 0.67 \pm 0.01$ for both parameterizations. Then we evaluate the branching fractions $BR({B_s} \to {D_s}\ell \nu )$ and $BR({B_s} \to {D_s}\ell \nu )$, which leads to $R({D_s}) = 0.298 \pm 0.123$. The ratios $\frac{{\Gamma (B_s^0 \to D_s^ - {\mu ^ + }{\nu _\mu })}}{{\Gamma (B_s^0 \to D_s^{* - }{\mu ^ + }{\nu _\mu })}}$ are found to be $0.4415 \pm 0.1860$ and $0.4406 \pm 0.1854$, which are in good agreement of recent LHCb collaboration measurement. We also calculate the physical observables, $A_{FB}^\ell ,P_L^\ell ,P_T^\ell ,C_F^\ell ,F_L^\ell $.