Form factors and branching fraction calculations for $B_s \to D_s^{(*)} \ell^+ \nu_\ell$ in view of LHCb observation

In light of the LHCb observations about the $B_s \to D_s^{(*)}\ell \nu_\ell$ semileptonic decays, we study these channels within the Standard Model framework of covariant confined quark model. The necessary transition form factors are computed in the entire dynamical range of momentum transfer squared with built-in infrared confinement. Our computed ratios of the decay widths from tau mode to muon mode for $D_s$ and $D_s^*$ mesons are found to be $R(D_s) = 0.271 \pm 0.069$ and $R(D_s^*) = 0.240 \pm 0.038$. We further determine the ratio of the decay width from $D_s$ and $D_s^*$ channel for muon mode $\Gamma(B_s \to D_s \mu^+ \nu_\mu)/\Gamma(B_s \to D_s^* \mu^+ \nu_\mu) = 0.451 \pm 0.093$. Our results are in excellent agreement with the data from the latest LHCb experiments as well as lattice quantum chromodynamics simulations. We also compare the shape of differential decay distribution for $B_s \to D_s^* \mu^+ \nu_\mu$ with the LHCb data and our results are in very good agreement throughout all the individual bins. Some other physical observables such as forward-backward asymmetry and longitudinal polarizations of leptons in the final state are also computed.