Heavy flavor conserved semi-leptonic decay of $B_s$ in the covariant light-front approach

We study the heavy flavor conserved semi-leptonic decay $B_s\to B\mathrm{\ell }\nu$ in the covariant light front approach. The covariant light front quark model is used to calculate the transition form factors of $B_s\to B^{(\ast )}$ as well as $D_s\to D$, which are consistent with the leading power predictions from the heavy quark symmetry. The angular distribution analysis on the $B_s\to B^{(\ast )}l\bar{\nu }$ decay is performed by investigating the forward-backward asymmetry of the lepton. We also study the angular distribution of $B_s\to B^{\ast }(\to B\gamma )l\bar{\nu }$ decay both through the lepton forward-backward asymmetry and the azimuth angle. The branching fractions of $B_s\to Bl\bar{\nu }$ and $B_s\to B^{\ast }l\bar{\nu }$ are at the order ${10}^{-8}$ and ${10}^{-9}$, respectively. The number of $B_s\to Bl\bar{\nu }$ events is estimated to be $1.76$. The branching fraction of $B_s\to B^{\ast }(\to B\gamma )l\bar{\nu }$ is at the order ${10}^{-11}$, which is calculated by introducing Breit-Wigner distribution for the intermediate $B^{\ast }$.