In this paper we study the semileptonic decays of $B^\ast$, $B_s^\ast$, and $B_c^\ast$ by using the Bethe-Salpeter method with instantaneous approximation. Both the $V\to Pl^-\bar\nu_l$ and $V\to Vl^-\bar\nu_l$ cases are considered. The largest partial width of these channels is of the order of $10^{ -14}$ GeV. The branching ratios of these semileptonic decays are also estimated by using the partial width of the one photon decay channel to approximate the total width. For $B^{ \ast-}\to D^{ (\ast)0}e^-\bar\nu_e$ and $B_s^{ \ast0}\to D_s^{ (\ast)+}e^-\bar\nu_e$, the branching ratios are of the order of $10^{ -8}$ and $10^{ -7}$, respectively. For $B_c^{ \ast-}$, the $J/\psi e^-\bar\nu_e$ and $B_s^{ \ast0}e^-\bar\nu_e$ channels have the largest branching ratio, which is of the order of $10^{ -6}$.
Categories: hep-ph