Semi-leptonic decays of $B^{\ast }$, $B_s^{\ast }$, and $B_c^{\ast }$ with the Bethe-Salpeter method

Abstract

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 $V\to P{l}^{-}{\bar{\nu }}_l$ and $V\to V{l}^{-}{\bar{\nu }}_l$ 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 $B_s^{\ast 0}\to D_s^{(\ast )+}{e}^{-}{\bar{\nu }}_e$, 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 $B_s^{\ast 0}{e}^{-}{\bar{\nu }}_e$ channels have the largest branching ratio, which is of the order of $10^{-6}$.

Comments: 14 pages, 6 figures