Possibility of searching for $B_c^{\ast }$ $\to$ $B_{u,d,s}V$, $B_{u,d,s}P$ decays

The $B_c^{\ast }$ $\to$ $B_{u,d,s}V$, $B_{u,d,s}P$ decays are investigated with the QCD factorization approach, where $V$ and $P$ denote the ground $SU(3)$ vector and pseudoscalar mesons, respectively. The $B_c^{\ast }$ $\to$ $B_{u,d,s}$ transition form factors are calculated with the Wirbel-Stech-Bauer model. It is found that branching ratios for the color-favored and Cabibbo-favored $B_c^{\ast }$ $\to$ $B_s\rho$, $B_s\pi$ decays can reach up to $\mathcal{O}({10}^{-7})$, which might be measurable in the future LHC experiments.