Study of Nonleptonic $B_{(s)}^{\ast }\to M_1{M}_2$ $(M=D$, $D_s$, $\pi$, $K)$ Weak Decays with Factorization Approach

Motivated by the experiments of heavy flavor physics at running LHC and upgrading SuperKEKB/Belle-II in the future, the nonleptonic $B^{\ast}{(s)}\to M_1 M_2$ $(M=D$, $D_s$, $\pi$, $K)$ weak decays are studied in this paper. The amplitudes are calculated with factorization approach, and the transition form factors $A_0^{B_{(s)}^{\ast }\to M_1}(0)$ are evaluated within BSW model. With the reasonable approximation $\Gamma{tot}(B^_{(s)})\simeq \Gamma(B^{(s)}\to B{(s)}\gamma)$, our predictions of branching fractions are presented. Numerically, the CKM-favored tree-dominated ${\bar{B}}^{\ast 0}\to D^{+}{D}_s^{-}$ and ${\bar{B}}_s^{\ast 0}\to D_s^{+}{D}_s^{-}$ decays have the largest branching fractions of the order $\sim \mathcal{O}({10}^{-8})$, and hence will be firstly observed by forthcoming Belle-II experiment. However, most of the other decay modes have the branching fractions~$<\mathcal{O}({10}^{-9})$ and thus are hardly to be observed soon. Besides, for the possible detectable $B_{(s)}^{\ast }$ decays with branching fractions $\gtrsim \mathcal{O}({10}^{-9})$, some useful ratios, such as $R_D$ {\it et al.,} are presented and discussed in detail.