Study of Nonleptonic $B^{\ast}_{(s)}\to M_1 M_2$ $(M=D$, $D_s$, $\pi$, $K)$ 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 $A_0^{B^{\ast}_{(s)}\to M_1}(0)$ 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 $\bar{B}^{*0} \to D^+D^-_s$ and $\bar{B}^{*0}_s \to D^+_sD^-_s$ decays have the largest branching fractions of the order $\sim{\cal O}(10^{-8})$, and hence will be firstly observed by forthcoming Belle-II experiment. However, most of the other decay modes have the branching fractions~$<{\cal O}(10^{-9})$ and thus are hardly to be observed soon. Besides, for the possible detectable $B^{\ast}_{(s)}$ decays with branching fractions $\gtrsim{\cal O}(10^{-9})$, some useful ratios, such as $R_D$ {\it et al.,} are presented and discussed in detail.