Branching fractions of $B^-\to D^-X_{0,1}(2900)$ and their implications

The exotic states $X_{0,1}(2900)$ with the quark flavor of $cs\bar{u}\bar{d}$ are recently observed in the mass spectrum of $D^+K^-$ in $B^-\to D^-D^+K^-$ by the LHCb collaboration. To explore the nature of $X_{0,1}(2900)$, except for analyzing their masses and decay widths as usually did in literatures, the study of their production mechanism in $B$-meson weak decays would provide another important information. The amplitude of $B^-\to D^- X_{0,1}$ is non-factorizable. We consider the final-state-interaction effects and calculate them via the rescattering mechanism. The measured branching fractions of $B^-\to D^- X_{0,1}$ are revealed. It is manifested by ${B}^-\to \Lambda_c^-\Xi_c^{(\prime)0}$ and $\Lambda_b^0\to P_c^+K^-$ that the rescattering mechanism can result in the relatively large branching fractions. The similar processes of $B^-\to \pi^-X_{0,1}$ are also analyzed. The isospins of $X_{0,1}$ can be investigated by $B\to DX_{0,1}^{\pm,0}$ decays.