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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 $B^-\to D^-D^+K^-$ bythe LHCb collaboration. To explore the nature of $X_{0,1}(2900)$, except foranalyzing their masses and decay widths as usually did in literatures, thestudy of their production mechanism in $B$-meson weak decays would provideanother important information. The amplitude of $B^-\to D^- X_{0,1}$ isnon-factorizable. We consider the final-state-interaction effects and calculatethem 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 therescattering mechanism can result in the relatively large branching fractions.The similar processes of $B^-\to \pi^-X_{0,1}$ are also analyzed. The isospinsof $X_{0,1}$ can be investigated by $B\to DX_{0,1}^{\pm,0}$ decays.

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