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

Abstract

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 $B^{-}\to \hat{I}{›}_c^{-}\hat{I}{ž}_c^{(\prime )0}$ and $\hat{I}{›}_b^0\to P_c^{+}{K}^{-}$ that the rescattering mechanism can result in the relatively large branching fractions. The similar processes of $B^{-}\to \ddot{I}{€}^{-}{X}_{0,1}$ are also analyzed. The isospins of $X_{0,1}$ can be investigated by $B\to D{X}_{0,1}^{\pm ,0}$ decays.

12 pages, 10 figures. Version published in EPJC. Additional contributions are added in $B\to \ddot{I}€X_{0,1}$ in Fig.8. Numerical results of the isospin-partner processes are changed by a factor of 2 in Eqs.(12) and (13)