Roles of ${\bar{D}}^{\ast }{K}^{\ast }$ and $D^{\ast }\bar{D}$ molecular states in decay $B^{+}\to D^{\ast +}{D}^{-}{K}^{+}$

Abstract

This study investigates the three-body decay process $B^{+}\to D^{\ast +}{D}^{-}{K}^{+}$, aiming to explore the possible origins of $T_{\bar{c}\bar{s}0}^{\ast }(2870{)}^0$ and ${\chi }_{c1}(3872)$ as intermediate states. Within the molecular state framework, $T_{\bar{c}\bar{s}0}^{\ast }(2870{)}^0$ and ${\chi }_{c1}(3872)$ are considered as possible ${\bar{D}}^{\ast }{K}^{}$ and $D^{\ast }\bar{D}$ molecular states, respectively. Using effective Lagrangians, the interaction kernels of the ${\bar{D}}^{\ast }{K}^{\ast }$ and $D^{\ast }\bar{D}$ systems are constructed within the one-boson-exchange model. The corresponding rescattering amplitudes and pole positions are obtained by solving the quasipotential Bethe-Salpeter equation. These amplitudes are incorporated into the decay amplitude of the three-body process, and the $D^{-}{K}^{+}$ and $D^{\ast +}{D}^{-}$ invariant mass spectra are simulated via Monte Carlo methods. To better reproduce the experimental data, additional Breit-Wigner contributions from $T_{\bar{c}\bar{s}1}^{\ast }(2900{)}^0$, ${\chi }_{c1}(4010)$, and $h_c(4300)$ are included. The results show a pronounced enhancement near 2900 MeV in the $D^{-}{K}^{+}$ invariant mass spectrum, strongly supporting the interpretation of $T_{\bar{c}\bar{s}0}^{\ast }(2870{)}^0$ as a ${\bar{D}}^{\ast }{K}^{\ast }$ molecular state. While the ${\bar{D}}^{\ast }{K}^{\ast }$ molecular state provides a reasonable contribution to the $D^{-}{K}^{+}$ spectrum, the $D^{\ast }\bar{D}$ molecular state yields no significant effect on either the $D^{-}{K}^{+}$ or $D^{\ast +}{D}^{-}$ distributions. This suggests that the observed ${\chi }_{c1}(3872)$ structure around 3872 MeV may not be interpreted as a $D^{\ast }\bar{D}$ molecular state.

Comments: 12 pages, 10 figures