Systematical study of $\hat{I}{\text{c◯}}_c$-like molecular states from interactions $\hat{I}{ž}_c^{{(}^{\prime },\ast )}{\bar{K}}^{(\ast )}$ and $\hat{I}{ž}^{(\ast )}{D}^{(\ast )}$

Abstract

In this work, the $\hat{I}{\text{c◯}}_c$-like molecular states are systematically investigated in a quasipotential Bethe-Salpeter equation approach. The relevant interactions $\hat{I}{ž}_c^{(\ast {,}^{\prime })}{\bar{K}}^{(\ast )}$, $\hat{I}{ž}^{(\ast )}{D}^{(\ast )}$, and $\hat{I}{\text{c◯}}_c^{(\ast )}(\ddot{I}€/\hat{I}\cdot /\ddot{I}/\ddot{I}‰)$ are described by light meson exchanges with the help of the effective Lagrangians with SU(3), chiral, and heavy quark symmetries. The obtained potential kernels of considered interactions are inserted into the quasipotential Bethe-Salpeter equation, and coupled-channel calculations are performed to find possible molecular states and its couplings to the channels considered. The results suggest that an isoscalar state can be produced from the $\hat{I}{ž}_c^{\ast }\bar{K}$ interaction with spin parity $3/2^{-}$, which can be related to state $\hat{I}{\text{c◯}}_c(3120)$. And its isoscalar partner is predicted with a dominant decay in the $\hat{I}{\text{c◯}}_c^{\ast }\ddot{I}€$ channel. The isoscalar and isovector states with $1/2^{-}$ can be produced from the $\hat{I}{ž}_c^{\prime }\bar{K}$ interaction with a threshold close to the mass of the $\hat{I}{\text{c◯}}_c(3050)$ and $\hat{I}{\text{c◯}}_c(3065)$. Their couplings to the $\hat{I}{ž}_c\bar{K}$ channel are very weak, and the isovector one has strong coupling to $\hat{I}{\text{c◯}}_c\ddot{I}€$. High precision measurement is helpful to confirm or search such molecular states. Experimental search of states with higher masses generated from interactions $\hat{I}{ž}_c^{(\ast {,}^{\prime })}{\bar{K}}^{\ast }$ and $\hat{I}{ž}^{\ast }{D}^{(\ast )}$ are also suggested by the current results.

11 pages, 3 figures