Dynamical study of $D^{\ast }DK$ and $D^{\ast }D\bar{D}$ systems at quark level

Abstract

Inspired by that Belle\uppercase\expandafter{\romannumeral2} Collaboration recently reported $T_{cc}$, which can be interpreted as a molecular $D{D}^{\ast }$, we investigated the trihadron system of $T_{cc}$ partner with $I{J}^P$=$01^{-}$ in the framework of a chiral quark model. It's widely accepted that the main component of $X(3872)$ contains the molecular $\bar{D}{D}^{\ast }$, while the main component of $D_{s0}^{\ast }(2317)$ is molecular $DK$. Based on these three well-known exotic states, $T_{cc}(D{D}^{\ast })$, $X(3872)(\bar{D}{D}^{\ast })$ and $D_{s0}^{\ast }(2317)(DK)$, we dynamically investigate $D^{\ast }DK$ and $D{D}^{\ast }\bar{D}$ systems at quark level to search for possible bound states. The results show that both of them are bound states, in which the binding energy of the molecular state $D{D}^{\ast }K$ is relatively small, only 0.8 MeV, while the binding energy of $D{D}^{\ast }\bar{D}$ is up to 1.9 MeV. According to the calculation results of the Root-square-mean distances, the spatial structure of the two systems shows obvious ($D{D}^{\ast }$)-($\bar{D}$/$K$) structure, in which $D$ is close to $D^{\ast }$ while $D{D}^{\ast }$ as a whole is relatively distant from the third hadron ($\bar{D}$/$K$), which are similar to the nucleon-electron structure. As a result, we strongly recommend that these bound states $D{D}^{\ast }\bar{D}$ and $D{D}^{\ast }K$ are searched for experimentally.