Dynamical study of D*DK and D*DD¯ systems at quark level

Inspired by the recent report from the LHCb Collaboration on $T_{cc}$, which can be interpreted as a molecular $D{D}^{*}$, we investigated two trimeson systems of the $T_{cc}$ partner with $I{J}^P=01^{-}$ in the framework of a chiral quark model. In the first case, because of the attraction between $D^{*}$ and $\overline{D}$, we explored the existence of bound states in the system $D^{*}D\overline{D}$, which is obtained by adding $\overline{D}$ into the molecular bound state $T_{cc}$ ($D{D}^{*}$). Similarly, in the second case, we explored whether there is a bound state in the $D^{*}DK$ system, which is obtained by adding $K$ into the $T_{cc}$, given the attraction between $D$ and $K$. The results show that both of them are bound states, in which the binding energy of the molecular state $D{D}^{*}K$ is relatively small, only $0.4\pm 0.4\mathrm{MeV}$, while the binding energy of $D{D}^{*}\overline{D}$ is up to $1.6\pm 0.3\mathrm{MeV}$. According to the calculation results of the root-square-mean distances, the spatial structure of the two systems shows the obvious $(D{D}^{*})\text{−}(\overline{D}/K)$ structure, in which $D$ is close to $D^{*}$ while $D{D}^{*}$ as a whole is relatively distant from the third hadron ($\overline{D}/K$), which are similar to the nucleon-electron structure. As a result, we strongly recommend that these bound states $D{D}^{*}\overline{D}$ and $D{D}^{*}K$ are searched for experimentally.