The bound and resonant states of $D^{(*)}D^{(*)}$ and $D^{(*)}\bar{D}^{(*)}$ with the complex scaling method

Abstract

We perform a systematic study of the possible molecular states composed of a pair of heavy mesons such as $D^{(*)}D^{(*)}$, $D^{(*)}\bar{D}^{(*)}$ in the framework of the one-boson-exchange model. The exchanged bosons include the pseudoscalar, scalar and vector mesons($\pi$, $\sigma$, $\rho$, $\omega$). We use the Bonn approximation to get the interaction potential of one-boson-exchange model, then apply the complex scaling method to calculate the bound and resonant states. The results indicate that the $D^{(*)}D^{(*)}$ and $D^{(*)}\bar{D}^{(*)}$ system can not only form several bound states, but also a P-wave resonant state. The hadron molecular state model can explain the structure of $T_{cc}^+$ as a bound state $DD^{*}$ with quantum number $I(J^P) = 0(1^+)$. In addition, we also discovered other bound and resonant states, which have the potential to be observed experimentally.