The bound and resonant states of $D^{(\ast )}{D}^{(\ast )}$ and $D^{(\ast )}{\bar{D}}^{(\ast )}$ 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 $D^{(\ast )}{D}^{(\ast )}$, $D^{(\ast )}{\bar{D}}^{(\ast )}$ 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 $D^{(\ast )}{D}^{(\ast )}$ and $D^{(\ast )}{\bar{D}}^{(\ast )}$ 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 $D{D}^{\ast }$ 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.

Comments: 11 pages, 6 figures, 5 tables, Accepted by EPJC