Investigation of the analog of the $P_{c}$ states-the doubly charmed molecular pentaquarks

Motivated by the LHCb Collaboration's observation of a doubly charmed tetraquark state $T_{cc}(3875)$, we systematically investigate the existence of doubly charmed pentaquark states using the resonating group method based on the QDCSM framework. The effective potential of the two involved hadrons and the bound state dynamics are included in the present work. Moreover, we have also calculated the scattering phase shifts of open channels by channel coupling to look for possible resonance states. Our estimations indicate that there is a bound state in $I(J^{P})=\frac{3}{2}(\frac{5}{2}^{-})$, with a mass of $4461.7$ MeV. Additionally, five resonance states can be obtained by coupling the open channel, which are $\Xi_{cc}\rho$ and $\Sigma_{c}D^{\ast}$ with $I(J^{P})=\frac{1}{2}(\frac{1}{2}^{-})$, $\Lambda_{c}D^{\ast}$ and $\Sigma_{c}D^{\ast}$ with $I(J^{P})=\frac{1}{2}(\frac{3}{2}^{-})$ and $\Sigma_{c}D^{\ast}$ with $I(J^{P})=\frac{3}{2}(\frac{1}{2}^{-})$respectively. The existence of these predicted doubly charmed pentaquark states needs to be supported by experimental measurements and discoveries. We hope that some experiments can find evidence of these states.