Molecule pictures for the LHCb $P_c$ states

The first two pentaquark candidates $P_c(4380)$ and $P_c(4450)$ were observed by LHCb Collaboration in 2015. Recently, they presented their improved measurements in the Pc energy range, that a new narrow signal denoted as $P_c(4312)$ is reported and the previous observed structure $P_c(4450)$ is resolved into two narrow states, $P_c(4440)$ and $P_c(4457)$ while there is no obvious signal for the broad state $P_c(4380)$. We analyze the strong decays of these $P_c$ states systematically in the hadronic molecule pictures. With the effective Lagrangian method, the partial widths of these $P_c$ decaying into all allowed channels are estimated. Our results show that these $P_c$ states are good candidates of the $S$-wave $\bar{D} \sum_c,\bar{D} \sum_c^*$ and $\bar{D}^*\sum_c$ molecules. Also other possible flavor and spin partners of $P_c$ states are investigated in the present work.