Interpretation of the LHCb $P_c$ States as Hadronic Molecules and Hints of a Narrow $P_c(4380)$

Abstract: Three hidden-charm pentaquark $P_c$ states, $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$ were revealed in the $\Lambda_b^0\to J/\psi p K^-$ process measured by LHCb using both run I and run II data. Their nature is under lively discussion, and their quantum numbers have not been determined. We analyze the $J/\psi p$ invariant mass distributions under the assumption that the crossed-channel effects provide a smooth background. For the first time, such an analysis is performed employing a coupled-channel formalism with the scattering potential involving both one-pion exchange as well as short-range operators constrained by heavy quark spin symmetry. We find that the data can be well described in the hadronic molecular picture, which predicts seven $\Sigma_c^{(*)}\bar D^{(*)}$ molecular states in two spin multiplets, such that the $P_c(4312)$ is mainly a $\Sigma_c\bar D$ bound state with $J^P=1/2^-$, while $P_c(4440)$ and $P_c(4457)$ are $\Sigma_c\bar D^*$ bound states with quantum numbers $3/2^-$ and $1/2^-$, respectively. We also show that there is evidence for a narrow $\Sigma_c^*\bar D$ bound state in the data which we call $P_c(4380)$, different from the broad one reported by LHCb in 2015. With this state included, all predicted $\Sigma_c \bar D$, $\Sigma_c^* \bar D$, and $\Sigma_c \bar D^*$ hadronic molecules are seen in the data, while the missing three $\Sigma_c^*\bar D^*$ states are expected to be found in future runs of the LHC or in photoproduction experiments.