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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 measuredby LHCb using both run I and run II data. Their nature is under livelydiscussion, and their quantum numbers have not been determined. We analyze the$J/\psi p$ invariant mass distributions under the assumption that thecrossed-channel effects provide a smooth background. For the first time, suchan analysis is performed employing a coupled-channel formalism with thescattering potential involving both one-pion exchange as well as short-rangeoperators constrained by heavy quark spin symmetry. We find that the data canbe well described in the hadronic molecular picture, which predicts seven$\Sigma_c^{(*)}\bar D^{(*)}$ molecular states in two spin multiplets, such thatthe $P_c(4312)$ 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 withquantum numbers $3/2^-$ and $1/2^-$, respectively. We also show that there isevidence 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 thisstate 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 missingthree $\Sigma_c^*\bar D^*$ states are expected to be found in future runs ofthe LHC or in photoproduction experiments.

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