Interpretation of the LHCb P_{c} States as Hadronic Molecules and Hints of a Narrow P_{c}(4380)

Three hidden-charm pentaquark P_{c} states, P_{c}(4312), P_{c}(4440), and P_{c}(4457) were revealed in the Λ_{b}^{0}→J/ψpK^{-} 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/ψp 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 Σ_{c}^{(*)}D[over ¯]^{(*)} molecular states in two spin multiplets, such that the P_{c}(4312) is mainly a Σ_{c}D[over ¯] bound state with J^{P}=1/2^{-}, while P_{c}(4440) and P_{c}(4457) are Σ_{c}D[over ¯]^{*} bound states with quantum numbers 3/2^{-} and 1/2^{-}, respectively. We also show that there is evidence for a narrow Σ_{c}^{*}D[over ¯] 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 Σ_{c}D[over ¯], Σ_{c}^{*}D[over ¯], and Σ_{c}D[over ¯]^{*} hadronic molecules are seen in the data, while the missing three Σ_{c}^{*}D[over ¯]^{*} states are expected to be found in future runs of the LHC or in photoproduction experiments.