Molecular Interpretation of the $P_c(4440)$ and $P_c(4457)$ States

A molecular model of the $P_c(4457)$ and $P_c(4440)$ LHCb states is proposed. The model relies on channels coupled by long range pion-exchange dynamics with features that depend crucially on the novel addition of the $\Lambda_c(2595)\bar D$ channel. A striking prediction of the model is the unusual combination of quantum numbers $J^P(4457) = 1/2^+$ and $J^P(4440) = 3/2^-$. Unlike in other models, a simultaneous description of both states is achieved without introducing additional short-range interactions. The model also gives a natural explanation for the relative widths of the states. We show that the usual molecular scenarios cannot explain the production rate of $P_c$ states in $\Lambda_b$ decays, and that this can be resolved by including $\Lambda_c(2595)\bar D$ and related channels. Experimental tests and other states are discussed in the conclusions.