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 ${\Sigma }_c^{(\ast )}{\bar{D}}^{(\ast )}$ 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 ${\Sigma }_c{\bar{D}}^{\ast }$ bound states with quantum numbers $3/2^{-}$ and $1/2^{-}$, respectively. We also show that there is evidence for a narrow ${\Sigma }_c^{\ast }\bar{D}$ 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 ${\Sigma }_c\bar{D}$, ${\Sigma }_c^{\ast }\bar{D}$, and ${\Sigma }_c{\bar{D}}^{\ast }$ hadronic molecules are seen in the data, while the missing three ${\Sigma }_c^{\ast }{\bar{D}}^{\ast }$ states are expected to be found in future runs of the LHC or in photoproduction experiments.

13 pages, version for publication

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