Based on our previous QCD sum rule studies on hidden-charm pentaquark states, we discuss possible interpretations of the $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$, which were recently observed by LHCb. Our results suggest that the $P_c(4312)$ can be well interpreted as the $[\Sigma_c^{ ++} \bar D^-]$ bound state with $J^P = 1/2^-$, while the $P_c(4440)$ and $P_c(4457)$ can be interpreted as the $[\Sigma_c^{ +} \bar D^0]$ bound state with $J^P = 1/2^-$, the $[\Sigma_c^{ *++} \bar D^{ -}]$ and $[\Sigma_c^{ +} \bar D^{ *0}]$ bound states with $J^P = 3/2^-$, or the $[\Sigma_c^{ *+} \bar D^{ *0}]$ bound state with $J^P = 5/2^-$. We propose to measure their spin-parity quantum numbers to verify these assignments.
Categories: hep-ph hep-ex