Heavy quark spin multiplet structure of $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$

Abstract

Very recently, the LHCb collaboration has reported the new result about the hidden-charm pentaquarks: $P_c(4312)$ near the $\bar{D}{\Sigma }_c$ threshold, and $P_c(4440)$ and $P_c(4457)$ near ${\bar{D}}^{\ast }{\Sigma }_c$ threshold. We study the heavy quark spin (HQS) multiplet structures of these newly $P_c$ pentaquarks under the heavy quark spin symmetry based on the hadronic molecular picture. We point out that $P_c(4312)$ is the $J^P=1/2^{-}$ member of an HQS triplet, and $P_c(4440)$ and $P_c(4457)$ are the $J^P=3/2^{-}$ member of the HQS triplet and an HQS singlet with $J^P=3/2^{-}$. Namely, the $P_c(4312)$ and one of $P_c(4440)$ and $P_c(4457)$ belong to an HQS triplet. The HQS multiplet structure predicts the existence of $J^P=5/2^{-}$ state near ${\bar{D}}^{\ast }{\Sigma }_c^{\ast }$ threshold.

Comments: 4 pages