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

Understand

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 $\bar{D}^*\Sigma_c$ 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.