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

TL;DR

This paper analyzes the heavy quark spin multiplet structure of recently observed pentaquarks, proposing their classification within heavy quark spin symmetry and predicting an additional state near the $ar{D}^*\Sigma_c^*$ threshold.

Contribution

It provides a novel classification of $P_c$ pentaquarks within heavy quark spin symmetry and predicts a new $J^P=5/2^-$ state based on molecular models.

Findings

$P_c(4312)$ is a $J^P=1/2^-$ member of an HQS triplet.

$P_c(4440)$ and $P_c(4457)$ are $J^P=3/2^-$ members, with one being a triplet and the other a singlet.

A new $J^P=5/2^-$ state is predicted near the $ar{D}^*\Sigma_c^*$ threshold.

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