Molecular states from $\Sigma^{(*)}_c\bar{D}^{(*)}-\Lambda_c\bar{D}^{(*)}$ interaction

TL;DR

This paper investigates hidden-charmed molecular pentaquark states using a quasipotential Bethe-Salpeter approach, matching observed LHCb states and predicting new states and decay patterns for future experimental verification.

Contribution

It systematically studies molecular states from $ ext{Sigma}_c^{(*)}ar{D}^{(*)}$ interactions with heavy quark and chiral symmetries, providing theoretical support for observed and predicted pentaquark states.

Findings

Masses and widths of states match LHCb observations.

Predicted additional molecular states with specific quantum numbers.

Decay channels dominated by $ ext{Lambda}_car{D}^*$ interactions.

Abstract

In this work, we systemically investigate the molecular states from the $\Sigma^{(*)}_c\bar{D}^{(*)}-\Lambda_c\bar{D}^{(*)}$ interaction with the help of the Lagrangians with heavy quark and chiral symmetries in a quasipotential Bethe-Salpeter equation (qBSE) approach. The molecular states are produced from isodoublet (I=1/2) $\Sigma_c\bar{D}$ interaction with spin parity $J^P=1/2^-$ and $\Sigma_c\bar{D}^*$ interaction with $1/2^-$ and $ 3/2^-$. Their masses and widths are consistent with the $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ observed at LHCb. The states, $\Sigma_c^*\bar{D}^*(1/2^-)$, $\Sigma_c^*\bar{D}^*(3/2^-)$ and $\Sigma^*_c\bar{D}(3/2^-)$, are also produced with the same parameters. The isodoublet $\Sigma_c^*\bar{D}^*$ interaction with $5/2^-$, as well as the isoquartet (I=3/2) $\Sigma_c\bar{D}^*$ interactions with $1/2^-$ and $3/2^-$, $\Sigma_c^*\bar{D}^*$ interaction with $3/2^-$ and $5/2^-$, are also attractive while very large cutoff is required to produce a molecular state. We also investigate the origin of the widths of these molecular states in the same qBSE frame. The $\Lambda\bar{D}^*$ channel is dominant in the decays of the states, $\Sigma_c\bar{D}^*(1/2^-)$, $\Sigma_c\bar{D}^*(3/2^-)$, $\Sigma_c^*\bar{D}(3/2^-)$, and $\Sigma_c\bar{D}(1/2^-)$. The $\Sigma^*_c\bar{D}^*(1/2^-)$ state has large coupling to $\Sigma_c\bar{D}$ channel while the $\Sigma_c\bar{D}^*$, $\Sigma^*_c\bar{D}$ and $\Lambda_c\bar{D}^*$ channels provide similar contributions to the width of the $\Sigma^*_c\bar{D}^*(3/2^-)$ state. These results will be helpful to understand the current LHCb experimental results, and the three predicted states and the decay pattern of these hidden-charmed molecular pentaquarks can be checked in future experiments.