Analysis of the $\bar{D}\Sigma_c$, $\bar{D}\Sigma_c^*$, $\bar{D}^{*}\Sigma_c$ and $\bar{D}^{*}\Sigma_c^*$ pentaquark molecular states with QCD sum rules

TL;DR

This paper uses QCD sum rules to analyze various pentaquark molecular states, supporting specific assignments for observed pentaquark candidates based on their mass and quantum numbers.

Contribution

It performs a comprehensive QCD sum rule analysis up to dimension 13 condensates, providing new insights into the structure of observed pentaquark states.

Findings

Supports $P_c(4312)$ as $ar{D}\Sigma_c$ with $J^P=1/2^-$

Identifies $P_c(4380)$ as $ar{D}\Sigma_c^*$ with $J^P=3/2^-$

Associates $P_c(4440/4457)$ with $ar{D}^*\Sigma_c$ or $ar{D}^*\Sigma_c^*$ states

Abstract

In this article, we study the $\bar{D}\Sigma_c$, $\bar{D}\Sigma_c^*$, $\bar{D}^{*}\Sigma_c$ and $\bar{D}^{*}\Sigma_c^*$ pentaquark molecular states with the QCD sum rules by carrying out the operator product expansion up to the vacuum condensates of dimension $13$ in a consistent way. The present calculations support assigning the $P_c(4312)$ to be the $\bar{D}\Sigma_c$ pentaquark molecular state with $J^P={\frac{1}{2}}^-$, assigning the $P_c(4380)$ to be the $\bar{D}\Sigma_c^*$ pentaquark molecular state with $J^P={\frac{3}{2}}^-$, assigning the $P_c(4440/4457)$ to be the $\bar{D}^{*}\Sigma_c$ pentaquark molecular state with $J^P={\frac{3}{2}}^-$ or the $\bar{D}^{*}\Sigma_c^*$ pentaquark molecular state with $J^P={\frac{5}{2}}^-$. Special attentions are payed to the operator product expansion.