# Analysis of the $P_c(4312)$, $P_c(4440)$, $P_c(4457)$ and related hidden-charm pentaquark states with QCD sum rules

## TL;DR

This paper uses QCD sum rules to analyze the mass spectrum of hidden-charm pentaquark states, providing theoretical support for their quantum number assignments and improving understanding of their structure.

## Contribution

The study applies an extensive operator product expansion in QCD sum rules to refine the mass predictions and quantum number assignments of specific hidden-charm pentaquark states.

## Key findings

- Mass predictions support $P_c(4312)$ as $J^{P}={1/2}^-$ state.
- Mass predictions suggest $P_c(4440)$ could be $J^{P}={1/2}^-, {3/2}^-, {5/2}^-$.
- Mass predictions indicate $P_c(4457)$ as $J^{P}={1/2}^-, {3/2}^-$.

## Abstract

In this article, we restudy the ground state mass spectrum of the diquark-diquark-antiquark type $uudc\bar{c}$ pentaquark states with the QCD sum rules by carrying out the operator product expansion up to the vacuum condensates of $13$ in a consistent way. The predicted masses support assigning the $P_c(4312)$ to be the hidden-charm pentaquark state with $J^{P}={\frac{1}{2}}^-$, assigning the $P_c(4440)$ to be the hidden-charm pentaquark state with $J^{P}={\frac{1}{2}}^-$, ${\frac{3}{2}}^-$ or ${\frac{5}{2}}^-$, assigning the $P_c(4457)$ to be the hidden-charm pentaquark state with $J^{P}={\frac{1}{2}}^-$ or ${\frac{3}{2}}^-$.