Study on possible molecular states composed of $\Lambda_c\bar D$ ($\Lambda_b B$) and $\Sigma_c\bar D$ ($\Sigma_b B$) within the Bethe-Salpeter framework

TL;DR

This paper uses the Bethe-Salpeter framework to analyze the structure, spectrum, and decay modes of the pentaquark $P_c(4312)$ and predicts other potential molecular pentaquark states for future experimental verification.

Contribution

It systematically studies pentaquark states, especially $P_c(4312)$, within the Bethe-Salpeter equation framework, providing new spectrum calculations and decay mode predictions.

Findings

Confirmed $P_c(4312)$ as a molecular state near $ ext{Σ}_c ar{D}$ threshold.

Predicted spectrum of $P_c(4312)$ and other pentaquark states.

Suggested decay modes and future experimental tests.

Abstract

$P_c(4312)$ observed by the LHCb collaboration is confirmed as a pentaquark and its structure, production, and decay behaviors attract great attention from theorists and experimentalists. Since its mass is very close to sum of $\Sigma_c$ and $\bar D$ masses, it is naturally tempted to be considered as a molecular state composed of $\Sigma_c$ and $\bar D$. Moreover, $P_c(4312)$ is observed in the channel with $J/\psi p$ final state, requiring that isospin conservation $P_c(4312)$ is an isospin-1/2 eigenstate. In literature, several groups used various models to estimate its spectrum. We systematically study the pentaquarks within the framework of the Bethe-Salpeter equation; thus $P_c(4312)$ is an excellent target because of the available data. We calculate the spectrum of $P_c(4312)$ in terms of the Bethe-Salpter equations and further study its decay modes. Some predictions on other possible pentaquark states that can be tested in future experiments are made.