# Anatomy of the newly observed hidden-charm pentaquark states: $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$

## TL;DR

This paper investigates the internal structure and composition of the newly observed hidden-charm pentaquark states $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$ using effective-range expansion and resonance compositeness relations, providing insights into their molecular components.

## Contribution

It introduces a detailed analysis of the pentaquark states' scattering properties and compositeness, revealing their likely molecular nature and channel contributions.

## Key findings

- Calculated scattering lengths and effective ranges for $Σ_c\bar{D}$ and $Σ_c\bar{D}^*$ channels.
- Estimated probabilities of $J/\psi p$ and $Σ_c\bar{D}$ components inside $P_c(4312)$.
- Determined partial decay widths and compositeness coefficients for $P_c(4440)$ and $P_c(4457)$.

## Abstract

We study the newly reported hidden-charm pentaquark candidates $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ from the LHCb Collaboration, in the framework of the effective-range expansion and resonance compositeness relations. The scattering lengths and effective ranges from the $S$-wave $\Sigma_c\bar{D}$ and $\Sigma_c\bar{D}^*$ scattering are calculated by using the experimental results of the masses and widths of the $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$. Then we calculate the couplings between the $J/\psi p,\,\Sigma_c\bar{D}$ channels and the pentaquark candidate $P_c(4312)$, with which we further estimate the probabilities of finding the $J/\psi p$ and $\Sigma_c\bar{D}$ components inside $P_c(4312)$. The partial decay widths and compositeness coefficients are calculated for the $P_c(4440)$ and $P_c(4457)$ states by including the $J/\psi p$ and $\Sigma_c\bar{D}^*$ channels. Similar studies are also carried out for the three $P_c$ states by including the $\Lambda_c\bar{D}^{*}$ and $\Sigma_c\bar{D}^{(*)}$ channels.