# $P_c(4457)^+$, $P_c(4440)^+$, and $P_c(4312)^+$: molecules or compact pentaquarks?

## TL;DR

This paper uses a chromomagnetic model to analyze the properties of recently observed pentaquark states, estimating their masses and possible internal structures, and discusses how open-charm decay channels can distinguish their nature.

## Contribution

It provides a detailed analysis of the $P_c$ states' masses and structures, proposing possible quantum number assignments and highlighting the importance of open-charm decay channels for structural identification.

## Key findings

- The $P_c(4457)^+$, $P_c(4440)^+$, and $P_c(4312)^+$ can be assigned specific $J^P$ quantum numbers.
- Isospin breaking effects on the spectrum are small.
- Open-charm decay channels are crucial for distinguishing the internal structure of the $P_c$ states.

## Abstract

In a chromomagnetic model, we analyse the properties of the newly observed $P_c(4457)^+$, $P_c(4440)^+$, and $P_c(4312)^+$ states. We estimate the masses of the $(uud)_{8_c}(c\bar{c})_{8_c}$ and $(uds)_{8_c}(c\bar{c})_{8_c}$ pentaquark states by considering the isospin breaking effects. Their values are determined by calculating mass distances from the $\Sigma_c^{++}D^-$ and $\Xi_c^{\prime+}D^-$ thresholds, respectively. It is found that the isospin breaking effects on the spectrum are small. From the uncertainty consideration and the rearrangement decay properties in a simple model, we find that it is possible to assign the $P_c(4457)^+$, $P_c(4440)^+$, and $P_c(4312)^+$ as $J^P=3/2^-$, $1/2^-$, and $3/2^-$ pentaquark states, respectively. The assignment in the molecule picture can be different, in particular for the $P_c(4312)^+$. The information from open-charm channels, e.g. ${\cal B}[P_c\to\Sigma_c^{++}D^-]/{\cal B}[P_c\to J/\psi p]$, will play an important role in distinguishing the inner structures of the $P_c$ states. Discussions and predictions based on the calculations are also given.