# Isospin breaking decays as a diagnosis of the hadronic molecular structure of the $P_c(4457)$

## TL;DR

This paper proposes that large isospin breaking decay ratios in the $P_c(4457)$ can serve as a diagnostic for its hadronic molecular structure, specifically as a $ ext{Sigma}_c ar{D}^*$ molecule, and suggests experimental verification at LHCb.

## Contribution

It introduces the idea that isospin breaking decay ratios can distinguish the molecular nature of the $P_c(4457)$ pentaquark, providing a new diagnostic tool.

## Key findings

- Predicted large isospin breaking decay ratio for $P_c(4457)$
- Large decay ratio is unique to the molecular model
- Suggests experimental test at LHCb

## Abstract

The LHCb Collaboration announced the observation of three narrow structures consistent with hidden-charm pentaquark states. They are candidates of hadronic molecules formed of a pair of a charmed baryon and an anticharmed meson. Among them, the $P_c(4457)$ mass is consistent with earlier predictions of a $\Sigma_c\bar D^*$ molecule with $I=1/2$. We point out that if such a picture were true, one would have $\mathcal{B}(P_c(4457)\to J/\psi \Delta^+)/\mathcal{B}(P_c(4457)\to J/\psi p)$ at the level ranging from a few percent to about 30%. Such a large isospin breaking decay ratio is two to three orders of magnitude larger than that for normal hadron resonances. It is a unique feature of the $\Sigma_c\bar D^*$ molecular model, and can be checked by LHCb.