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

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.