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 ${\Sigma }_c{\bar{D}}^{\ast }$ 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 ${\Sigma }_c{\bar{D}}^{\ast }$ molecular model, and can be checked by LHCb.

Comments: Version to be published as a Rapid Communication in Phys. Rev. D, selected as Editors' Suggestion