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

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 Pc(4457) mass is consistent with earlier predictions of a ΣcD¯* molecule with I = 1/2. We point out that if such a picture were true, one would have B(Pc(4457) → J/ψΔ+)/B(Pc(4457) → J/ψp) 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 ΣcD¯* molecular model, and can be checked by LHCb.