How to reveal the nature of three or more pentaquark states

Within the chiral unitary approach and with the constraints of heavy quark spin symmetry, we study the coupled channel interactions of D¯(∗)ςc(∗) channels, close to whose thresholds three pentaquarklike Pc states have been reported by the LHCb Collaboration. In the present work, we take into account the contributions of pion exchanges via box diagrams to the interaction potentials, and therefore lift the degeneracy in the masses of D¯∗ςc(∗) spin multiplets. Fitting the J/ψp invariant mass distributions in the Λb0→J/ψK-p decay, we find that the LHCb pentaquark states cannot be reproduced in the direct J/ψp production in the Λb0 decay, and can only be indirectly produced in the final state interactions of the Λb0 decay products, D¯(∗)ςc(∗), which further supports the nature of these states as D¯(∗)ςc molecules. Based on the fit results obtained, we study the partial decay widths/branching ratios to the other decay channels, D¯∗Λc, D¯Λc, and ηcN, and the corresponding invariant mass distributions. The resonances with JP=12-, Pc(4312), Pc(4440) and the one of D¯∗ςc∗ around 4500 MeV, have large partial decay width into ηcN, and thus can be easily seen in the ηcN invariant mass distributions. By contrast, the states with JP=32-, Pc(4457), the (predicted) narrow Pc(4380), and the bound state of D¯∗ςc∗ with a mass of about 4520 MeV do not decay into ηcN. Therefore, the ηcN channel should be studied in the future to provide further insights into the nature of these states, especially that of Pc(4440) and Pc(4457).