Pole analysis on the hadron spectroscopy of

In this paper we study the $$J/\Psi p$$ spectroscopy in the process of $$\Lambda _b\rightarrow J/\Psi p K^-$$. The final state interactions of coupled channel $$J/\Psi p$$–$$\bar{D} \Sigma _c$$–$$\bar{D}^{*} \Sigma _c$$ are constructed based on K-matrix with the Chew–Mandelstam function. We build the $$\Lambda _b\rightarrow J/\Psi p K^-$$ amplitude according to the Au–Morgan–Pennington method. The event shape is fitted and the decay width of $$\Lambda _b\rightarrow J/\Psi p K^-$$ is used to constrain the parameters, too. With the amplitudes we extract out the poles and their residues. Our amplitude and pole analysis suggest that the $$P_c(4312)$$ should be $$\bar{D}\Sigma _c$$ molecule, the $$P_c(4440)$$ could be an S-wave compact pentaquark state, and the structure around $$P_c(4457)$$ is caused by the cusp effect. The future experimental measurement of the decays of $$\Lambda _b\rightarrow \bar{D}\Sigma _c K^-$$ and $$\Lambda _b\rightarrow \bar{D}^*\Sigma _c K^-$$ would further help to study the nature of these resonances