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In this paper we study the $J/\Psi p$ spectroscopy in the process of$\Lambda_b\to J/\Psi p K^-$. The final state interactions of coupled channel$J/\Psi p$ ~-~ $\bar{D} \Sigma_c$~-~$\bar{D}^{*} \Sigma_c$ are constructedbased on K-matrix with the Chew-Mandelstam function. We build the $\Lambda_b\toJ/\Psi p K^-$ amplitude according to the Au-Morgan-Pennington method. The eventshape is fitted and the decay width of $\Lambda_b\to J/\Psi p K^-$ is used toconstrain the parameters, too. With the amplitudes we extract out the poles andtheir 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-wavecompact pentaquark state, and the structure around $P_c(4457)$ is caused by thecusp effect. The future experimental measurement of the decays of $\Lambda_b\to\bar{D}\Sigma_c K^-$ and $\Lambda_b\to \bar{D}^*\Sigma_c K^-$ would furtherhelp to study the nature of these resonances.

Pole analysis on the hadron spectroscopy of $\Lambda_b\to J/\Psi p K^-$