Pole analysis on the hadron spectroscopy of ${\Lambda }_b\to J/\Psi p{K}^{-}$

Abstract

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 $J/\Psi p$ ~-~ $\bar{D}{\Sigma }_c$~-~${\bar{D}}^{\ast }{\Sigma }_c$ are constructed based on K-matrix with the Chew-Mandelstam function. We build the ${\Lambda }_b\to J/\Psi p{K}^{-}$ amplitude according to the Au-Morgan-Pennington method. The event shape is fitted and the decay width of ${\Lambda }_b\to J/\Psi p{K}^{-}$ 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 ${\Lambda }_b\to \bar{D}{\Sigma }_c{K}^{-}$ and ${\Lambda }_b\to {\bar{D}}^{\ast }{\Sigma }_c{K}^{-}$ would further help to study the nature of these resonances.

arXiv commentupdated to the published version

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