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

Abstract

AbstractIn this paper we study the $$J/\Psi p$$J/Ψp spectroscopy in the process of $$\Lambda _b\rightarrow J/\Psi p K^-$$Λb→J/ΨpK-. The final state interactions of coupled channel $$J/\Psi p$$J/Ψp–$$\bar{D} \Sigma _c$$D¯Σc–$$\bar{D}^{*} \Sigma _c$$D¯∗Σc are constructed based on K-matrix with the Chew–Mandelstam function. We build the $$\Lambda _b\rightarrow J/\Psi p K^-$$Λb→J/ΨpK- amplitude according to the Au–Morgan–Pennington method. The event shape is fitted and the decay width of $$\Lambda _b\rightarrow J/\Psi p K^-$$Λb→J/ΨpK- 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 $$P_c(4312)$$Pc(4312) should be $$\bar{D}\Sigma _c$$D¯Σc molecule, the $$P_c(4440)$$Pc(4440) could be an S-wave compact pentaquark state, and the structure around $$P_c(4457)$$Pc(4457) is caused by the cusp effect. The future experimental measurement of the decays of $$\Lambda _b\rightarrow \bar{D}\Sigma _c K^-$$Λb→D¯ΣcK- and $$\Lambda _b\rightarrow \bar{D}^*\Sigma _c K^-$$Λb→D¯∗ΣcK- would further help to study the nature of these resonances.