Analysis of J/ψp and χc1p interaction with S-wave and P-wave coupling using the separable potential model

Abstract

A revived interest for hadron spectroscopy lead to the discovery of many exotic hadrons, including the discovery of Pentaquark signals by the LHCb collaboration. One of the pentaquark signals that they observed was the P_cc̅(4457)⁺, which appears in the decay of Λ_b⁰ → P_c⁺ K⁻. Different models have been used to explain this structure, one of them being the Triangle singularity, which is a purely kinematic description of the interaction. The rescattering of χ_c1p to produce J/ψp is involved in this triangle interaction, which is hypothesized to have an S-P wave coupling to accommodate the quantum numbers associated with the signal. To analyze the effects of this coupled partial wave in a coupled channel scenario, we introduce the separable potential model, which is ideal to isolate the effects of ℓ^th partial waves for each channel. From the separable potential model, we were able to generate a coupled channel pole trajectory and amplitude plots.