Pentaquarks \(P_c\) in a dynamical coupled-channel approach of \(\gamma p \rightarrow J/\psi p\) reaction

We construct a dynamical coupled-channel approach to photon-induced \(J/\psi \) production to search for the trace of the pentaquarks \(P_c.\) In this approach, the considered open-charm intermediate states are \(\Lambda _c \bar{D}^{(*)}\) and \(\Sigma _c \bar{D}^{(*)}.\) Scattering amplitude involving \(\Lambda _c \bar{D}^{(*)},\) \(\Sigma _c \bar{D}^{(*)}\) and \(J/\psi p\) interactions is calculated from solving a set of coupled-channel integral equations. The coupled-channel interaction potentials are generated from one-boson-exchange. The pentaquarks \(P_c\) are dynamically generated from the coupled-channel interactions. Moreover, the background contributions to the \(P_c\) signals are assumed to be the Pomeron exchange and \(\sigma \) exchange. We analyze the total and differential cross sections of \(J/\psi \) photoproduction measured by the GlueX and \(J/\psi \)-007 experiments. It is found that both \(\sigma \) exchange and open-charm state rescattering have contributions in describing the total and differential cross section. The total cross section gets enhanced due to the open-charm state rescattering in the pentaquark production regions, and is of order 1 nb or smaller.