Pentaquarks $P_c$ in a dynamical coupled-channel approach of $\gamma p \to J/\psi p$ 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. The predicted total and differential cross sections of $J/\psi$ photoproduction are within the range of the data from the GlueX and $J/\psi$-$007$ experiments. It is found that the $\sigma$ exchange plays a crucial role for determining the very near threshold cross section. The total cross section gets enhanced due to the open-charm state rescattering in the $P_c(4312)$, $P_c(4440)$ and $P_c(4457)$ production regions, and is of order 1 nb.