Heavy pentaquark states $P_c(4380)$ and $P_c(4450)$ in the $J/\psi$ production induced by pion beams off the nucleon

Understand

In this study, we investigate the $J/\psi$ production induced by pion beams off the nucleon, particularly the heavy pentaquarks $P_c(4380)$ and $P_c(4450)$ in intermediate states, based on a hybridized Regge model.

• The process involving $\rho$ and $\pi$ meson exchange in the $t$ channel is considered as background, and the heavy pentaquark exchange is included in the $s$ channel.
• The coupling constants such as the $\rho NN$ and $\pi NN$ vertices are taken from the $NN$ potentials, whereas those for the $J/\psi\rho\pi$ and $J/\psi\pi\pi$ vertices are determined by using experimental data based on the branching ratios.
• In order to estimate the $P_c(4380)$ and $P_c(4450)$ coupling constants, we use the experimental upper limit on the total cross section as a guide for the $\pi N\to J/\psi N$ reaction.