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

Abstract

We investigate the \(J/\psi\) production induced by pion beams off the nucleon, emphasizing the heavy pentaquarks \(P_c(4380)\) and \(P_c(4450)\) in the intermediate states, based on a hybridized Regge model. We consider the \(\rho\) and \(\pi\) mesons in the \(t\) channel as a background, and include the heavy pentaquarks 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 the experimental data on the branching ratios. In order to estimate the \(P_c(4380)\) and \(P_c(4450)\) coupling constants, we are guided by the experimental upper limit on the total cross section for the \(\pi N\to J/\psi N\) reaction. The background total cross section turns out to be of order \(10^{-4}-10^{-3}\) nb. In the vicinity of the heavy pentaquark masses, we find that the total cross section reaches about \(1\) nb.