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

TL;DR

This paper models $J/a$ production via pion beams off nucleons, highlighting the roles of heavy pentaquarks $P_c(4380)$ and $P_c(4450)$ using a hybridized Regge approach, and estimates their effects on cross sections.

Contribution

It introduces a hybridized Regge model to analyze heavy pentaquark contributions in pion-induced $J/a$ production, incorporating experimental data for coupling constants and cross section estimates.

Findings

Background cross section is about 10^{-4} to 10^{-3} nb.

Pentaquark contributions can increase cross section to about 1 nb near resonance.

Model provides estimates consistent with experimental upper limits.

Abstract

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. The background total cross section is the order of $10^{-4}-10^{-3}$ nb. In the vicinity of the heavy pentaquark masses, the total cross section reaches about $1$ nb.