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.
Highlights
Finding new exotic hadrons is one of the most important issues for hadron and particle physics
The experimental data on π−p → φn are taken from Dahl et al [19] and the data on the upper limit of the π−p → J/ψn reaction are taken from Jenkins et al [6] and Chiang et al [7]
Sections are drawn as a function of s/sth so we can compare the total cross section of the π−p → φn reaction with that of J/ψ production. sth denotes the threshold value of s, i.e., ssth = (Mφ + Mn)2 = 3.84 GeV2 and scth = (MJ/ψ + Mn)2 = 16.3 GeV2 for the π−p → φn and π−p → J/ψn reactions, respectively
Summary
Finding new exotic hadrons is one of the most important issues for hadron and particle physics. The LHCb Collaboration announced the observation of two heavy pentaquarks in Λb → J/ψK−p decays [1], where the quark content is uudcc. The significance of these pentaquarks is more than 9σ. The masses and widths were reported as: MPc = (4380 ± 8 ± 29) MeV and ΓPc = (205 ± 18 ± 86) MeV for the lower state, whereas MPc = (4449.8 ±1.7 ±2.5) MeV and ΓPc = (39 ±5 ±19) MeV for the higher state. It is very important to confirm these pentaquark states in other possible reactions. The energy of the pion beam at the Japan Proton Accelerator Research Complex (J-PARC)
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