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Production of $J/Ψ$ on the nucleon and deuteron targets

A coupled-channel model with $πN$, $ρN$ and $J/ΨN$ channels is developed to predict the $π+ N \rightarrow J/Ψ+ N $ cross sections. The $J/Ψ$-$N$ interaction is parameterized in a form related to what has been predicted by the effective field theory approach and Lattice QCD. The other interactions within the model are constrained by the decay width of $J/Ψ\rightarrow ρ+ π$ and the total cross section data of $πN$ reactions. The calculated meson-baryon amplitudes are then used to predict the cross sections of the $J/Ψ$ production on the deuteron target by including the contributions from the impulse term and the one-loop calculations of the final $NN$ and $J/ΨN$ re-scattering effects. Predictions of the dependence of the cross sections of $π^- + p \rightarrow J/Ψ+ n$, $γ+ d \rightarrow J/Ψ+ n + p$, and $π^+ d \rightarrow J/Ψ+p +p$ on the $J/Ψ$-$N$ potentials are presented for experimental determinations of the $J/Ψ$-$N$ interaction. Within the vector meson dominance model, we have also applied the constructed coupled-channel model to predict the $γ+ p\rightarrow J/Ψ+ p$ cross sections near the $J/Ψ$ production threshold.