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Models of $J/Ψ$ photo-production reactions on the nucleon

The $J/Ψ$ photo-production reactions on the nucleon can provide information on the roles of gluons in determining the $J/Ψ$-nucleon ($J/Ψ$-N) interactions and the structure of the nucleon. The information on the $J/Ψ$-N interactions is needed to test lattice QCD (LQCD) calculations and to understand the nucleon resonances such as $N^*(P_c)$ recently reported by the LHCb Collaboration. In addition, it is also needed to investigate the production of nuclei with hidden charms and to extract the gluon distributions in nuclei. The main purpose of this article is to review six reaction models of $γ+ p \rightarrow J/Ψ+p$ reactions which have been and can be applied to analyze the data from Thomas Jefferson National Accelerator Facility (JLab). The formulae for each model are given and used to obtain the results to show the extent to which the available data can be described. The models presented include the Pomeron-exchange model of Donnachie and Landshoff (Pom-DL) and its extensions to include $J/Ψ$-N potentials extracted from LQCD (Pom-pot) and to also use the constituent quark model (CQM) to account for the quark substructure of $J/Ψ$ (Pom-CQM). The other three models are developed from applying the perturbative QCD approach to calculate the two-gluon exchange using the generalized parton distribution (GPD) of the nucleon (GPD-based), two- and three-gluon exchanges using the parton distribution of the nucleon ($2g+3g$), and the exchanges of scalar ($0^{++}$) and tensor ($2^{++}$) glueballs within the holographic formulation (holog). The results of investigating the excitation of the nucleon resonances $N^*(P_c)$ in the $γ+ p \rightarrow J/Ψ+p$ reactions are also given.