Dynamical Model of $J/\Psi$ photo-production on the nucleon

A dynamical model based on a phenomenological charm quark-nucleon($c$-N) potential $v_{cN}$ and the Pomeron-exchange mechanism is constructed to investigate the $J/\Psi$ photo-production on the nucleon from threshold to invariant mass $W=300$ GeV. The $J/\Psi$-N potential,$V_{J/\Psi N}(r)$,is constructed by folding $v_{cN}$ into the wavefunction $\Phi_{J/\Psi}(c\bar{c})$ of $J/\Psi$ within a Constituent Quark Model(CQM) of Ref.[43]. A photo-production amplitude is also generated by $v_{cN}$ by a $c\bar{c}$-loop integration over the $\gamma\rightarrow c\bar{c}$ vertex function and $\Phi_{J/\Psi}(c\bar{c})$. No commonly used Vector Meson Dominance assumption is used to define this photo-production amplitude which is needed to describe the data near the threshold. The potential $v_{cN}(r)$ is parameterized in a form such that the predicted $V_{J/\Psi N}(r)$ at large distances has the same Yukawa potential form extracted from a Lattice QCD(LQCD) calculation of Ref.[18]. The parameters of $v_{cN}$ are determined by fitting the total cross section data of JLab by performing calculations that include $J/\Psi$-N final state interactions(FSI). The resulting differential cross sections are found in good agreements with the data. It is shown that the FSI effects dominate the cross section in the very near threshold region, allowing for sensitive testing of the predicted $J/\Psi$-N scattering amplitudes. By imposing the constraints of $J/\Psi$-N potential extracted from the LQCD calculation, we have obtained three $J/\Psi$-N potentials which fit the JLab data equally well. The resulting $J/\Psi$-N scattering lengths are in the range of $a=(-0.05$ fm $\sim$ $-0.25$ fm). With the determined $v_{cN}(r)$ and the wavefunctions generated from the same CQM, the constructed model is used to predict the cross sections of photo-production of $\eta_c(1S)$ and $\Psi(2S)$ mesons for future experimental tests.