Dynamical model of J/ψ photoproduction on the nucleon

A dynamical model based on a phenomenological charm quark-nucleon (c-N) potential vcN and the Pomeron-exchange mechanism is constructed to investigate the J/ψ photoproduction on the nucleon from threshold to invariant mass $W=300$ GeV. The J/ψ-N potential, V_J/ψN(r), is constructed by folding vcN into the wave function φ_J/ψ(cc̄) of J/ψ within a constituent quark model (CQM) of Segovia et al. [Int. J. Mod. Phys. E 22, 1330026 (2013)]. A photoproduction amplitude is also generated by vcN by a cc̄-loop integration over the γ→cc̄ vertex function and φ_J/ψ(cc̄). No commonly used vector meson dominance assumption is used to define this photoproduction amplitude which is needed to describe the data near the threshold. The c-N potential vcN(r) is parameterized in a form such that the predicted V_J/ψN(r) at large distances has the same Yukawa potential form extracted from a lattice QCD (LQCD) calculation of Kawanai and Sasaki, [Phys. Rev. D 82, 091501(R) (2010)]. The parameters of vcN are determined by fitting the total cross-section data of Jefferson Laboratory (JLab) by performing calculations that include J/ψ-N final-state interactions (FSI). The resulting differential cross sections dσ/dt 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/ψ-N scattering amplitudes. By imposing the constraints of J/ψ-N potential extracted from the LQCD calculation of Kawanai and Sasaki, [Phys. Rev. D 82, 091501(R) (2010)], we have obtained three J/ψ-N potentials which fit the JLab data equally well. The resulting J/ψ-N scattering lengths are in the range of a=[-0.05,-0.25] fm. With the determined vcN(r) and the wave functions generated from the same CQM, the constructed model is used to predict the cross sections of photoproduction of ηc(1S) and ψ(2S) mesons for future experimental tests.