Dynamical model of J/ψ photoproduction on the nucleon

A dynamical model based on a phenomenological charm quark-nucleon (c-N) potential v₂₍ and the Pomeron-exchange mechanism is constructed to investigate the J/ photoproduction on the nucleon from threshold to invariant mass W=300 GeV. The J/-N potential, V₉/ (r), is constructed by folding v₂₍ into the wave function ₉/ (cc) of J/ 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 v₂₍ by a cc-loop integration over the vertex function and ₉/ (cc). 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 v₂₍ (r) is parameterized in a form such that the predicted V₉/ (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 v₂₍ are determined by fitting the total cross-section data of Jefferson Laboratory (JLab) by performing calculations that include J/-N final-state interactions (FSI). The resulting differential cross sections d/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/-N scattering amplitudes. By imposing the constraints of J/-N potential extracted from the LQCD calculation of Kawanai and Sasaki, Phys. Rev. D 82, 091501 (R) (2010), we have obtained three J/-N potentials which fit the JLab data equally well. The resulting J/-N scattering lengths are in the range of a=-0. 05, -0. 25 fm. With the determined v₂₍ (r) and the wave functions generated from the same CQM, the constructed model is used to predict the cross sections of photoproduction of ₂ (1S) and (2S) mesons for future experimental tests.