Dynamical model of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>J</mml:mi><mml:mo>/</mml:mo><mml:mi>ψ</mml:mi></mml:mrow></mml:math> photoproduction on the nucleon

Abstract

A dynamical model based on a phenomenological charm quark-nucleon ($c\ensuremath{-}N$) potential ${v}_{cN}$ and the Pomeron-exchange mechanism is constructed to investigate the $J/\ensuremath{\psi}$ photoproduction on the nucleon from threshold to invariant mass $W=300$ GeV. The $J/\ensuremath{\psi}\ensuremath{-}N$ potential, ${V}_{J/\ensuremath{\psi}N}(r)$, is constructed by folding ${v}_{cN}$ into the wave function ${\ensuremath{\phi}}_{J/\ensuremath{\psi}}(c\overline{c})$ of $J/\ensuremath{\psi}$ 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 ${v}_{cN}$ by a $c\overline{c}$-loop integration over the $\ensuremath{\gamma}\ensuremath{\rightarrow}c\overline{c}$ vertex function and ${\ensuremath{\phi}}_{J/\ensuremath{\psi}}(c\overline{c})$. 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 $c\ensuremath{-}N$ potential ${v}_{cN}(r)$ is parameterized in a form such that the predicted ${V}_{J/\ensuremath{\psi}N}(r)$ 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 ${v}_{cN}$ are determined by fitting the total cross-section data of Jefferson Laboratory (JLab) by performing calculations that include $J/\ensuremath{\psi}\ensuremath{-}N$ final-state interactions (FSI). The resulting differential cross sections $d\ensuremath{\sigma}/dt$ 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 $J/\ensuremath{\psi}\ensuremath{-}N$ scattering amplitudes. By imposing the constraints of $J/\ensuremath{\psi}\ensuremath{-}N$ potential extracted from the LQCD calculation of Kawanai and Sasaki, [Phys. Rev. D 82, 091501(R) (2010)], we have obtained three $J/\ensuremath{\psi}\ensuremath{-}N$ potentials which fit the JLab data equally well. The resulting $J/\ensuremath{\psi}\ensuremath{-}N$ scattering lengths are in the range of $a=[\ensuremath{-}0.05,\ensuremath{-}0.25]$ fm. With the determined ${v}_{cN}(r)$ and the wave functions generated from the same CQM, the constructed model is used to predict the cross sections of photoproduction of ${\ensuremath{\eta}}_{c}(1S)$ and $\ensuremath{\psi}(2S)$ mesons for future experimental tests.

Topics & Concepts