Exclusive $J/\psi$ photo-production on nuclei

Motivated by the recent experimental developments, the Pom-CQM model of the $\gamma + N \to J/\psi + N$ reaction of Lee et al. [Eur. Phys. J. A. 58, 252 (2022)] and Sakinah et al. [Phys. Rev. C. 109, 065204 (2024)] has been applied to predict the exclusive $J/\psi$ photo-production on nuclei ($A$). Within the multiple scattering theory, the calculations have been performed by including the impulse amplitude $T^{\rm IMP}_{J/\psi A,\gamma A}$ and the $J/\psi$-nucleus final state interaction (FSI) amplitude $T^{\rm FSI}_{J/\psi A,\gamma A}$. For the deuteron target, $T^{\rm IMP}_{J/\psi d,\gamma d}$ is calculated exactly using the wave function generated from the realistic nucleon-nucleon potentials. It is found that, near the threshold region, the $J/\psi$ photo-production cross sections depend sensitively on the $d$-state of the deuteron wave function. The FSI amplitude $T^{\rm FSI}_{J/\psi A,\gamma A}$ is calculated using the first-order optical potential constructed from the $J/\psi$-$N$ scattering amplitude generated from the employed Pom-CQM model. It turns out that the FSI has significant effects in the large momentum-transfer region. By using the conventional fixed scatter approximation (FSA) and the nuclear form factors from the variational Monte-Carlo (VMC) calculations of Lonardoni et al. [Phys. Rev.C. 96, 024326 (2017)], the cross sections of the $J/\psi$ photo-production on ${^4\rm He}$, ${^{16}\rm O}$, and ${^{40}\rm Ca}$ are also predicted for future experimental investigations at JLab and EIC.