Associative production of $J/\psi$-mesons and direct photons at the energy of the NICA collider

The article considers the associated production of $J/\psi$-mesons and direct photons at the energy of the NICA collider, $\sqrt s =27$ GeV, in the Generalized Parton Model in the leading order of perturbation theory of the quantum chromodynamics. Hadronization of a pair of $c\bar c$-quarks to a $J/\psi$-meson is described in terms of two approaches: the color singlet model and the color evaporation model. Nonperturbative parameters of the models are fixed from comparison with the available experimental data on inclusive production of $J/\psi$-mesons obtained at energies from $\sqrt s = 19$ up to $\sqrt s = 200$ GeV. It is shown that the processes of the associative production of $J/\psi + \gamma$ can be used to study of gluon distribution functions depending on the transverse momentum in a proton.