Associated production of $J/\psi$ and direct photon in the parton reggeization approach

We study the associated $J/\psi$ and direct photon production in the high energy factorization, as it is formulated in the parton Reggeization approach, using two different models for the hadronization of a heavy quark-antiquark pair into a heavy quarkonium, namely the non-relativistic quantum chromodynamics (NRQCD) and the improved color evaporation model (ICEM). We find essential differences in predictions for cross section and transverse momenta spectra obtained using the NRQCD and the ICEM, which can be used for the discrimination between these models. Our prediction for cross sections of the associated $J/\psi$ and direct photon production at the LHC energies slightly overestimate the results early obtained in the next-to-leading order (NLO) calculation in the collinear parton model (CPM). We predict different two-particle correlation spectra in the associated $J/\psi$ and direct photon production which may be interesting for an experimental study.