Associated production of $J\mathrm{/}\psi$ and direct photon in the NRQCD and the ICEM using the high-energy factorization

We study the associated $J\mathrm{/}\psi$ 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 the predictions for cross-section and transverse momenta spectra obtained using the NRQCD and the ICEM, which can be used to discriminate between these models. Our prediction for cross-sections of the associated $J\mathrm{/}\psi$ and direct photon production at the LHC energies slightly overestimates the results obtained early in the next-to-leading order (NLO) calculation in the collinear parton model (CPM). We predict different two-particle correlation spectra in the associated $J\mathrm{/}\psi$ and direct photon production which may be of interest for experimental study.