The next-to-leading order of the differential cross section of the subprocess of annihilation of quark-antiquark pair of prompt photon production in proton-proton collisions at NICA energies

Next-to-the leading order of the differential cross-section of the subprocess of annihilation of quark-antiquark pair $q\bar{q}\to g\gamma$ of prompt photon production in nonpolarized and longitudinally polarized proton-proton collisions at NICA energies has been investigated. Shown, that contribution of the next-to-leading order to the differential cross-section of annihilation of quark-antiquark pair $q\bar{q}\to g\gamma$ is significant at the high energies of colliding protons and consist around 15% of leading order calculation. The influence of longitudinal polarization of colliding protons on the contributions of the next-to-leading order is more significant than, on the contributions of the leading order and it is significant at high energies of colliding protons. PYTHIA 8.316 $\mathbf{\text{+}}$ POWHEG BOX Monte Carlo (MC) event generator has been used for numerically simulation of prompt photon production in annihilation of quark-antiquark pair in NLO approximation for determination of the dependences of cross section on the sum of energies of colliding protons $\sqrt{s}$, transverse momentum $p_T$, cosine of scattering angle $Cos(\theta )$, rapidity y of photon and $x_T$. The NLO+PS simulation accurately reproduces the fundamental signatures of pQCD.