Radiative corrections to the subprocess of annihilation of quark-antiquark pair of prompt photon production in proton-proton collisions at NICA energies $\sqrt{\mathbf{s}}$= 10 GeV
In this work, a comprehensive theoretical and numerical study of the quantum-chromodynamic and quantum-electrodynamic radiative corrections: 1. $q\bar{q} \rightarrow q\bar{q}γ$, 2. $q\bar{q} \rightarrow ggγ$, and 3. $q\bar{q} \rightarrow gγγ$ to the annihilation of a quark-antiquark pair $q\bar{q} \rightarrow gγ$ of prompt photon production in proton-proton collisions at NICA energies $\sqrt{s}$ = 10 GeV was performed. The differential cross-sections and double spin asymmetries $A_{LL}$ of the radiative corrections were investigated analytically using the FeynCalc and modulated in PYTHIA 8.316. Radiative corrections are significant at low collision energies of protons $\sqrt{s}$ and small transverse momentum of photons $p_{T}$. It was shown that radiative corrections to the annihilation of a quark-antiquark pair process satisfy the following relations: $$ 2. σ_{\sqrt{s}}(q\bar{q} \rightarrow ggγ) > 1. σ_{\sqrt{s}}(q\bar{q} \rightarrow q\bar{q}γ) > 3. σ_{\sqrt{s}}(q\bar{q} \rightarrow gγγ) $$ $$ 1. \frac{dσ(q\bar{q} \rightarrow q\bar{q}γ)}{dp_{T}^{2}} > 3. \frac{dσ(q\bar{q} \rightarrow gγγ)}{dp_{T}^{2}} > 2. \frac{dσ(q\bar{q} \rightarrow ggγ)}{dp_{T}^{2}} $$ The polarization of colliding protons has almost the same effect on processes 1. $q\bar{q} \rightarrow q\bar{q}γ$, 2. $q\bar{q} \rightarrow ggγ$, and 3. $q\bar{q} \rightarrow gγγ$ and in this case above indicated relation is also satisfied. A direct comparison between strict leading order analytical calculations in FeynCalc and PYTHIA 8.316 modulations revealed excellent agreement in the central kinematic regions.