Production of three isolated photons in the high-energy factorization approach

We study large-$p_T$ three-photon production at the LHC at the center-of-mass energy $\sqrt{s}=8$ TeV. We use the LO approximation of the parton Reggeization approach consistently merged with the real NLO corrections. For numerical calculations use the parton-level generator KaTie and modified KMR-type unintegrated parton distribution functions. We find good agreement between our predictions and data with the same accuracy as in the NNLO calculations based on the collinear parton model of QCD. At higher energies ($\sqrt{s}=13$ and 27 TeV) parton Reggeization approach predicts larger cross sections, up to $\sim 10$ \% and $\sim 20$ \%, respectively.