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In this article, we study the triple-collinear limit of scatteringamplitudes, focusing the discussion in processes which include at least onephoton. To deal with infrared divergences we applied dimensional regularization(DREG) and we worked in the time-like (TL) kinematical region in order toensure the validity of strict-collinear factorization. Both polarized andunpolarized splitting functions were obtained using independent codes, whichallowed to implement a first cross-check among them. The divergent structure ofall the triple-collinear splittings was compared with the Catani's formula, andwe found a complete agreement. Moreover, in the polarized case, this comparisonimposed additional constraints in the finite part of some master integrals(MI). The analysis of photon-started splittings led to very compactexpressions, because of gauge invariance. These contributions were identifiedwith the Abelian terms of the remaining splitting functions, which constitutesanother cross-check of the results.

NLO QCD corrections to triple collinear splitting functions