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Sborlini, G. F. R., de Florian, D., & Rodrigo, G. (2015). Polarized triple-collinear splitting functions at NLO for processes with photons. J. High Energy Phys., 03(3), 021–30pp.
Abstract: We compute the polarized splitting functions in the triple collinear limit at next-to-leading order accuracy (NLO) in the strong coupling alpha(S), for the splitting processes gamma -> qq gamma, gamma -> qqg and g -> qq gamma. The divergent structure of each splitting function was compared to the predicted behaviour according to Catani's formula. The results obtained in this paper are compatible with the unpolarized splitting functions computed in a previous article. Explicit results for NLO corrections are presented in the context of conventional dimensional regularization (CDR).
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Sborlini, G. F. R., de Florian, D., & Rodrigo, G. (2014). Double collinear splitting amplitudes at next-to-leading order. J. High Energy Phys., 01(1), 018–55pp.
Abstract: We compute the next-to-leading order (NLO) QCD corrections to the 1 -> 2 splitting amplitudes in different dimensional regularization (DREG) schemes. Besides recovering previously known results, we explore new DREG schemes and analyze their consistency by comparing the divergent structure with the expected behavior predicted by Catani's formula. Through the introduction of scalar-gluons, we show the relation among splittings matrices computed using different schemes. Also, we extended this analysis to cover the double collinear limit of scattering amplitudes in the context of QCD+QED.
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