Polarized triple-collinear splitting functions at NLO for processes with photons

Abstract

We compute the polarized splitting functions in the triple collinear limit at next-to-leading order accuracy (NLO) in the strong coupling ${\alpha }_{\mathrm{S}}$, for the splitting processes $\gamma \to q\bar{q}\gamma$, $\gamma \to q\bar{q}g$ and $g\to q\bar{q}\gamma$. 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).

arXiv comment31 pages, no figures. Exact results for photon started-processes available in Appendix A. Improved discussion about implementation and typos corrected. Final version published in JHEP

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• Soft gluon-quark-antiquark emission in QCD hard scattering
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• Four-dimensional representation of scattering amplitudes and physical observables through the application of the Loop-Tree Duality theorem
• One-loop triple collinear splitting amplitudes in QCD
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