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

TL;DR

This paper calculates polarized triple-collinear splitting functions at NLO accuracy for processes involving photons, providing explicit results and confirming their divergence structure aligns with theoretical predictions.

Contribution

It presents the first NLO polarized splitting functions for photon-involving processes in the triple collinear limit, extending previous unpolarized results.

Findings

Divergent structures match Catani's formula predictions

Explicit NLO corrections are provided in CDR

Results are compatible with previous unpolarized calculations

Abstract

We compute the polarized splitting functions in the triple collinear limit at next-to-leading order accuracy (NLO) in the strong coupling $\alpha_{\rm S}$, 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).