NLO QCD corrections to triple collinear splitting functions

TL;DR

This paper computes NLO QCD corrections to triple collinear splitting functions, including photon processes, verifying divergence structures and deriving compact, gauge-invariant expressions with cross-checks against established formulas.

Contribution

It provides the first detailed calculation of NLO triple collinear splitting functions including photons, with independent code validation and consistency checks against Catani's formula.

Findings

Complete agreement with Catani's divergence formula.

Compact gauge-invariant expressions for photon-started splittings.

Validation of finite parts through independent code comparison.

Abstract

In this article, we study the triple-collinear limit of scattering amplitudes, focusing the discussion in processes which include at least one photon. To deal with infrared divergences we applied dimensional regularization (DREG) and we worked in the time-like (TL) kinematical region in order to ensure the validity of strict-collinear factorization. Both polarized and unpolarized splitting functions were obtained using independent codes, which allowed to implement a first cross-check among them. The divergent structure of all the triple-collinear splittings was compared with the Catani's formula, and we found a complete agreement. Moreover, in the polarized case, this comparison imposed additional constraints in the finite part of some master integrals (MI). The analysis of photon-started splittings led to very compact expressions, because of gauge invariance. These contributions were identified with the Abelian terms of the remaining splitting functions, which constitutes another cross-check of the results.