Collinear Factorization and Splitting Functions for Next-to-next-to-leading Order QCD Calculations

TL;DR

Catani and Grazzini address the triple-collinear limit of tree-level QCD amplitudes at NNLO accuracy. They derive a universal factorization formula for infrared singularities and present explicit spin-dependent three-parton splitting functions at $\mathcal{O}(\alpha_S^2)$ in $d = 4 - 2\epsilon$ dimensions, covering all relevant parton channels and including azimuthal spin correlations. They verify that spin-averaged results agree with prior work by Campbell and Glover, while detailing the color structure into Abelian and non-Abelian components. These results provide essential ingredients for NNLO subtraction schemes, fixed-order jet cross sections, and improvements to parton showers and resummation techniques. Overall, the work advances practical high-precision QCD calculations by clarifying the infrared structure in the triple-collinear regime.

Abstract

We consider the singular behaviour of tree-level QCD amplitudes when the momenta of three partons become simultaneously parallel. We discuss the universal factorization formula that controls the singularities of the multiparton matrix elements in this collinear limit and present the explicit expressions of the corresponding splitting functions. The results fully include spin (azimuthal) correlations up to ${\cal O}(\as^2)$. In the case of spin-averaged splitting functions we confirm similar results obtained by Campbell and Glover.