Tree-level splitting amplitudes for a gluon into four collinear partons

TL;DR

This paper calculates the fundamental tree-level splitting amplitudes for a gluon splitting into four collinear partons, advancing the understanding of QCD scattering amplitudes at N$^3$LO accuracy.

Contribution

It provides the complete set of tree-level splitting amplitudes for a gluon into four collinear partons, completing the N$^3$LO collinear splitting framework.

Findings

Derived explicit formulas for gluon to four partons splitting amplitudes.

Analyzed iterated collinear limits of the four-parton configurations.

Contributes to precise QCD calculations at high perturbative orders.

Abstract

We compute in conventional dimensional regularisation the tree-level splitting amplitudes for a gluon parent which splits into four collinear partons. This is part of the universal infrared behaviour of the QCD scattering amplitudes at next- to-next-to-next-to-leading order (N$^3$LO) in the strong coupling constant. Combined with our earlier results for a quark parent, this completes the set of tree-level splitting amplitudes required at this order. We also study iterated collinear limits where a subset of the four collinear partons become themselves collinear.