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

TL;DR

This paper calculates the detailed tree-level splitting amplitudes for a quark splitting into four collinear partons, advancing the understanding of infrared behavior in QCD at high precision.

Contribution

It provides the first complete computation of four-parton collinear splitting amplitudes at tree level, crucial for N3LO QCD calculations.

Findings

Derived explicit formulas for four-parton collinear splitting amplitudes.

Analyzed multiple collinear and soft limits within the same framework.

Enhanced the theoretical tools for precision QCD predictions.

Abstract

We compute in conventional dimensional regularisation the tree-level splitting amplitudes for a quark parent in the limit where four partons become collinear to each other. This is part of the universal infrared behaviour of the QCD scattering amplitudes at next-to-next-to-next-to-leading order (${\rm N^3LO}$) in the strong coupling constant. Further, we consider the iterated limit when $m'$ massless partons become collinear to each other within a bigger set of $m$ collinear partons, as well as the limits when one gluon or a $q\bar{q}$ pair or two gluons become soft within a set of $m$ collinear partons.