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

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 ((NLO)-L-3) 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 qq over bar pair or two gluons become soft within a set of m collinear partons.