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 (${\mathrm{N}}^3\mathrm{LO}$) in the strong coupling constant. Further, we consider the iterated limit when $m^{\prime }$ 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.

52 pages, 4 figures