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 (N3LO) 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¯ pair or two gluons become soft within a set of m collinear partons.
Del Duca, V., Duhr, C., Haindl, R., Lazopoulos, A., & Michel, M. (2020). Tree-level splitting amplitudes for a quark into four collinear partons. Journal of High Energy Physics, 2020(2). https://doi.org/10.1007/jhep02(2020)189 (Original work published 2020)