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

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 (N$^{3}$LO) 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$ \overline{q} $ pair or two gluons become soft within a set of m collinear partons.