Leading Order Triple Collinear Splitting Functions Revisited

Abstract

I review the factorisation properties of tree level amplitudes when three particles $i$, $j$, $k$ are collinear. The triple collinear splitting functions contain both iterated single unresolved contributions, and genuine double unresolved contributions. I make this explicit by rewriting the known triple collinear splitting functions for a quark and two gluons in terms of products of two-particle splitting functions, and a remainder that is explicitly finite when any two of $\{i,j,k\}$ are collinear.