Leading Order Triple Collinear Splitting Functions Revisited

TL;DR

This paper revisits the factorisation properties of tree-level amplitudes in triple collinear limits, explicitly separating iterated single unresolved and genuine double unresolved contributions for quark-gluon systems.

Contribution

It provides a new explicit decomposition of triple collinear splitting functions into products of two-particle functions and finite remainders, clarifying their structure.

Findings

Explicit decomposition of triple collinear splitting functions.

Identification of finite remainders in the splitting functions.

Clarification of the factorisation properties in triple collinear limits.

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.