Massive tree-level splitting functions beyond kinematical limits

TL;DR

This paper derives a compact form of massive 1-to-3 QCD splitting functions, introducing novel two-gluon radiator functions that extend beyond soft and collinear approximations, enhancing understanding of parton splitting at tree level.

Contribution

It provides a new, compact expression for massive 1-to-3 splitting functions and introduces generalized two-gluon radiator functions that do not rely on soft or collinear limits.

Findings

Derived compact massive 1-to-3 splitting functions

Introduced novel two-gluon radiator functions

Results are valid beyond soft and collinear limits

Abstract

We present a compact form of the massive $1\to 3$ tree-level QCD splitting functions and discuss a decomposition of the results in terms of lower-order expressions, scalar dipole antenna functions and pure higher-order remainders. The two-gluon radiator functions introduced in this context are novel and generalize expressions obtained from the double-soft approximation. Our results are obtained without reference to soft or quasi-collinear limits.