Complete collection of one-loop triple-collinear splitting operators for dimensionally-regulated QCD

TL;DR

This paper provides comprehensive one-loop triple-collinear splitting operators in dimensionally-regulated QCD, essential for NN3LO subtraction schemes in precise particle physics calculations.

Contribution

It offers exact expressions for five key triple-collinear splitting processes at one-loop, expanding the dimensional regularisation parameter to second order.

Findings

Derived explicit splitting operators for five processes

Evaluated related splitting functions

Facilitates NN3LO subtraction schemes

Abstract

We provide results for the one-loop triple-collinear color/spin-space splitting operators for the five possible processes, $q \to qq'\bar{q}'$, $q \to qq\bar{q}$, $q \to qgg$, $g \to gq\bar{q}$ and $g \to ggg$. The expressions are exact in dimensionally-regulated massless QCD up to a single integral, which we expand to second order in the dimensional-regularisation parameter. We also evaluate the related splitting functions. Our results are both sufficient and indispensable for the construction of subtraction and integrated-subtraction terms for triple-collinear singularities of one-loop double-real-emission cross-section contributions as part of a next-to-next-to-next-to leading order subtraction scheme.