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

arXiv (Cornell University)

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.

Authors 2

1. Michał Czakon Aachen Institut für Theoretische Teilchenphysik und Kosmologie

   RWTH Aachen University

   Affiliation as printed

   Institut für Theoretische Teilchenphysik und Kosmologie , RWTH Aachen University , D-52056 Aachen , Germany

2. Sebastian Sapeta

   Institute of Nuclear Physics, Polish Academy of Sciences

   Affiliation as printed

   Institute of Nuclear Physics , Polish Academy of Sciences , Radzikowskiego 152 , 31-342 Kraków , Poland