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

Journal of High Energy Physics, vol. 2022

Abstract

Abstract We provide results for the one-loop triple-collinear color/spin-space splitting operators for the five possible processes, q → $$ {qq}^{\prime }{\overline{q}}^{\prime } $$ qq ′ q ¯ ′ , q → $$ qq\overline{q} $$ qq q ¯ , q → qgg, g → $$ gq\overline{q} $$ gq q ¯ and g → 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 corresponding

   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