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

Abstract

We provide results for the one-loop triple-collinear color/spin-space splitting operators for the five possible processes, $q\to q{q}^{\prime }{\bar{q}}^{\prime }$, $q\to qq\bar{q}$, $q\to qgg$, $g\to gq\bar{q}$ 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.

Comments: 35 pages, 7 figures; complete set of ancillary files attached; v3: minor textual changes, version accepted by JHEP