Subtraction scheme for next-to-next-to-leading order computations

Abstract

We use the known soft and collinear limits of tree- and one-loop scattering amplitudes---computed over a decade ago---to explicitly construct a subtraction scheme for next-to-next-to-leading order (NNLO) computations. Our approach combines partitioning of the final-state phase-space together with the technique of sector decomposition, following recent suggestions in Ref. [34]. We apply this scheme to a toy example: the NNLO QED corrections to the decay of the $Z$ boson to a pair of massless leptons. We argue that the main features of this subtraction scheme remain valid for computations of processes of arbitrary complexity with NNLO accuracy.