A subtraction scheme for NNLO computations

TL;DR

This paper introduces a subtraction scheme for NNLO calculations in particle physics, utilizing known amplitude limits and sector decomposition, demonstrated on Z boson decay with potential for broader applications.

Contribution

The paper presents a novel subtraction scheme for NNLO computations that combines phase space partitioning with sector decomposition, applicable to complex processes.

Findings

Successfully applied to NNLO QED corrections in Z decay

Scheme effectively manages soft and collinear divergences

Potential for extension to more complex processes

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. [1]. 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.