Matching of Singly- and Doubly-Unresolved Limits of Tree-level QCD Squared Matrix Elements

TL;DR

The paper tackles the infrared challenge of NNLO QCD for jet production by developing a unified subtraction framework that disentangles singly- and doubly-unresolved soft and collinear limits. It derives comprehensive factorization formulae for colour- and spin-correlated tree-level matrix elements, including iterated singly-unresolved limits and strongly-ordered doubly-unresolved regions, and uses them to construct subtraction terms A1, A2, and A12 that avoid double and triple subtractions. A central result is the explicit demonstration that combining A1, A2, and A12 yields a regulator that makes the NNLO cross section finite and integrable in four dimensions, provided momenta are mapped and phase-space factorization is handled carefully. The authors outline a general subtraction strategy for NNLO jet cross sections, discuss phase-space considerations, and validate the approach in the simplest e+e- two-jet case, with plans to extend to initial-state partons and more complex final states.

Abstract

We describe how to disentangle the singly- and doubly-unresolved (soft and/or collinear) limits of tree-level QCD squared matrix elements. Using the factorization formulae presented in this paper, we outline a viable general subtraction scheme for computing next-to-next-to-leading order corrections for electron-positron annihilation into jets.