A new method for real radiation at NNLO
C. Anastasiou, Kirill Melnikov, Frank Petriello
TL;DR
This work introduces a sector-decomposition–based method to compute NNLO real-emission contributions in QCD by factorizing and exhaustively extracting phase-space singularities before any integration, thereby preserving the full kinematics of the final state. It demonstrates the approach at NLO and applies it to 1→4 massless final states, providing a concrete, automated framework for handling double-real emissions and their infrared structure, while keeping compatibility with jet algorithms. The authors validate the method through unitarity-based cross-checks and implement N_f-dependent NNLO contributions to e^+e^- → jets, showing pole cancellation and agreement with known analytic results. The approach promises a practical path toward differential, Monte Carlo–ready NNLO predictions and can be extended to more complex final states or integrated with existing subtraction formalisms.
Abstract
We propose a new method of computing real emission contributions to hard QCD processes. Our approach uses sector decomposition of the exclusive final-state phase space to enable extraction of all singularities of the real emission matrix elements before integration over any kinematic variable. The exact kinematics of the real emission process are preserved in all regions of phase space. Traditional approaches to extracting singularities from real emission matrix elements, such as phase space slicing and dipole subtraction, require both the determination of counterterms for double real emission amplitudes in singular kinematic limits and the integration of these contributions analytically to cancel the resulting singularities against virtual corrections. Our method addresses both of these issues. The implementation of constraints on the final-state phase space, including various jet algorithms, is simple using our approach. We illustrate our method using electron-positron --> jets at NNLO as an example.