The sector decomposition approach to real radiation at NNLO

TL;DR

This work tackles the challenge of achieving NNLO accuracy for $e^+e^- \to 3$ jets by applying sector decomposition to isolate and numerically integrate infrared poles in the $D=4-2\epsilon$ expansion, enabling a fully differential Monte Carlo implementation. It extends sector decomposition to the massless $1\to 5$ real radiation at NNLO and demonstrates pole cancellation among all cuts of a renormalised diagram, providing a consistent framework to combine double virtual, real-virtual, and real-emission contributions. The approach yields a flexible, fully differential event generator capable of accommodating arbitrary infrared-safe observables, with practical strategies to manage expression sizes via preselection rules. The work promises significant impact by enabling precise, differential NNLO predictions for jet observables and thus improving determinations of fundamental parameters like $\alpha_s$ at future colliders.

Abstract

A method based on sector decomposition is briefly described which is suitable for the calculation of the double real radiation part of e^+e^- to 3 jets at next-to-next-to-leading order in a fully differential way.

Figures (2)

• Figure 1: Cancellation of IR divergences in the sum over all cuts of the renormalised graph
• Figure 2: 3--, 4-- and 5--jet rates at order $\alpha_s^3$ for the toy matrix element