Steps towards the QCD calculation for e+ e- --> 3 jets at NNLO

TL;DR

Problem: achieving fully differential NNLO predictions for electron-positron to three-jet final states requires new two-loop multi-scale amplitudes and a robust NNLO subtraction framework to handle infrared divergences. Approach: the paper surveys progress in calculating multi-scale two-loop amplitudes using nested sums and Z-sums, and outlines an NNLO subtraction strategy including double unresolved and one-loop-with-one-unresolved contributions. Key contributions: demonstration that nested sums yield epsilon-expanded analytic results in a sum basis and presentation of an explicit integrated counterterm for a gluon to quark-antiquark splitting, illustrating the practical path to infrared cancellation. Significance: these methods enable more precise determinations of alpha_s and improved modeling of jet structure at NNLO, with potential for stable, efficient Monte Carlo implementation.

Abstract

High precision analyses of experimental data for e+ e- annihillation, such as determination of jet rates or event shape observables, call for complete next-to-next-to-leading order (NNLO) perturbative QCD predictions. In this talk, we discuss the various ingredients entering the calculation of the NNLO corrections in e+ e- annihillation.