Infrared structure of $e^+e^- \to 3$ jets at NNLO - the $C_F^2$ contribution

TL;DR

This paper addresses the infrared structure of $e^+e^-\to$ 2 and 3 jets at NNLO in QCD, focusing on constructing and integrating subtraction terms to render each partonic contribution finite. It extends the NLO dipole subtraction framework to NNLO, detailing four-parton and one-loop three-parton subtraction terms and leveraging master integrals to cancel infrared poles. The authors identify and analytically integrate the $C_F^2$ contribution for three-jet event shapes, implementing the results in the EERAD2 framework and reporting first NNLO results for a 3-jet observable, with remaining colour structures in progress. The work advances precision QCD predictions for jet observables and lays groundwork for more accurate determinations of the strong coupling constant from $e^+e^-$ data.

Abstract

We discuss the infrared structure of e+e- -> 2 and 3 jets at NNLO in QCD perturbation theory and describe subtraction terms that render the separate parton-level contributions finite. As a first result, we find that the NNLO C_F^2 contribution to the first moment of the Thrust distribution <1-T> = -20.4 +/- 4.