NNLO final-state quark-pair corrections in four dimensions

TL;DR

This paper presents a four-dimensional method for calculating NNLO quark-pair corrections in QCD, avoiding dimensional regularization by enforcing gauge invariance and unitarity directly in the regularization process.

Contribution

It introduces a novel four-dimensional approach to NNLO calculations that simplifies renormalization and combines virtual and real contributions without dimensional regularization.

Findings

Recomputed ${ H} o b ar b + {jets}$ decay rate at NNLO.

Recomputed $\gamma^ o {jets}$ production rate at NNLO.

Demonstrated gauge invariance and unitarity in the FDR framework.

Abstract

We describe how NNLO final state quark-pair corrections are computed in FDR by directly enforcing gauge invariance and unitarity in the definition of the regularized divergent integrals. The whole procedure is strictly four-dimensional and renormalization is performed by simply fixing bare parameters in terms of physical measurements. We give details of our approach and demonstrate how virtual and real contributions can be merged together without relying on dimensional regularization. As an example, we recompute the ${ H} \to b \bar b + {jets}$ and $\gamma^\ast \to {jets}$ inclusive rates at the NNLO accuracy in the large $N_F$ limit of QCD.