NNLO final-state quark-pair corrections in four dimensions

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. We give details of our approach and show how virtual and real contributions can be merged together without relying, explicitly or implicitly, on dimensional regularization. As an example, we recompute the H→b$\overline{b}$+jets and γ${}^{\text{â}}\text{ˆ}\text{—}$→jets inclusive rates at the NNLO accuracy in the large N${}_F$ limit of QCD. This demonstrates, for the first time, that physical results with intermediate infrared singularities can be obtained at NNLO using a fully four-dimensional procedure.