Two-loop off-shell QCD amplitudes in FDR

We link the FDR treatment of ultraviolet (UV) divergences to dimensional regularization up to two loops in QCD. This allows us to derive the one-loop and two-loop coupling constant and quark mass shifts necessary to translate infrared finite quantities computed in FDR to the MS¯\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \overline{\mathrm{MS}} $$\end{document} renormalization scheme. As a by-product of our analysis, we solve a problem analogous to the historical difficulties of the Four Dimensional Helicity (FDH) method beyond one loop. An alternative formulation of FDH is then presented that preserves the renormalizability properties of QCD without introducing evanescent quantities.