The SUSY-QCD β function to three loops

A number of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\overline {\mbox {\textsc{D}R}}$\end{document} renormalization constants in softly broken SUSY- QCD are evaluated to three-loop level: the wave function renormalization constants for quarks, squarks, gluons, gluinos, ghosts, and ε-scalars, and the renormalization constants for the quark and gluino mass as well as for all cubic vertices. The latter allow us to derive the corresponding β functions through three loops, all of which we find to be identical to the expression for the gauge β function obtained by Jack et al. (Phys. Lett. B 386:138, 1996, hep-ph/9606323) (see also Pickering et al. in Phys. Lett. B 510, 347, 2001, hep-ph/0104247). This explicitly demonstrates the consistency of DRED with SUSY and gauge invariance, an important pre-requisite for precision calculations in supersymmetric theories.