Four-loop β function and mass anomalous dimension in dimensional reduction

Abstract

Within the framework of QCD we compute renormalization constants for the strong coupling and the quark masses to four-loop order. We apply the DR scheme and put special emphasis on the additional couplings which have to be taken into account. This concerns the ε-scalar-quark Yukawa coupling as well as the vertex containing four ε-scalars. For a supersymmetric Yang Mills theory, we find, in contrast to a previous claim, that the evanescent Yukawa coupling equals the strong coupling constant through three loops as required by supersymmetry. © SISSA 2006.