Dimensional Reduction applied to QCD at three loops

Abstract

Dimensional Reduction is applied to \qcd{} in order to compute various renormalization constants in the \drbar{} scheme at higher orders in perturbation theory. In particular, the ${\hat{I}}^2$ function and the anomalous dimension of the quark masses are derived to three-loop order. Special emphasis is put on the proper treatment of the so-called $\hat{I}\mu$-scalars and the additional couplings which have to be considered.

13 pages, minor changes, references added