TTP06-08 Dimensional Reduction applied to QCD at three and four loops

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 $\beta$ 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 $\varepsilon$-scalars and the additional
 couplings which have to be considered.