Relation between the pole and the minimally subtracted mass in dimensional regularization and dimensional reduction to three-loop order

We compute the relation between the pole quark mass and the minimally subtracted quark mass in the framework of QCD applying dimensional reduction as a regularization scheme. Special emphasis is put on the evanescent couplings and the renormalization of the ε  -scalar mass. As a by-product we obtain the three-loop on-shell renormalization constants ZmOS and Z2OS in dimensional regularization and thus provide the first independent check of the analytical results computed several years ago.