Three-loop MSSM Higgs-boson mass predictions and regularization by dimensional reduction

The evaluation of three-loop contributions to the MSSM Higgs-boson mass is considered at the orders enhanced by the strong gauge coupling and top or bottom Yukawa couplings, i.e. at the orders O(αt,bαs2,αt,b2αs,αt,b3). We prove that regularization by dimensional reduction preserves supersymmetry at the required level. Thus generating counterterms by multiplicative renormalization is correct. Technically, we extend a previous two-loop analysis to the three-loop level. The extension covers not only the genuine three-loop Higgs potential counterterms but also a large sector of two-loop counterterms, required for subrenormalization.