Three-loop MSSM Higgs-Boson Mass Predictions and Regularization by Dimensional Reduction

Abstract: 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 $$O(\alpha_{t,b}\alpha_s<sup>2,\alpha_{t,b}<sup>2\alpha_s,\alpha_{t,b}<sup>3)$$. 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.