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

TL;DR

This paper calculates three-loop contributions to the MSSM Higgs-boson mass, demonstrating that dimensional reduction preserves supersymmetry and validating the renormalization approach at this high loop order.

Contribution

It extends previous two-loop analysis to three loops, including genuine three-loop counterterms and a large sector of two-loop counterterms, confirming the validity of dimensional reduction.

Findings

Dimensional reduction preserves supersymmetry at three loops.

Validated multiplicative renormalization for three-loop counterterms.

Extended the analysis to include two-loop counterterms needed for subrenormalization.

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 $O(\alpha_{t,b}\alpha_s^2,\alpha_{t,b}^2\alpha_s,\alpha_{t,b}^3)$. 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.