The Mass of the Lightest MSSM Higgs Boson: A Compact Analytical Expression at the Two-Loop Level

A compact approximation formula for the mass of the lightest neutral CP-even Higgs boson, m_h, in the Minimal Supersymmetric Standard Model (MSSM) is derived from the diagrammatic two-loop result for m_h up to O(alpha alpha_s). By analytically expanding the diagrammatic result the leading logarithmic and non-logarithmic as well as the dominant subleading contributions are obtained. The approximation formula is valid for general mixing in the scalar top sector and arbitrary choices of the parameters in the Higgs sector of the model. Its quality is analyzed by comparing it with the full diagrammatic result. We find agreement with the full result better than 2 GeV for most parts of the MSSM parameter space.