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

TL;DR

This paper tackles the challenge of predicting the MSSM lightest Higgs mass $m_h$ with high precision across the SUSY parameter space. The authors derive a compact analytic expression for $m_h^2$ by performing a Taylor expansion of the full diagrammatic two-loop result up to ${\cal O}(\alpha\alpha_s)$, capturing leading logarithmic and non-logarithmic terms as well as dominant subleading pieces, for general stop mixing and arbitrary Higgs-sector parameters. They incorporate leading ${\cal O}(\alpha^2)$ and beyond-${\cal O}(\alpha\alpha_s)$ corrections, and present explicit forms for both general $M_A$ and the large-$M_A$ regime, relying on the MS-bar top mass to include higher-order QCD effects. The compact formula is implemented in the FeynHiggs code (and a faster FeynHiggsFast version), enabling rapid yet accurate evaluation of $m_h$ in phenomenological studies; the results show agreement with the full two-loop diagrammatic calculation to better than about $2\,\mathrm{GeV}$ across most of the MSSM parameter space, with larger deviations only at strong stop mixing or near thresholds. The work provides both a practical computational tool for collider phenomenology (LEP2–LHC) and deeper insight into the origin and size of the dominant two-loop corrections affecting the lightest MSSM Higgs mass.

Abstract

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.

Figures (4)

• Figure 1: $m_h$ as a function of $M_{t}^{LR}/m_{\tilde{q}}$, calculated from the full formula and from the approximation formula for $M_A = 500 \,\, \mathrm{GeV}, m_{\tilde{g}} = 500 \,\, \mathrm{GeV}$ and $\tan \beta = 1.6$ or $40$.
• Figure 2: $m_h$ as a function of $m_{\tilde{q}}$, calculated from the full formula and from the approximation formula for $M_A = 500 \,\, \mathrm{GeV}, m_{\tilde{g}} = 500 \,\, \mathrm{GeV}$ and $\tan \beta = 1.6$ or $40$.
• Figure 3: $m_h$ as a function of $M_A$, calculated from the full formula and from the approximation formula for $m_{\tilde{q}} = 1000 \,\, \mathrm{GeV}, m_{\tilde{g}} = 500 \,\, \mathrm{GeV}$ and $\tan \beta = 1.6$ or $40$.
• Figure 4: $m_h$ as a function of $M_{\tilde{t}_R}$ or $M_{\tilde{t}_L}$, calculated from the full formula and from the approximation formula for varied $M_{\tilde{t}_R}~(M_{\tilde{t}_L})$, $M_{\tilde{t}_L}~(M_{\tilde{t}_R}) = 300 \,\, \mathrm{GeV}$, $M_A = 500 \,\, \mathrm{GeV}, m_{\tilde{g}} = 500 \,\, \mathrm{GeV}$ and $\tan \beta = 1.6$ or $40$.