FeynHiggsFast: a program for a fast calculation of masses and mixing angles in the Higgs Sector of the MSSM

TL;DR

Problem: precise MSSM Higgs masses and mixing angles require radiative corrections up to two loops. Approach: a compact analytical approximation based on the full one-loop results and dominant two-loop corrections (O(alpha alpha_s)) plus leading Yukawa terms, evaluated with Delta_rho from squarks; the self-energies are computed at zero external momentum and the Higgs basis diagonalized by alpha_eff. Contributions: outputs include m_h, m_H, alpha_eff, m_Hplus, and Delta_rho; accuracy is typically better than 2 GeV for m_h across most parameter space, with a vastly faster runtime (~1e-5 to 1e-4 s per evaluation) compared to the full diagrammatic calculation. Significance: enables rapid scans and easy integration as a fast subroutine in collider phenomenology workflows.

Abstract

FeynHiggsFast is a Fortran code for the calculation of the masses and the mixing angle of the neutral CP-even Higgs bosons in the MSSM up to two-loop order. It is based on a compact analytical approximation formula of the complete diagrammatic one-loop and the dominant two-loop contributions. At the one-loop level a leading logarithmic result is used, taking into account all sectors of the MSSM. At the two-loop level at O(alpha alpha_s) the leading logarithmic and non-logarithmic contributions are taken into account. The approximation formula is valid for arbitrary choices of the parameters in the Higgs sector of the model. Comparing its quality to the full diagrammatic result, we find agreement better than 2 GeV for most parts of the MSSM parameter space.

Figures (3)

• Figure 1: $m_h$ 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 2: $m_h$ 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 3: The relative difference $(\sin\alpha_{\rm eff} - \sin\alpha_{\rm eff}{\rm (approx)})/\sin\alpha_{\rm eff}$ is shown as a function of $M_A$ for three values of $\tan \beta$ in the no mixing and the maximal mixing scenario. The other parameters are $\mu = -100 \,\, \mathrm{GeV}$, $M = m_{\tilde{q}}$, $m_{\tilde{g}} = 500 \,\, \mathrm{GeV}$ and $A_b = A_t$.