Towards High-Precision Predictions for the MSSM Higgs Sector

TL;DR

The paper delivers high-precision predictions for the MSSM Higgs sector by incorporating complete two-loop $O(\alpha_t^2)$ and $O(\alpha_b\alpha_s)$ corrections into FeynHiggs1.3, raising the theoretical upper bound on $m_h$ and thus weakening LEP-derived lower bounds on $\tan\beta$. It also analyzes how $\alpha_{\rm eff}$ and $\Delta_d$ reshape Higgs couplings to down-type fermions, altering $h\to b\bar{b}$ phenomenology in certain $M_A$–$\tan\beta$ regions. The authors assess theoretical uncertainties from missing momentum-dependent two-loop pieces and potential three-loop effects, estimating a conservative overall uncertainty of 1–3 GeV for $m_h$. These improvements enhance the reliability of MSSM parameter-space constraints and guide interpretation of current and future collider Higgs data.

Abstract

The status of the evaluation of the MSSM Higgs sector is reviewed. The phenomenological impact of recently obtained corrections is discussed. In particular it is shown that the upper bound on m_h within the MSSM is shifted upwards. Consequently, lower limits on tan beta obtained by confronting the upper bound as function of tan beta with the lower bound on m_h from Higgs searches are significantly weakened. Furthermore, the region in the M_A-tan beta-plane where the coupling of the lightest Higgs boson to down-type fermions is suppressed is modified. The presently not calculated higher-order corrections to the Higgs-boson mass matrix are estimated to shift the mass of the lightest Higgs boson by up to 3 GeV.

Figures (5)

• Figure 1: Two-loop corrected $m_h$ as a function of $X_t$ in various steps of approximation. The relevant MSSM parameters are chosen as $\tan \beta=3\,,\, m_{t}^{\rm pole} = 174.3 \,\, \mathrm{GeV}$, $M_{\tilde{t}_L} = M_{\tilde{t}_R} = M_A = \mu = 1 \,\, \mathrm{TeV}$ and $m_{\tilde{g}} = 800 \,\, \mathrm{GeV}$. The meaning of the different curves is explained in the text.
• Figure 2: The result for the lightest ${\cal CP}$-even Higgs-boson mass in the MSSM, $m_h$, as obtained with the program FeynHiggs is shown as a function of $\tan \beta$ for $M_A = 120$ GeV, $\mu = -1$ TeV, $M_{\tilde{t}_L} = M_{\tilde{t}_R} = M_{\tilde{b}_R} = m_{\tilde{g}} = 1$ TeV, $A_t = A_b = 2$ TeV. The meaning of the different curves is explained in the text.
• Figure 3: The result for the lightest ${\cal CP}$-even Higgs-boson mass, $m_h$, as a function of $\tan \beta$ in the $m_h^{\rm max}$ scenario. The dotted curve has been obtained with a renormalization-group improved effective potential method, using the code subhpoledm. The dashed curve corresponds to the result obtained with FeynHiggs1.0, while the full curve shows the result of FeynHiggs1.3, where the improvements described in Sect. \ref{['sec:fhstatus']} are included. The dot-dashed curve, also obtained with FeynHiggs1.3, employs $m_{t} = 179.4 \,\, \mathrm{GeV}$ and $M_{\rm SUSY} = 2 \,\, \mathrm{TeV}$. The vertical long-dashed line corresponds to the LEP exclusion bound for the SM Higgs boson of $114.4 \,\, \mathrm{GeV}$.
• Figure 4: Regions of significant suppression of the coupling of $h$ to down-type fermions in the $M_A$--$\tan \beta$-plane within the "small $\alpha_{\rm eff}$" benchmark scenario. The upper left plot shows the ratio $\sin^2 \alpha_{\rm eff}/\cos^2\beta\space$ as evaluated with FeynHiggs1.0 (i.e. without ${\cal O}(\alpha_b\alpha_s)$ and ${\cal O}(\alpha_b (\alpha_s\tan \beta)^n)$ corrections), while the upper right plot shows the same quantity as evaluated with FeynHiggs1.3 (i.e. including these corrections). The plot in the lower row shows the ratio $\Gamma(h \rightarrow b\bar{b})_{\rm MSSM} \,/\,\Gamma(h\rightarrow b\bar{b})_{\rm SM}$, i.e. the partial width for $h \to b \bar{b}$ normalized to its SM value, where the other term in eq. (\ref{['effcoupling']}) and further genuine loop corrections are taken into account (see text).
• Figure 5: $m_h$ as a function of $X_t$, using either $m_{t}^{\rm pole}$ or $\overline{m}_t$ in the two-loop corrections. The relevant MSSM parameters are chosen as $\tan \beta=3\,,\, M_{\rm SUSY} = M_A = \mu = 1 \,\, \mathrm{TeV}$ and $m_{\tilde{g}} = 800 \,\, \mathrm{GeV}$. For the different lines see text.