Constraints on tan beta in the MSSM from the Upper Bound on the Mass of the Lightest Higgs boson

TL;DR

This work constrains $tan beta$ in the MSSM by combining the theoretical upper bound on the lightest Higgs mass $m_h$ with direct Higgs searches. It compares diagrammatic (FD) and RG calculations of $m_h$ and analyzes the conventional benchmark scenario ($m_t$ around 174–175 GeV, $M_{SUSY}=1$ TeV), while exploring how variations in other SUSY inputs modify the bound. The study shows that the recent FD two-loop corrections raise $m_h^{max}$ by several GeV and that slight generalizations of the benchmark further shift the bound, reducing LEP2 exclusions on $tan beta$. It emphasizes strong sensitivity to $m_t$ and $M_{SUSY}$, and notes that extensions of the Higgs sector can raise the upper bound toward ~200 GeV, making $tan beta$ constraints highly scenario-dependent.

Abstract

We investigate the possibilities for constraining tan beta within the MSSM by combining the theoretical result for the upper bound on the lightest Higgs-boson mass as a function of tan beta with the informations from the direct experimental search for this particle. We discuss the commonly used ``benchmark'' scenario, in which the parameter values m_top = 175 GeV and M_susy = 1 TeV are chosen, and analyze in detail the effects of varying the other SUSY parameters. We furthermore study the impact of the new diagrammatic two-loop result for mh, which leads to an increase of the upper bound on mh by several GeV, on present and future constraints on tan beta. We suggest a slight generalization of the ``benchmark'' scenario, such that the scenario contains the maximal possible values for mh(tan beta) within the MSSM for fixed m_top and M_susy. The implications of allowing values for m_top, M_susy beyond the ``benchmark'' scenario are also discussed.

Figures (5)

• Figure 1: $m_h$ is shown as a function of $X_t/m_{\tilde{q}}$ for $\tan \beta = 1.6$ evaluated in the Feynman-diagrammatic (program FeynHiggs) and in the renormalization group (program subhpole) approach, where $m_{\tilde{q}} \equiv M_{\mathrm{SUSY}}$. The maximal value of $m_h$ is obtained for $X_t \approx 2 \, m_{\tilde{q}}$ in the FD approach and $X_t \approx 2.4 \, m_{\tilde{q}}$ in the RG approach.
• Figure 2: $m_h$ is shown as a function of $\tan \beta$, evaluated in the RG approach. The left (long-dashed) curve displays the benchmark scenario. For the dotted (dashed) curves one deviation from the benchmark scenario, $M_2 = 100 \,\, \mathrm{GeV}$ ($M_A = 1000 \,\, \mathrm{GeV}$), is taken into account. The solid curve displays the maximal possible $m_h$ value for $m_{t} = 174.3 \,\, \mathrm{GeV}$ and $M_{\mathrm{SUSY}} = 1 \,\, \mathrm{TeV}$.
• Figure 3: $m_h$ is shown as a function of $\tan \beta$. The dashed curve displays the benchmark scenario. The dotted curve shows the $m_h^{\rm max}$-RG scenario (program subhpole), while the solid curve represents the $m_h^{\rm max}$-FD scenario (HHW, program FeynHiggs).
• Figure 4: $m_h$ is shown as a function of $\tan \beta$, evaluated in the FD approach. We give the results for three different values of the top-quark mass, $m_{t} = 174.3, 179.4, 184.5 \,\, \mathrm{GeV}$.
• Figure 5: $m_h$ is shown as a function of $\tan \beta$. The dotted curve displays the benchmark scenario in the RG approach, which has been used for phenomenological analyses up to now. The solid curve displays the $m_h^{\rm max}$-FD scenario, while the dashed curve corresponds to the "increased $m_h$" scenario with $m_{t} = 179.4 \,\, \mathrm{GeV}$ and $M_{\mathrm{SUSY}} = 2000 \,\, \mathrm{GeV}$.