The upper bound on m_h in the MSSM

The most important radiative corrections to m_h arise from the top and scalar top sector of the MSSM, with the input parameters m_t, M_SUSY and X_t. Here we assume the soft SUSY breaking parameters in the diagonal entries of the scalar top mixing matrix to be equal for simplicity, M_SUSY = M_{$\tilde{t}_{L}$} = M_{$\tilde{t}_{R}$}. This has been shown to yield upper values for m_h which comprise also the case where M_{$\tilde{t}_{L}$} $\neq$ M_{$\tilde{t}_{R}$}, if M_SUSY is identified with the heavier one of M_{$\tilde{t}_{L}$}, M_{$\tilde{t}_{R}$} [9]. For the off-diagonal entry of the mixing matrix we use the convention

$$\mu \beta$$ (1)

Note that the sign convention used for $\mu$ here is the opposite of the one used in .

Since the predicted value of m_h depends sensitively on the precise numerical value of m_t, it has become customary to discuss the constraints on tan$\beta$ within a so-called ``benchmark'' scenario (see and references therein), in which m_t is kept fixed at the value m_t = 175  GeV and in which furthermore a large value of M_SUSY is chosen, M_SUSY = 1  TeV, giving rise to large values of m_h(tan$\beta$). In it has recently been analyzed how the values chosen for the other SUSY parameters in the benchmark scenario should be modified in order to obtain the maximal values of m_h(tan$\beta$) for given m_t and M_SUSY. The corresponding scenario ( m_h^max scenario) is defined as [17,18]

$$\mu \tilde{g}$$

$$\sqrt{2}$$ (2)

where the parameters are chosen such that the chargino masses are beyond the reach of LEP2 and that the lightest $\cal {C}$P-even Higgs boson does not dominantly decay invisibly into neutralinos. In $\mu$ is the Higgs mixing parameter, M₂ denotes the soft SUSY breaking parameter in the gaugino sector, and M_A is the $\cal {C}$P-odd Higgs boson mass. The gluino mass, m_$\tilde{g}$, can only be specified as a free parameter in the FD result (program FeynHiggs [19]). The effect of varying m_$\tilde{g}$ on m_h is up to $\pm$2  GeV [9]. Within the RG result (program subhpole [5]) m_$\tilde{g}$ is fixed to m_$\tilde{g}$ = M_SUSY. Compared to the maximal values for m_h (obtained for m_$\tilde{g}$ $\approx$ 0.8 M_SUSY) this leads to a reduction of the Higgs boson mass by up to 0.5  GeV. Different values of X_t are specified in for the results of the FD and the RG calculation, since within the two approaches the maximal values for m_h are obtained for different values of X_t. This fact is partly due to the different renormalization schemes used in the two approaches [20].

The maximal values for m_h as a function of tan$\beta$ within the m_h^max scenario are higher by about 5 GeV than in the previous benchmark scenario. The constraints on tan$\beta$ derived within the m_h^max scenario are thus more conservative than the ones based on the previous scenario.

The investigation of the constraints on tan$\beta$ that can be obtained from the experimental search limits on m_h has so far been based on the results for m_h obtained within the RG approach [5]. The recently obtained FD [8,9] result differs from the RG result by a more complete treatment of the one-loop contributions [3] and in particular by genuine non-logarithmic two-loop terms that go beyond the leading logarithmic two-loop contributions contained in the RG result [20,21]. Comparing the FD result (program FeynHiggs) with the RG result (program subhpole) we find that the maximal value for m_h as a function of tan$\beta$ within the FD result is higher by up to 4 GeV.

In we show both the effect of modifying the previous benchmark scenario to the m_h^max scenario and the impact of the new FD two-loop result on the prediction for m_h. The maximal value for the Higgs boson mass is plotted as a function of tan$\beta$ for m_t = 174.3 GeV and M_SUSY = 1 TeV. The dashed curve displays the benchmark scenario, used up to now by the LEP collaborations [16]. The dotted curve shows the m_h^max scenario. Both curves are based on the RG result (program subhpole). The solid curve corresponds to the FD result (program FeynHiggs) in the m_h^max scenario. The increase in the maximal value for m_h by about 4 GeV from the new FD result and by further 5 GeV if the benchmark scenario is replaced by the m_h^max scenario has a significant effect on exclusion limits for tan$\beta$ derived from the Higgs boson search. Combining both effects, which of course have a very different origin, the maximal Higgs boson masses are increased by almost 10  GeV compared to the previous benchmark scenario.

Figure: The upper bound on m_h is shown as a function of tan$\beta$ for given m_t and M_SUSY. The dashed curve displays the previous benchmark scenario. The dotted curve shows the RG result for the m_h^max scenario, while the solid curve represents the FD result for the m_h^max scenario.

From the FD result we find the upper bound of m_h  $\raisebox{-.3em}{$\stackrel{\displaystyle <}{\sim}$}$  129 GeV in the region of large tan$\beta$ within the MSSM for m_t = 174.3  GeV and M_SUSY = 1 TeV. Higher values for m_h are obtained if the experimental uncertainty in m_t of currently $\Delta$m_t = 5.1  GeV is taken into account and higher values are allowed for the top quark mass. As a rule of thumb, increasing m_t by 1 GeV roughly translates into an upward shift of m_h of 1 GeV. An increase of M_SUSY from 1 TeV to 2 TeV enhances m_h by about 2 GeV in the large tan$\beta$ region. As an extreme case, choosing m_t = 184.5 GeV, i.e. two standard deviations above the current experimental central value, and using M_SUSY = 2 TeV leads to an upper bound on m_h of m_h  $\raisebox{-.3em}{$\stackrel{\displaystyle <}{\sim}$}$  141 GeV within the MSSM.