Combined fit of low energy constraints to minimal supersymmetry and discovery potential at LEP II

Within the Constrained Minimal Supersymmetric Standard Model (CMSSM) it is possible to predict the low energy gauge couplings and masses of the 3. generation particles from a few parameters at the GUT scale. In addition the MSSM predicts electroweak symmetry breaking due to large radiative corrections from Yukawa couplings, thus relating the Z⁰ boson mass to the top quark mass. From a χ² analysis, in which these constraints can be considered simultaneously, one can calculate the probability for each point in the MSGUT parameter space. The recently measured top quark mass prefers two solutions for the mixing angle in the Higgs sector: tan β in the range between 1 and 3 or alternatively tan β ≈ 25 - 50. For both cases we find a unique χ² minimum in the parameter space. From the corresponding most probable parameters at the GUT scale, the masses of all predicted particles can be calculated at low energies using the RGE, albeit with rather large errors due to the logarithmic nature of the running of the masses and coupling constants. Our fits include full second order corrections for the gauge and Yukawa couplings, low energy threshold effects, contributions of all (s)particles to the Higgs potential and corrections to m_b from gluinos and higgsinos, which exclude (in our notation) positive values of the mixing parameter μ in the Higgs potential for the large tan β region. Further constraints can be derived from the branching ratio for the radiative (penguin) decay of the 6-quark into sγ and the lower limit on the lifetime of the universe, which requires the dark matter density due to the Lightest Supersymmetric Particle (LSP) not to overdose the universe. For the low tan β solution these additional constraints can be fulfilled simultaneously for quite a large region of the parameter space. In contrast, for the high tan β solution the correct value for the b → sγ rate is obtained only for small values of the gaugino scale and electroweak symmetry breaking is difficult, unless one assumes the minimal SU(5) to be a subgroup of a larger symmetry group, which is broken between the Planck scale and the unification scale. In this case small splittings in the Yukawa couplings are expected at the unification scale and electroweak symmetry breaking is easily obtained, provided the Yukawa coupling for the top quark is slightly above the one for the bottom quark, as expected e.g. if the larger symmetry group would be SO(10). For particles, which are most likely to have masses in the LEP II energy range, the cross sections are given for the various energy scenarios at LEP II. For low tan β the production of the lightest Higgs boson, which is expected to have a mass below 103 GeV, is the most promising channel, while for large tan β the production of charginos and/or neutralinos covers the preferred parameter space.