Radiative symmetry breaking in minimal N=1 supergravity with large Yukawa couplings

We systematically study the radiative breaking of the electroweak gauge symmetry in minimal N=1 supergravity models with a heavy top quark, mt≥90 GeV, emphasizing the case of large tan β for which the Yukawa couplings for bottom and tau play an important role. We found that three different solutions for tan β can exist for fixed values of mt and the soft supersymmetry breaking parameters. Two of these solutions have large tan β and lead to a large mass splitting and mixing for all third-generations fermions, as well as a light Higgs spectrum, giving rise to rich phenomenological consequences. The reduced masses of the light b tilde- and t tilde-eigenstates lead to large enhancements of gluino branching ratios into b- and t-quarks, which can easily be the dominant gluino decay modes. We also show that combination of soft breaking parameters that lead to unacceptably large neutralino relic densities for small vertical stroketan βvertical stroke are cosmologically safe if there is a light τ tilde or a light pseudoscalar Higgs boson; both of these particles can be arbitrarily light for solutions with large vertical stroketan βvertical stroke. (orig.)