Implications of a Heavy Top in Supersymmetric Theories

In the context of the radiative electroweak symmetry breaking scenario, we investigate the implications of a heavy top quark mass, close to its infrared fixed point, on the low energy parameters of the minimal supersymmetric standard model. We use analytic expressions to calculate the Higgs masses as well as the supersymmetric masses of the third generation. We further assume bottom-tau unification at the GUT scale and examine the constraints put by this condition on the parameter space ($\tan \beta$,${\alpha }_3$), using the renormalization group procedure at the two-loop level. We find only a small fraction of the parameter space where the above conditions can be satisfied, namely $1\le \tan \beta \le 2$, while $0.111\le {\alpha }_3(M_Z)\le 0.118$. We further analyse the case where all three Yukawa couplings reach the perturbative limit just after the unification scale. In this latter case, the situation turns out to be very strict demanding $\tan \beta \sim 63$.