Unification of Couplings and the Top Quark Sector in the Minimal Supersymmetric Standard Model

I analyze the predictions for the strong gauge coupling, $\alpha_3(M_Z) $, and the top quark and light Higgs masses in the framework of gauge and bottom-tau Yukawa coupling unification in the minimal supersymmetric standard model. These predictions depend on the effective supersymmetric threshold scale $T_{SUSY}$, which is only very slightly dependent on the squark and slepton masses, and strongly dependent on the Higgsino masses as well as on the mass ratio of the gauginos of the strong and weak interactions. Within the minimal supersymmetry breaking scheme and for supersymmetric masses below or of the order of 1 TeV, I obtain $\alpha_3(M_Z) \geq 0.116$, while, if the running bottom quark mass at the physical mass is constrained to be $ m_b(M_b) \leq 4.1 $GeV, then, for moderate values of $\tan \beta$, perturbative unification is achieved only if $\alpha_3(M_Z) \leq 0.124$. Unification of gauge and bottom-tau Yukawa couplings yield predictions for the top quark mass, 140 GeV $\leq M_t \leq 210 $ GeV for $1 \leq \tan \beta \leq 30$, which are remarkably close to the infrared quasi fixed point values for this quantity. For the light Higgs mass I obtain $m_h \leq 130(165)$ GeV if the characteristic squark mass is below 1 (10) TeV.