ON THE UNIFICATION OF COUPLINGS IN THE MINIMAL SUPERSYMMETRIC STANDARD MODEL

The unification of gauge and Yukawa couplings within the minimal super symmetric standard model is studied at the two loop level. We derive a n expression for the effective scale, T(SUSY), which characterizes the supersymmetric particle threshold corrections to the gauge couplings, and demonstrate that T(SUSY) is only 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 inter actions. Thus, if the gaugino masses proceed from a common soft supers ymmetry breaking term at the unification scale, and there is no signif icant gaugino-higgsino mixing, T(SUSY) will have a strong dependence o n the supersymmetric mass parameter mu. Moreover, the value of the top quark Yukawa coupling necessary to achieve the unification of bottom and tau Yukawa couplings is also governed by T(SUSY), and it yields pr edictions for the top quark mass which are close to the quasi infrared fixed point results associated with the triviality bounds on this qua ntity. From the requirement of perturbative consistency of the top qua rk Yukawa sector of the theory, we obtain constraints on the allowed s plitting of the supersymmetric spectrum, which, for certain values of the running bottom quark mass, m(b), are stronger than those ones comi ng from the experimental constraints on the strong gauge coupling. For example, for m(b)(M(b)) less-than-or-equal-to 4.1 GeV, which approxim ately corresponds to a physical mass M(b) less-than-or-equal-to 4.7 Ge V, we obtain that, for moderate values of tan beta, perturbative unifi cation may be achieved only if alpha3(M(Z)) less-than-or-equal-to 0.12 4.