On the unification of couplings in the minimal supersymmetric standard model

The unification of gauge and Yukawa couplings within the minimal supersymmetric standard model is studied at the two loop level. We derive an expression for the effective scale, TSUSY, which characterizes the supersymmetric particle threshold corrections to the gauge couplings, and demonstrate that TSUSY 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 interactions. Thus, if the gaugino masses proceed from a common soft supersymmetry breaking term at the unification scale, and there is no significant gaugino-higgsino mixing, TSUSY will have a strong dependence on the supersymmetric mass parameter μ. Moreover, the value of the top quark Yukawa coupling necessary to achieve the unification of bottom and tau Yukawa couplings is also governed by TSUSY, and it yields predictions for the top quark mass which are close to the quasi infrared fixed point results associated with the triviality bounds on this quantity. From the requirement of perturbative consistency of the top quark Yukawa sector of the theory, we obtain constraints on the allowed splitting of the supersymmetric spectrum, which, for certain values of the running bottom quark mass, mb, are stronger than those ones coming from the experimental constraints on the strong gauge coupling. For example, for mb(Mb)≤4.1 GeV, which approximately corresponds to a physical mass Mb≤4.7 GeV, we obtain that, for moderate values of tan β, perturbative unification may be achieved only if α3(MZ)≤0.124. (orig.)