The successful prediction of the weak mixing angle suggests that the effective theory beneath the grand unification scale is the minimal supersymmetric standard model (MSSM) with just two Higgs doublets. If we further assume that the unified gauge group contains S0(10), that the two light Higgs doublets lie mostly in a single irreducible SO(10) representation, and that the t , b, and T masses originate in renormalizable Yukawa interactions of the form 1630163, then also the top quark mass can be predicted in terms of the MSSM parameters. To compute mt we present a precise analytic approximation to the solution of the two-loop renormalization group equations, and study supersymmetric and GUT threshold corrections and the input value of the b quark mass. The large ratio of top to bottom quark masses derives from a large ratio, tanp, Higgs vacuum expectation values. We point out that when tanp is large, so we certain corrections to the b quark mass prediction, unless a particular hierarchy exists in the parameters of the model. With such a hierarchy, which may result from approximate symmetries, the top mass prediction depends only weakly on the spectrum. Our results may be applied to any supersymmetric SO (10) model as long as At -X b N AT at the GUT scale and there are no intermediate mass scales in the desert. PACS number(s): 12.10.Dm, 12.15.Ff, 12.60.Jv, 14.65.Ha

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The consequences of assuming the third-generation Yukawa couplings are all large and comparable are studied in the context of the minimal supersymmetric extension of the standard model. General aspects of the RG evolution of the parameters, theoretical constraints needed to ensure proper electroweak symmetry breaking, and experimental and cosmological bounds on low-energy parameters are presented. We also present complete and exact semi-analytic solutions to the 1-loop RG equations. Focusing on SU(5) or SO(10) unification, we analyze the relationship between the top and bottom masses and the superspectrum, and the phenomenological implications of the GUT conditions on scalar masses. Future experimental measurements of the superspectrum and of the strong coupling will distinguish between various GUT-scale scenarios. And if present experimental knowledge is to be accounted for most naturally, a particular set of predictions is singled out.

The prediction for α s in the minimal supersymmetric SU(5) grand unified theory is studied in the presence of a gravitationally-induced dimension-five operator. Unless the coefficient of this operator is small, the correlation between α s and the mass scale which governs proton decay to Kν is destroyed. Furthermore, a reduction of the experimental uncertainty in α s would not provide a significant test of the theory.