On Supersymmetric b-tau Unification, Gauge Unification, and Fixed Points

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The equality assumption of the b and tau Yukawa couplings at the grand-unification scale can strongly constrain the allowed parameter space of supersymmetric models. We examine the constraints in the case that there is a discrepancy > 10% in the gauge coupling unification assumption (which necessarily implies large perturbations at the grand scale). The constraints are shown to diminish in that case [most significantly so if alphaₛ(MZ) ≈ 0.11]. In particular, the requirement that the t Yukawa coupling, hₜ, is near its quasi-fixed point may not be necessary. We discuss the colored-triplet threshold as a simple example of a source for the discrepancies, and comment on its possible implications. In addition, we point out that supersymmetric (as well as unification-scale) threshold corrections to hₜ shift the fixed-point curve in the mₜ - βplane. The implications for the prediction of the Higgs boson mass are briefly discussed.