Supersymmetric b-τ unification, gauge unification, and fixed points

The equality assumption of the b and τ 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 approx-gt 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 αs(MZ)≅0.11]. In particular, the requirement that the t Yukawa coupling ht is near its quasifixed 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-tanβ plane. The implications for the prediction of the Higgs boson mass are briefly discussed. copyright 1996 The American Physical Society