Supersymmetricb−τunification, gauge unification, and fixed points

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 ${\alpha }_s\left(M_Z\right)\approx 0.11$]. In particular, the requirement that the $t$ Yukawa coupling $h_t$ 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 $h_t$ shift the fixed-point curve in the $m_t-tan\beta$ plane. The implications for the prediction of the Higgs boson mass are briefly discussed.