X iv : h ep - p h / 93 06 20 5 v 1 1 J un 1 99 3 The Bottom Mass Prediction in Supersymmetric Grand Unification : Uncertainties and Constraints

Grand unified theories often predict unification of Yukawa couplings (e.g., h b = h τ), and thus certain relations among fermion masses. The latter can distinguish these from models that predict only coupling constant unification. The implications of Yukawa couplings of the heavy-family in the supersymmetric extension of the standard model (when embedded in a GUT) are discussed. In particular, uncertainties associated with m t and m b , threshold corrections at the low-scale, and threshold and nonrenormalizable-operator corrections associated with a grand-unified sector at the high-scale are parametrized and estimated. The implication of these and of the correlation between m t and the prediction for α s are discussed. Constraints on the tan β range in such models and an upper bound on the t-quark pole mass are given and are shown to be affected by the α s − m t correlation. Constraints on the low-scale thresholds are found to be weakened by uncertainties associated with the high-scale.