The Bottom Mass Prediction in Supersymmetric Grand Unification; Uncertainties and Constraints

Abstract

Grand unified theories often predict unification of Yukawa couplings (e.g., $h_b=h_{\tau }$), 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 ${\alpha }_s$ are discussed. Constraints on the $\tan \beta$ range in such models and an upper bound on the $t$-quark pole mass are given and are shown to be affected by the ${\alpha }_s-m_t$ correlation. Constraints on the low-scale thresholds are found to be weakened by uncertainties associated with the high-scale.

23 pages + 7 figures (figures are available upon request), LaTex + RevTex 3.0, UPR-0556T

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