Coupling Constant and Yukawa Coupling Unifications: Uncertainties and Constraints

The status of coupling constant unification (with and without a unification of Yukawa couplings) is discussed. Uncertainties associated with the input coupling constants, $m_{b}$ and $m_{t}$, threshold corrections at the low and high scale, and possible nonrenormalizable operators are described and a discrepancy between effective and physical scales is pointed out. Theoretical uncertainties in the predictions of $\alpha_{s}(M_{Z})$, $m_{b}$, and the unification scale, $M_{G}$, are discussed and estimated. Constraints on the super-partner spectrum are found to be weak if uncertainties associated with the high-scale are included. However, requiring $h_{b} = h_{\tau}$ at $M_{G}$ excludes $3 < \tan \beta < 40$ (for $m_{t} < 200$ GeV).