Precise Predictions for the Masses and Couplings in the Minimal Supersymmetric Standard Model

We present selected results of our program to determine the masses, gauge couplings, and Yukawa couplings of the minimal supersymmetric model in a full one-loop calculation. We focus on the precise prediction of the strong coupling alpha_s(M_Z) in the context of supersymmetric unification. We discuss the importance of including the finite corrections and demonstrate that the leading-logarithmic approximation can significantly underestimate alpha_s(M_Z) when some superpartner masses are light. We show that if GUT thresholds are ignored, and the superpartner masses are less than about 500 GeV, the prediction for alpha_s(M_Z) is quite large. We impose constraints from nucleon decay experiments and find that minimal SU(5) GUT threshold corrections increase alpha_s(M_Z) over most of the parameter space. We also consider the missing-doublet SU(5) model and find that it predicts preferred values for the strong coupling, even for a very light superpartner spectrum. We briefly discuss predictions for the bottom-quark mass in the small tan beta region.