The Strong Coupling and the Bottom Mass in Supersymmetric Grand Unified Theories

We apply the full one-loop corrections to the masses, gauge couplings, and Yukawa couplings in the minimal supersymmetric standard model. We focus on predictions for the strong coupling and the bottom-quark pole mass in the context of SU(5) supersymmetric grand unification. We discuss our results in both the small and large $\tan\beta$ regimes. We demonstrate that the finite (non-logarithmic) corrections to the weak mixing angle are essential in determining $\alpha_s$ and $m_b$ when some superpartner masses are light. Minimal SU(5) predicts acceptable $\alpha_s$ and $m_b$ only at small $\tan\beta$ with SUSY masses of $\cal O$(TeV). The missing doublet model accommodates gauge and Yukawa coupling unification for small or large $\tan\beta$, and for any SUSY mass scale. In the large $\tan\beta$ case, the bottom mass is acceptable only if the Higgsino mass parameter $\mu$ is positive.