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

Abstract

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 $\mathcal{O}$(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.

Comments: 10 pages, epsf, 7 figures included. Talk given at the PASCOS Symposium/Johns Hopkins Workshop, Baltimore, MD, March 22-25, 1995