Implications of precision electroweak experiments for $m_t$, ${\rho }_0$, ${{sin}^2\theta }_W$, and grand unification

The implications of precision $Z$-pole, $W$-mass, and weak-neutral-current data for SU(2)×U(1) models are described. Within the minimal model one finds ${{sin}^2\hat{\theta }}_W\left(M_Z\right)=0.2334\mathrm{}\pm 0.0008$ in the modified minimal subtraction scheme or ${{sin}^2\theta }_W\equiv 1-\frac{M_W^2}{M_Z^2}=0.2291\mathrm{}\pm 0.0034$ in the on-shell scheme, where the uncertainties include the $m_t$ and $M_H$ dependence. The top-quark mass is predicted to be ${124}_{-34-15\mathrm{}}^{+28+20\mathrm{}}$ GeV, where the second uncertainty is from $M_H$, with $m_t<174\mathrm{}\mathrm{}\left(182\right)\mathrm{}$ GeV at 90 (95)% C.L. For the first time subleading effects and vertex corrections allow a significant separation of $m_t$ and ${\rho }_0$ in models with a nonminimal Higgs structure. Allowing arbitrary $m_t$ and Higgs representations one obtains ${{sin}^2\hat{\theta }}_W\left(M_Z\right)=0.2333\mathrm{}\pm 0.0008$, ${\rho }_0=0.992\mathrm{}\pm 0.011$, and $m_t<294\mathrm{}\mathrm{}\left(310\right)\mathrm{}$ GeV. The implications of these results for ordinary and supersymmetric grand unified theories are considered. Supersymmetric theories with a grand desert between the supersymmetry and unification scales are in striking agreement with data for $M_{\mathrm{SUSY}}$ in the $M_Z-1\mathrm{}$ TeV range. Ordinary grand unified theories breaking to the standard model in more than one step are also discussed.