Implications of precision electroweak experiments formt,ρ0,sin2θW, and grand unification
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Abstract
The implications of precision $Z$-pole, $W$-mass, and weak-neutral-current data for SU(2)\ifmmode\times\else\texttimes\fi{}U(1) models are described. Within the minimal model one finds ${{sin}^{2}\stackrel{^}{\ensuremath{\theta}}}_{W}({M}_{Z})=0.2334\ifmmode\pm\else\textpm\fi{}0.0008$ in the modified minimal subtraction scheme or ${{sin}^{2}\ensuremath{\theta}}_{W}\ensuremath{\equiv}1\ensuremath{-}\frac{{M}_{W}^{2}}{{M}_{Z}^{2}}=0.2291\ifmmode\pm\else\textpm\fi{}0.0034$ in the on-shell scheme, where the uncertainties include the ${m}_{t}$ and ${M}_{H}$ dependence. The top-quark mass is predicted to be ${124}_{\ensuremath{-}34\ensuremath{-}15}^{+28+20}$ GeV, where the second uncertainty is from ${M}_{H}$, with ${m}_{t}<174(182)$ GeV at 90 (95)% C.L. For the first time subleading effects and vertex corrections allow a significant separation of ${m}_{t}$ and ${\ensuremath{\rho}}_{0}$ in models with a nonminimal Higgs structure. Allowing arbitrary ${m}_{t}$ and Higgs representations one obtains ${{sin}^{2}\stackrel{^}{\ensuremath{\theta}}}_{W}({M}_{Z})=0.2333\ifmmode\pm\else\textpm\fi{}0.0008$, ${\ensuremath{\rho}}_{0}=0.992\ifmmode\pm\else\textpm\fi{}0.011$, and ${m}_{t}<294(310)$ 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 ${M}_{Z}\ensuremath{-}1$ TeV range. Ordinary grand unified theories breaking to the standard model in more than one step are also discussed.