Search

In this paper, we continue our study of calculating the cross section by the spinor method, i.e., performing the phase space integration using the spinor method. We have focused on the case where the physical momenta are massive and in pure 4D. We established the framework of such a new method and presented several examples, including two real progresses: $Z^0\to l^+ l^- H$ and $\bar{qq} \to \bar{ff} H^0$., 23 pages, 1 figure;further comments and references added

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 ${m}_{t}l174(182)$ 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 ${m}_{t}l294(310)$ 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.

The complete set of two-loop renormalization group equations in general gauge field theories is presented. This includes the $\ensuremath{\beta}$ functions of parameters with and without a mass dimension.