Incorporation of QCD Effects in Basic Corrections of the Electroweak Theory

Abstract

We study the incorporation of QCD effects in the basic electroweak corrections \drcar, \drcarw, and \dr. They include perturbative \Ord{\alpha\alpha_s} contributions and $t\bar{t}$ threshold effects. The latter are studied in the resonance and Green-function approaches, in the framework of dispersion relations that automatically satisfy relevant Ward identities. Refinements in the treatment of the electroweak corrections, in both the \ms\ and the on-shell schemes of renormalization, are introduced, including the decoupling of the top quark in certain amplitudes, its effect on $\hat{e}^2(\mz)$ and \sincarmz, the incorporation of recent results on the leading irreducible \Ord{\alpha^2} corrections, and simple expressions for the residual, i.e.\ ``non-electromagnetic'', parts of \drcar, \drcarw, and \dr. The results are used to obtain accurate values for \mw\ and \sincarmz, as functions of \mt\ and \mh. The higher-order effects induce shifts in these parameters comparable to the expected experimental accuracy, and they increase the prediction for \mt\ derived from current measurements. The \ms\ and the on-shell calculations of \dr, in a recently proposed formulation, are compared and found to be in excellent agreement over the wide ranges $60\GeV \leq \mh \leq 1 \TeV$, $\mz \leq \mt \leq 250 \GeV$.