Two-Loop Corrections and Top Threshold Effects in Calculation of Observables at the Z Peak.

Increasingly precise high-energy experiments now make possible tests at the quantum level of the Standard Model. This requires computation of the experimental observables in the field theory beyond tree level. Through these higher -order calculations one can relate experimental measurements to unknown parameters of the theory, such as the masses of the top quark and Higgs boson. We put limits on allowable values for the top quark mass, and once that mass is known our results will provide either a consistency check of the gauge field theory or evidence for new physics beyond the Standard Model. In this thesis electroweak observables at the Z peak, recently measured with very high precision, are evaluated, consistently including all of the dominant two -loop corrections. Corrections are expressed using the parameters Delta{r, rho} , and sin^2=theta_ {W}, which are formulated in terms of the dressed gauge boson propagators and are properly resummed. Top quark threshold effects are also studied in this framework. These are essentially non-perturbative; that is, they do not appear as a result of loop calculations. The effect of the threshold is calculated using dispersion relation techniques. We discuss the variation of the values of m_ {t} extracted from the LEP observables caused by inclusion of the two-loop corrections and of the threshold, comparing them to the uncertainty created by our lack of knowledge of M_{H} . The two-loop corrections are sizeable, and should be included in any attempt to extract the unknown top and Higgs masses from high-energy data. The threshold likewise changes the extracted value of m_{t } significantly.