Gauge checks, consistency of approximation schemes and numerical evaluation of realistic scattering amplitudes [Elektronische Ressource] / von Christian Schwinn

Gauge checks, consistency ofapproximation schemes and numericalevaluation of realistic scatteringamplitudesVom Fachbereich Physikder Technischen Universitat Darmstadt¨zur Erlangung des Gradeseines Doktors der Naturwissenschaften(Dr. rer. nat.)genehmigte Dissertation vonDipl.-Phys. Christian Schwinnaus DarmstadtReferent: Prof. Dr. P.ManakosKorreferent: Prof.Dr. N.GreweTag der Einreichung: 18.4.2003Tag der Prufung: 23.6.2003¨Darmstadt 2003D1723AbstractIn this work we discuss both theoretical tools to verify gauge invariance innumerical calculations of cross sections and the consistency of approximationschemes used in realistic calculations.We determine a finite set of Ward Identities for 4 point scattering ampli-tudes that is sufficient to verify the correct implementation of Feynman rulesof a spontaneously broken gauge theory in a model independent way. Theseidentities have been implemented in the matrix element generator O’Mega andhave been used to verify the implementation of the complete Standard ModelinR gauge. As a theoretical tool, we derive a new identity for vertex functionsξwith several momentum contractions.The problem of the consistency of approximation schemes in tree level cal-culations is discussed in the last part of this work. We determine the gauge in-variance classes of spontaneously broken gauge theories, providing a new prooffor the formalism of gauge and flavor flips.