Gauge checks, consistency of approximation schemes and numerical evaluation of realistic scattering amplitudes

Abstract

We discuss both theoretical tools to verify gauge invariance in numerical calculations of cross sections and the consistency of approximation schemes used in realistic calculations. A finite set of Ward Identities for 4 point scattering amplitudes is determined, that is sufficient to verify the correct implementation of Feynman rules of a spontaneously broken gauge theory in a model independent way. These identities have been implemented in the matrix element generator O'Mega and have been used to verify the implementation of the complete Standard Model in R_\xi gauge. The consistency of approximation schemes in tree level calculations is discussed in the last part of this work. We determine the gauge invariance classes of spontaneously broken gauge theories, providing a new proof for the formalism of gauge and flavor flips. The schemes for finite width effects that have been implemented in O'Mega are reviewed. As a comparison with existing calculations, we study the consistency of these schemes in the process e^-e^+\to e^- \bar \nu_e u\bar d. The violations of gauge invariance caused by the introduction of running coupling constants are analyzed.