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

Christian Schwinn
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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_ξgauge. 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 ν_e u\bar d. The violations of gauge invariance caused by the introduction of running coupling constants are analyzed.

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Christian Schwinn. 2003-12-17. Gauge checks, consistency of approximation schemes and numerical evaluation of realistic scattering amplitudes. https://arxiv.org/abs/hep-ph/0307057

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