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Feynman rules for the rational part of the electroweak 1-loop amplitudes. (English) Zbl 1269.81214
Summary: We present the complete set of Feynman rules producing the rational terms of kind \(R_{2}\) needed to perform any 1-loop calculation in the Electroweak Standard Model. Our results are given both in the ’t Hooft-Veltman and in the Four Dimensional Helicity regularization schemes. We also verified, by using both the ’t Hooft-Feynman gauge and the Background Field Method, a huge set of Ward identities -up to 4-points- for the complete rational part of the Electroweak amplitudes. This provides a stringent check of our results and, as a by-product, an explicit test of the gauge invariance of the Four Dimensional Helicity regularization scheme in the complete Standard Model at 1-loop. The formulae presented in this paper provide the last missing piece for completely automatizing, in the framework of the OPP method, and in any other approach using 4-dimensional numerators, the 1-loop calculations in the \(SU(3) \times SU(2) \times U(1)\) Standard Model.

MSC:
81V22 Unified quantum theories
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
81T18 Feynman diagrams
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