Gauge invariance, gauge-parameter independence and properties of Green functions

The application of the background-field method to the electroweak Standard Model is reviewed and further explored. Special emphasis is put on questions of gauge invariance and gauge-parameter (in-)dependence. Owing to the gauge invariance of the background-field effective action, the vertex functions obey simple Ward identities which imply important properties of the vertex functions. Carrying out the renormalization in a way respecting background-field gauge invariance leads to considerable simplifications. The generalization of the background-field method to the non-linear realization of the scalar sector of the Standard Model is illustrated. Furthermore, the interplay between gauge independence of the S-matrix and Ward identities of vertex functions is investigated. Finally, the Standard Model contributions to the S, T , and U parameters are calculated and discussed within the background-field method. To appear in the proceedings of the Ringberg Workshop “Perspectives for electroweak interactions in ee collisions”, Ringberg Castle, February 5-8, 1995, ed. B.A. Kniehl. E-mail: [email protected] Supported by the Bundesministerium für Bildung und Forschung, Bonn, Germany. GAUGE INVARIANCE, GAUGE-PARAMETER INDEPENDENCE AND PROPERTIES OF GREEN FUNCTIONS A. DENNER Institut für Theoretische Physik, Universität Würzburg Am Hubland, D-97074 Würzburg, Germany and S. DITTMAIER, G. WEIGLEIN Theoretische Physik, Universität Bielefeld Postfach 10 01 31, D-33501 Bielefeld, Germany ABSTRACT The application of the background-field method to the electroweak Standard Model is reviewed and further explored. Special emphasis is put on questions of gauge invariance and gauge-parameter (in-)dependence. Owing to the gauge invariance of the background-field effective action, the vertex functions obey simple Ward identities which imply important properties of the vertex functions. Carrying out the renormalization in a way respecting background-field gauge invariance leads to considerable simplifications. The generalization of the background-field method to the non-linear realization of the scalar sector of the Standard Model is illustrated. Furthermore, the interplay between gauge independence of the S-matrix and Ward identities of vertex functions is investigated. Finally, the Standard Model contributions to the S, T , and U parameters are calculated and discussed within the background-field method.The application of the background-field method to the electroweak Standard Model is reviewed and further explored. Special emphasis is put on questions of gauge invariance and gauge-parameter (in-)dependence. Owing to the gauge invariance of the background-field effective action, the vertex functions obey simple Ward identities which imply important properties of the vertex functions. Carrying out the renormalization in a way respecting background-field gauge invariance leads to considerable simplifications. The generalization of the background-field method to the non-linear realization of the scalar sector of the Standard Model is illustrated. Furthermore, the interplay between gauge independence of the S-matrix and Ward identities of vertex functions is investigated. Finally, the Standard Model contributions to the S, T , and U parameters are calculated and discussed within the background-field method.