Application of the Background-Field Method to the electroweak Standard Model

TL;DR

The paper demonstrates that applying the background-field method to the electroweak Standard Model yields a gauge-invariant effective action and simple Ward identities, which in turn streamline renormalization and the calculation of Green functions. It develops a complete set of one-loop Feynman rules for the SM within the BFM, showing that counterterm structures become simpler and field renormalizations of gauge bosons become gauge-independent. The authors establish a consistent on-shell renormalization framework and discuss running couplings defined via Dyson summation, whose leading-log behavior aligns with renormalization-group expectations and remains robust against the quantum gauge parameter. Overall, the BFM offers conceptual and practical advantages for off-shell quantities and loop calculations, with Ward identities guaranteeing gauge-invariant results across schemes.

Abstract

Application of the background-field method yields a gauge-invariant effective action for the electroweak Standard Model, from which simple QED-like Ward identities are derived. As a consequence of these Ward identities, the background-field Green functions are shown to possess very desirable theoretical properties. The renormalization of the Standard Model in the background-field formalism is studied. A consistent on-shell renormalization procedure retaining the full gauge symmetry is presented. The structure of the counterterms is shown to greatly simplify compared to the conventional formalism. A complete list of Feynman rules for the Standard Model in the background-field method is given for arbitrary values of a quantum gauge parameter including all counterterms necessary for one-loop calculations.