The Callan-Symanzik equation of the electroweak Standard Model and its 1-loop functions

Abstract

We derive the Callan-Symanzik equation of the electroweak Standard Model in the QED-like on-shell parameterization. The various coefficient functions, the $β$-functions and anomalous dimensions, are determined in one-loop order in the most general linear gauge compatible with rigid symmetry. In this way the basic elements for a systematic investigation of higher-order leading logarithmic contributions in the Standard Model are provided. The one-loop $β$-function of the electromagnetic coupling turns out to be independent of mass ratios and it is QED-like in this sense. Besides the QED-contributions of fermions it contains non-abelian contributions from vectors and ghosts with negative sign, which overcompensate the contributions of the fermions if one restricts the latter to one fermion generation. We also compare our results with the symmetric theory and give relations between the $β$-functions of the spontaneously broken and the symmetric theory valid in one-loop order.