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

We derive the Callan-Symanzik equation of the electroweak Standard Model in the QED-like on-shell parameterization. The various coefficient functions, the beta-functions and anomalous dimensions, are determined in one-loop or der in the most general linear gauge compatible with rigid symmetry. In thi s way the basic elements for a systematic investigation of higher-order lea ding logarithmic contributions in the Standard Model are provided. The one- loop beta-function of the electromagnetic coupling turns out to be independ ent of mass ratios and it is QED-like in this sense. Besides the QED-contri butions of fermions it contains non-abelian contributions from vectors and ghosts with negative sign, which overcompensate the contributions of the fe rmions if one restricts the latter to one fermion generation. We also compa re our results with the symmetric theory and give relations between the bet a-functions of the spontaneously broken and the symmetric theory valid in o ne-loop order. (C) 1999 Elsevier Science B.V. All rights reserved.