The Renormalization of the Electroweak Standard Model to All Orders

TL;DR

This paper establishes a comprehensive algebraic renormalization framework for the electroweak Standard Model, ensuring consistent, scheme-independent Green functions to all perturbation orders, with detailed attention to gauge symmetry and mass diagonalization.

Contribution

It provides the first all-orders algebraic renormalization of the electroweak Standard Model based on symmetry principles without relying on specific regularization schemes.

Findings

Green functions are uniquely constructed to all orders.

Normalization conditions align with algebraic symmetry constraints.

Mass diagonalization of neutral vectors and ghosts is explicitly addressed.

Abstract

We give the renormalization of the standard model of electroweak interactions to all orders of perturbation theory by using the method of algebraic renormalization, which is based on general properties of renormalized perturbation theory and not on a specific regularization scheme. The Green functions of the standard model are uniquely constructed to all orders, if one defines the model by the Slavnov-Taylor identity, Ward-identities of rigid symmetry and a specific form of the abelian local gauge Ward-identity, which continues the Gell-Mann Nishijima relation to higher orders. Special attention is directed to the mass diagonalization of massless and massive neutral vectors and ghosts. For obtaining off-shell infrared finite expressions it is required to take into account higher order corrections into the functional symmetry operators. It is shown, that the normalization conditions of the on-shell schemes are in agreement with the most general symmetry transformations allowed by the algebraic constraints.