The Standard Model and its Generalisations in Epstein-Glaser Approach to Renormalisation Theory

TL;DR

This paper extends the Epstein-Glaser approach to non-Abelian gauge theories with massive spin-one bosons, revealing new group-theoretical conditions and mass relations, and generalizing the standard model's uniqueness without restrictions on gauge groups or mass spectra.

Contribution

It generalizes the Epstein-Glaser renormalization framework to include massive gauge bosons and derives new group-theoretical conditions and mass relations in the standard model context.

Findings

Emergence of a gauge group structure with massive bosons

Existence of a representation of the gauge group related to Higgs fields

Mass relations connecting structure constants and boson masses

Abstract

We continue our study of non-Abelian gauge theories in the framework of Epstein-Glaser approach to renormalisation theory. We consider the case when massive spin-one Bosons are present into the theory and we modify appropriately the analysis of the origin of gauge invariance performed in a preceding paper in the case of null-mass spin-one Bosons. Then we are able to extend a result of D\"utsch and Scharf concerning the uniqueness of the standard model consistent with renormalisation theory. In fact we consider the most general case i.e. the consistent interaction of $r$ spin-one Bosons and we do not impose any restriction on the gauge group and the mass spectrum of the theory. We show that, beside the natural emergence of a group structure (like in the massless case) we obtain, new conditions of group-theoretical nature, namely the existence of a certain representation of the gauge group associated to the Higgs fields. Some other mass relations connecting the structure constants of the gauge group and the masses of the Bosons emerge naturally. The proof is done using Epstein-Glaser approach to renormalisation theory.