Symmetry breaking of gauge theories down to Abelian sub-groups

TL;DR

This paper presents a novel derivation of the effective Lagrangian for electro-weak symmetry breaking, avoiding Goldstone's theorem and custodial symmetry assumptions, by analyzing gauge symmetry breaking from G to an Abelian subgroup K.

Contribution

It introduces a gauge-invariant functional with a free parameter that interpolates between the full gauge group G and its Abelian subgroup K, providing new insights into symmetry breaking mechanisms.

Findings

Derived the effective Lagrangian without Goldstone's theorem.

Constructed a gauge-invariant functional with a tunable parameter.

Connected gauge symmetry breaking to a continuous parameter v.

Abstract

I re-derive the lowest order effective Lagrangian for electro-weak symmetry breaking without the use of Goldstone's theorem for spontaneously broken global symmetries and without the assumption of a custodial symmetry. I consider the breaking of a local symmetry with gauge group G down to an Abelian sub-group K and construct a gauge-invariant functional with one free parameter v, such that v=0 corresponds to a gauge theory with gauge group G, while v --> infinity corresponds to a gauge theory with gauge group K.