Classically Scale-invariant B-L Model and Conformal Gravity

TL;DR

This paper explores a conformal gravity model coupled with a classically scale-invariant B-L extended standard model, showing spontaneous symmetry breaking and gauge field mass generation without relying on the Coleman-Weinberg mechanism.

Contribution

It demonstrates that in conformal gravity, B-L symmetry breaks spontaneously at tree level, fixing parameters and avoiding a massless dilaton, which is a novel insight.

Findings

B-L gauge symmetry breaks spontaneously without Coleman-Weinberg mechanism.

Massive B-L gauge field generated via Higgs mechanism.

Parameters fixed by conformal gravity, no massless dilaton appears.

Abstract

We consider a coupling of conformal gravity to the classically scale-invariant B-L extended standard model which has been recently proposed as a phenomenologically viable model realizing the Coleman-Weinberg mechanism of breakdown of the electro-weak symmetry. As in a globally scale-invariant dilaton gravity, it is also shown in a locally scale-invariant conformal gravity that without recourse to the Coleman-Weinberg mechanism, the B-L gauge symmetry is broken in the process of spontaneous symmetry breakdown of the local scale invariance (Weyl invariance) at the tree level and as a result the B-L gauge field becomes massive via the Higgs mechanism. As a bonus of conformal gravity, the massless dilaton field does not appear and the parameters in front of the non-minimal coupling of gravity are completely fixed in the present model. This observation clearly shows that the conformal gravity has a practical application even if the scalar field does not possess any dynamical degree of freedom owing to the local scale symmetry.