Planck and Electroweak Scales Emerging from Conformal Gravity

TL;DR

This paper demonstrates how conformal gravity can generate both the Planck and electroweak scales through the Coleman-Weinberg mechanism, explaining the hierarchy via a tiny coupling constant.

Contribution

It introduces a two-step process where conformal gravity induces the Planck scale and transmits it to generate the electroweak scale, providing a novel explanation for the hierarchy.

Findings

Planck scale generated via conformal gravity and Coleman-Weinberg mechanism.

Electroweak scale transmitted through scalar field vacuum expectation value.

Hierarchy explained by a very small scalar-Higgs coupling.

Abstract

We show that both the Planck and electroweak mass scales can be generated from conformal gravity via the Coleman-Weinberg mechanism of dimensional transmutation. At the first step, the Planck scale is generated via the Coleman-Weinberg mechanism in the sector of conformal gravity, which means that radiative corrections associated with gravitons induce spontaneous symmetry breakdown of a local conformal symmetry. At the second step, the vacuum expectation value of a scalar field is transmitted to the sector of the standard model via a potential involving the conformally invariant part and the contribution from the Coleman-Weinberg mechanism, thereby generating the electroweak scale. The huge hierarchy between the two scales can be explained in terms of a very tiny coupling constant between the scalar and the Higgs field in a consistent way.