[Paper Review] Higgs Mechanism in Scale-Invariant Gravity

Ichiro Oda|arXiv (Cornell University)|Aug 20, 2013

Cosmology and Gravitation Theories11 references4 citations

TL;DR

This paper proposes a novel Higgs mechanism in scale-invariant gravity where spontaneous breaking of scale invariance—driven by non-minimal coupling of scalar fields to curvature—induces spontaneous gauge symmetry breaking without a Higgs potential. The mechanism generates masses for gauge bosons and predicts a dilaton with a GeV-scale mass due to quantum corrections, even if classically massless.

ABSTRACT

We consider a Higgs mechanism in scale-invariant theories of gravitation. It is shown that in spontaneous symmetry breakdown of scale invariance, gauge symmetries are also broken spontaneously even without the Higgs potential if the corresponding charged scalar fields couple to a scalar curvature in a non-minimal way. In this gravity-inspired new Higgs mechanism, the non-minimal coupling term, which is scale-invariant, plays a critical role. Various generalizations of this mechanism are possible and particularly the generalizations to non-abelian gauge groups and a scalar field with multi-components are presented in some detail. Moreover, we apply our finding to a scale-invariant extension of the standard model (SM) and calculate radiative corrections. In particular, we elucidate the coupling between the dilaton and the Higgs particle and show that the dilaton mass takes a value around the GeV scale owing to quantum effects even if the dilaton is massless at the classical level.

Motivation & Objective

• To resolve the hierarchy problem in the Standard Model by replacing supersymmetry with scale invariance.
• To demonstrate that spontaneous gauge symmetry breaking can occur without a Higgs potential, relying instead on non-minimal coupling in scale-invariant gravity.
• To extend the mechanism to non-Abelian gauge groups and multi-component scalar fields.
• To compute radiative corrections in a scale-invariant extension of the Standard Model and determine the dilaton mass.
• To show that the dilaton acquires a quantum-generated mass around the GeV scale despite being massless at the classical level.

Proposed method

• Formulates a scale-invariant gravitational theory with a scalar field coupled non-minimally to the Ricci scalar via a coupling parameter ξ.
• Introduces a Higgs-like scalar field Φ with a U(1) gauge symmetry and non-minimal coupling to gravity: ξΦ†ΦR.
• Applies the principle of scale invariance to derive the dilatation current and identify the dilaton as the Nambu-Goldstone boson of broken scale symmetry.
• Uses dimensional regularization in D dimensions to compute one-loop radiative corrections to the scalar potential.
• Applies Feynman parameter techniques and beta function identities to evaluate loop integrals and extract divergent and finite parts.
• Derives the effective potential and determines the quantum-corrected mass of the dilaton from the curvature of the potential at the minimum.

Experimental results

Research questions

• RQ1 Can spontaneous gauge symmetry breaking occur in the absence of a Higgs potential in a scale-invariant gravitational framework?
• RQ2 What is the role of non-minimal coupling between scalar fields and curvature in triggering spontaneous symmetry breaking?
• RQ3 How do radiative corrections affect the mass of the dilaton in a scale-invariant extension of the Standard Model?
• RQ4 Can the hierarchy problem be resolved through scale invariance rather than supersymmetry?
• RQ5 What is the physical mass scale of the dilaton after quantum corrections are included?

Key findings

• Spontaneous breaking of scale invariance via non-minimal coupling to gravity induces spontaneous breaking of gauge symmetries even without a Higgs potential.
• The non-minimal coupling term ξΦ†ΦR is essential and scale-invariant, serving as the dynamical trigger for symmetry breaking.
• The model generalizes naturally to non-Abelian gauge groups and multi-component scalar fields, preserving scale invariance.
• In the scale-invariant extension of the Standard Model, radiative corrections generate a quantum mass for the dilaton.
• The dilaton mass is predicted to be on the order of the GeV scale, despite being massless at the classical level.
• The effective potential calculation shows that quantum corrections stabilize the scalar field at a non-zero vacuum expectation value, leading to mass generation.