Minima of Classically Scale-Invariant Potentials

Abstract

We propose a new formalism to analyse the extremum structure of scale-invariant effective potentials. The problem is stated in a compact matrix form, used to derive general expressions for the stationary point equation and the mass matrix of a multi-field RG-improved effective potential. Our method improves on (but is not limited to) the Gildener-Weinberg approximation and identifies a set of conditions that signal the presence of a radiative minimum. When the conditions are satisfied at different scales, or in different subspaces of the field space, the effective potential has more than one radiative minimum. We illustrate the method through simple examples and study in detail a Standard-Model-like scenario where the potential admits two radiative minima. Whereas we mostly concentrate on biquadratic potentials, our results carry over to the general case by using tensor algebra.

43 pages, 6 figures, published version

References in corpus (20)

• Conformal Symmetry and the Standard Model
• Scale invariance, unimodular gravity and dark energy
• A solution to the hierarchy problem from an almost decoupled hidden sector within a classically scale invariant theory
• Gravitational Waves from Warped Spacetime
• Electroweak Higgs as a pseudo-Goldstone boson of broken scale invariance
• The Minimal Scale Invariant Extension of the Standard Model
• Taming Infrared Divergences in the Effective Potential
• Taming the Goldstone contributions to the effective potential
• Neutrino mass in radiatively-broken scale-invariant models
• Dark Matter from a Classically Scale-Invariant $SU(3{)}_X$
• Coleman-Weinberg linear inflation: metric vs. Palatini formulation
• Embedding inflation into the Standard Model - more evidence for classical scale invariance
• Light Dark Matter, Naturalness, and the Radiative Origin of the Electroweak Scale
• Majorana dark matter in a classically scale invariant model
• Avoiding the Goldstone Boson Catastrophe in general renormalisable field theories at two loops
• Inflation and reheating in scale-invariant scalar-tensor gravity
• Multi-scale Renormalization Group Methods for Effective Potentials with Multiple Scalar Fields
• Renormalization Group Improvement of the Effective Potential: an EFT Approach
• Singular Values and Eigenvalues of Tensors: A Variational Approach
• Dynamical Symmetry Breaking and Fermion Mass Hierarchy in the Scale-Invariant 3-3-1 Model

Cited by in corpus (4)

• Conformal model for gravitational waves and dark matter: A status update
• Scale-Invariant Quadratic Gravity and Inflation in the Palatini Formalism
• Scale Invariant FIMP Miracle
• Grand unification and the Planck scale: An $SO(10)$ example of radiative symmetry breaking