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.

arXiv comment43 pages, 6 figures, published version

References in corpus (74)

• SARAH 4: A tool for (not only SUSY) model builders
• Conformal Symmetry and the Standard Model
• The effective potential and the renormalisation group
• Classically Conformal B-L extended Standard Model
• Vacuum Stability Conditions From Copositivity Criteria
• Scale invariance, unimodular gravity and dark energy
• Two-loop effective potential for a general renormalizable theory and softly broken supersymmetry
• A solution to the hierarchy problem from an almost decoupled hidden sector within a classically scale invariant theory
• Stability and Symmetry Breaking in the General Two-Higgs-Doublet Model
• Gravitational Waves from Warped Spacetime
• Two-loop Renormalization Group Equations in General Gauge Field Theories
• Emergence of the Electroweak Scale through the Higgs Portal
• Dynamically Induced Planck Scale and Inflation
• Electroweak Higgs as a pseudo-Goldstone boson of broken scale invariance
• Some Cosmological Implications of Hidden Sectors
• Physical Naturalness and Dynamical Breaking of Classical Scale Invariance
• Towards Completing the Standard Model: Vacuum Stability, EWSB and Dark Matter
• Inflation and Dark Matter in the Higgs Portal of Classically Scale Invariant Standard Model
• Vacuum Stability of a General Scalar Potential of a Few Fields
• Dark matter and neutrino masses from a scale-invariant multi-Higgs portal
• The Minimal Scale Invariant Extension of the Standard Model
• Taming Infrared Divergences in the Effective Potential
• Phase transition and gravitational wave phenomenology of scalar conformal extensions of the Standard Model
• Taming the Goldstone contributions to the effective potential
• Neutrino mass in radiatively-broken scale-invariant models
• Dark Matter from a Classically Scale-Invariant $SU(3{)}_X$
• Two-Higgs-doublet model from the group-theoretic perspective
• Accidental Dark Matter: Case in the Scale Invariant Local $B-L$ Models
• Leptogenesis and Neutrino Oscillations in the Classically Conformal Standard Model with the Higgs Portal
• Improving the Effective Potential:Multi-Mass-Scale Case
• Coleman-Weinberg linear inflation: metric vs. Palatini formulation
• Dynamically induced Planck scale and inflation in the Palatini formulation
• Embedding inflation into the Standard Model - more evidence for classical scale invariance
• Constant-Roll (Quasi-)Linear Inflation
• The 1-loop effective potential for the Standard Model in curved spacetime
• Light Dark Matter, Naturalness, and the Radiative Origin of the Electroweak Scale
• Dark Matter in Classically Scale-Invariant Two Singlets Standard Model
• Stable mass hierarchies and dark matter from hidden sectors in the scale-invariant standard model
• A Radiative Model for the Weak Scale and Neutrino Mass via Dark Matter
• Radiative Corrections to Scalar Masses and Mixing in a Scale Invariant Two Higgs Doublet Model
• Nonminimal Coleman--Weinberg Inflation with an $R^2$ term
• Gravitational Waves from Pati-Salam Dynamics
• Linear inflation from quartic potential
• Viable dark matter via radiative symmetry breaking in a scalar singlet Higgs portal extension of the standard model
• The Effective Potential, the Renormalisation Group and Vacuum Stability
• Conformal Extensions of the Standard Model with Veltman Conditions
• Majorana dark matter in a classically scale invariant model
• The effective potential in the presence of several mass scales
• Minimal but non-minimal inflation and electroweak symmetry breaking
• Minimal conformal extensions of the Higgs sector
• Avoiding the Goldstone Boson Catastrophe in general renormalisable field theories at two loops
• Upgrading Sterile Neutrino Dark Matter to FI$m$P Using Scale Invariance
• Evolving Planck Mass in Classically Scale-Invariant Theories
• Natural Inflation with Hidden Scale Invariance
• Inflation and reheating in scale-invariant scalar-tensor gravity
• On three-loop RGE for the Higgs sector of 2HDM
• Conformal Complex Singlet Extension of the Standard Model: Scenario for Dark Matter and a Second Higgs Boson
• Multi-scale Renormalization
• First Order Electroweak Phase Transition from (Non)Conformal Extensions of the Standard Model
• A Scale-invariant Higgs Sector and Structure of the Vacuum
• A Multi-scale Subtraction Scheme and Partial Renormalization Group Equations in the $O(N)$-symmetric ${\varphi }^4$-theory
• Single-scale Renormalisation Group Improvement of Multi-scale Effective Potentials
• Algorithmic Boundedness-From-Below Conditions for Generic Scalar Potentials
• Multi-scale Renormalisation Group Improvement of the Effective Potential
• Cosmological constant in scale-invariant theories
• Systematic analysis of radiative symmetry breaking in models with extended scalar sector
• Multi-scale Renormalization Group Methods for Effective Potentials with Multiple Scalar Fields
• Renormalization Group Improvement of the Effective Potential: an EFT Approach
• Conformal Standard Model, Leptogenesis and Dark Matter
• Light Dark Matter
• Geometry of Flat Directions in Scale-Invariant Potentials
• Singular Values and Eigenvalues of Tensors: A Variational Approach
• Dynamical Symmetry Breaking and Fermion Mass Hierarchy in the Scale-Invariant 3-3-1 Model
• $WW$ scattering in a radiative electroweak symmetry breaking scenario

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• Scale Invariant FIMP Miracle
• Grand unification and the Planck scale: An $SO(10)$ example of radiative symmetry breaking