Single-scale Renormalisation Group Improvement of Multi-scale Effective Potentials

Abstract

We present a new method for renormalisation group improvement of the effective potential of a quantum field theory with an arbitrary number of scalar fields. The method amounts to solving the renormalisation group equation for the effective potential with the boundary conditions chosen on the hypersurface where quantum corrections vanish. This hypersurface is defined through a suitable choice of a field-dependent value for the renormalisation scale. The method can be applied to any order in perturbation theory and it is a generalisation of the standard procedure valid for the one-field case. In our method, however, the choice of the renormalisation scale does not eliminate individual logarithmic terms but rather the entire loop corrections to the effective potential. It allows us to evaluate the improved effective potential for arbitrary values of the scalar fields using the tree-level potential with running coupling constants as long as they remain perturbative. This opens the possibility of studying various applications which require an analysis of multi-field effective potentials across different energy scales. In particular, the issue of stability of the scalar potential can be easily studied beyond tree level.

38 pages (including 8 pages of appendices), 9 figures, v2: minor changes, matches published version

References in corpus (5)

• Consistent Use of the Standard Model Effective Potential
• Consistent Use of Effective Potentials
• Neutrino Masses and Conformal Electro-Weak Symmetry Breaking
• Interplay of Infrared Divergences and Gauge-Dependence of the Effective Potential
• Multi-scale Renormalization Group Methods for Effective Potentials with Multiple Scalar Fields

Cited by in corpus (29)

• Strong gravitational radiation from a simple dark matter model
• Primordial Black Holes in Higgs-$R^2$ Inflation as a Whole Dark Matter
• Field-theoretic derivation of bubble-wall force
• Gravitational waves from conformal symmetry breaking
• Conformal model for gravitational waves and dark matter: A status update
• The 1-loop effective potential for the Standard Model in curved spacetime
• Gravitational waves from supercooled phase transitions: dimensional transmutation meets dimensional reduction
• Algorithmic Boundedness-From-Below Conditions for Generic Scalar Potentials
• Systematic analysis of radiative symmetry breaking in models with extended scalar sector
• Renormalization Group Improvement of the Effective Potential: an EFT Approach
• Vacuum Stability Conditions for Higgs Potentials with $SU(2{)}_L$ Triplets
• The BRST-invariant vacuum state of the Gribov-Zwanziger theory
• Finite-temperature bubble nucleation with shifting scale hierarchies
• Consistent Conformal Extensions of the Standard Model
• Geometry of Flat Directions in Scale-Invariant Potentials
• Grand unification and the Planck scale: An $SO(10)$ example of radiative symmetry breaking
• Conformal symmetry and the cosmological constant problem
• Minima of Classically Scale-Invariant Potentials
• Electroweak phase transition triggered by fermion sector
• High Scale Boundary Conditions in Models with Two Higgs Doublets
• Vacuum Stability in the one-loop approximation of a 331 Model
• Supercooled phase transitions in conformal dark sectors explain NANOGrav data
• Gravitational waves from supercooled phase transitions in conformal Majoron models of neutrino mass
• The KSVZ Axion Model with Quasi-Degenerate Minima: A Unified Model for Dark Matter and Dark Energy
• Construction of RG improved effective potential in a two real scalar system
• The hierarchy problem and fine-tuning in a decoupling approach to multi-scale effective potentials
• Vacuum stability of Froggatt-Nielsen models
• A model with light and heavy scalars in view of the effective theory
• Theoretical and Experimental Constraints on ${\mathbb{Z}}_{2n}$ Multi-Component Dark Matter Models