Dynamical generation of electroweak scale from the conformal sector: A strongly coupled Higgs via the Dyson--Schwinger approach

Abstract

We propose a novel pathway to generate the electroweak (EW) scale via non-perturbative dynamics of a conformally invariant scalar sector at the classical level. We provide a method to estimate the non-perturbative EW scale generation using the exact solution of the background equations of motion in a scalar theory via the Dyson-Schwinger approach. Particularly, we find an analytical result for the Higgs mass in the strongly coupled regime in terms of its quartic self interaction term and the cut-off scale of the theory. We also show that the Higgs sector is an essential part of the Standard Model as, without it, a Yang--Mills gauge theory cannot acquire mass even if a self-interaction term is present. Our analysis lead to a more realistic model building with possible solutions to the gauge hierarchy problem and, in general, to the dynamical generation of any scales scales in nature, be it the visible sector or the dark sector.

18 pages, 1 figure; comments are welcome

References in corpus (18)

• Conformal Symmetry and the Standard Model
• A solution to the hierarchy problem from an almost decoupled hidden sector within a classically scale invariant theory
• Electroweak Higgs as a pseudo-Goldstone boson of broken scale invariance
• The Minimal Scale Invariant Extension of the Standard Model
• Dark Matter from a Classically Scale-Invariant $SU(3{)}_X$
• Dynamical generation of the weak and Dark Matter scales from strong interactions
• Infrared Gluon and Ghost Propagators
• Embedding inflation into the Standard Model - more evidence for classical scale invariance
• Naturalness and Dimensional Transmutation in Classically Scale-Invariant Gravity
• Inflation in scale-invariant theories of gravity
• Light Dark Matter, Naturalness, and the Radiative Origin of the Electroweak Scale
• Dimensional Transmutation in Gravity and Cosmology
• Mapping a Massless Scalar Field Theory on a Yang-Mills Theory: Classical Case
• Inflation and reheating in scale-invariant scalar-tensor gravity
• Proof of triviality of $\lambda {\varphi }^4$ theory
• Yang-Mills Propagators and QCD
• Quark confinement in QCD in the 't Hooft limit
• Effective potential in non-perturbative gauge theories

Cited by in corpus (3)

• Discrete Dyson-Schwinger equations
• Non-perturbative Origin of Electroweak Scale via Higgs-portal: Dyson-Schwinger in Conformally Invariant Scalar Sector
• Non-perturbative Origin of the Electroweak Scale: RGE in Strongly-coupled Dark Gauge Theories via Dyson-Schwinger