Non-perturbative Origin of the Electroweak Scale: RGE in Strongly-coupled Dark Gauge Theories via Dyson-Schwinger

Abstract

We propose a novel pathway to generate the electroweak scale (EW) via non-perturbative dynamics of a dark gauge sector based on the SU(N) gauge group. Imposing the scale invariance of the theory, we investigate the electroweak symmetry breaking (EWSB) which is triggered dynamically via the condensation of gauge fields. Instead of the usual dimension-4 triggered breaking, a dimension 6 term (with Wilson coefficient compatible with SMEFT bounds) coupling the Higgs boson and the Yang-Mills field quadratic term in the Lagrangian provides feedback from the gauge to the Higgs sector. We provide a novel method to estimate a non-perturbative EW scale generation using the exact solution of a truncated set of the background equations of motion in Yang-Mills theory in terms of Jacobi elliptic functions and the exact beta-function valid in the strongly coupled regimes via the Dyson-Schwinger approach. Particularly, we find an analytical result for the Renormalization Group Equation (RGE) of the gauge coupling in the $SU(N)$ sector in the strongly-coupled regime. The dynamics studied in this paper pave the way to a more realistic model building with possible resolution to the hierarchy problem and, in general, dynamical generation of scales.

arXiv comment28 pages, 3 figures. Version matches the published one

References in corpus (67)

• Conformal Symmetry and the Standard Model
• Classically Conformal B-L extended Standard Model
• Agravity
• A solution to the hierarchy problem from an almost decoupled hidden sector within a classically scale invariant theory
• The minimal B-L model naturally realized at TeV scale
• Electroweak Symmetry Breaking induced by Dark Matter
• Emergence of the Electroweak Scale through the Higgs Portal
• Scale invariant extension of the standard model with strongly interacting hidden sector
• Dynamically Induced Planck Scale and Inflation
• Dynamical generation of the weak and Dark Matter scale
• Electroweak Higgs as a pseudo-Goldstone boson of broken scale invariance
• Natural Electroweak Symmetry Breaking from Scale Invariant Higgs Mechanism
• Supersymmetry Inspired QCD Beta Function
• Inflation and Dark Matter in the Higgs Portal of Classically Scale Invariant Standard Model
• Dark matter and neutrino masses from a scale-invariant multi-Higgs portal
• Electroweak and Conformal Symmetry Breaking by a Strongly Coupled Hidden Sector
• The Minimal Scale Invariant Extension of the Standard Model
• Solution of Schwinger-Dyson Equations for $\mathcal{P}\mathcal{T}$-Symmetric Quantum Field Theory
• Dark Matter from a Classically Scale-Invariant $SU(3{)}_X$
• Dynamical generation of the weak and Dark Matter scales from strong interactions
• Radiative Symmetry Breaking of the Minimal Left-Right Symmetric Model
• Infrared Gluon and Ghost Propagators
• Embedding inflation into the Standard Model - more evidence for classical scale invariance
• Electroweak Symmetry Breaking via QCD
• 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
• TeV Scale B-L model with a flat Higgs potential at the Planck scale -- in view of the hierarchy problem
• Dimensional Transmutation in Gravity and Cosmology
• Transmutation of nonlocal scale in infinite derivative field theories
• Mapping a Massless Scalar Field Theory on a Yang-Mills Theory: Classical Case
• Classically Scale Invariant Inflation, Supermassive WIMPs, and Adimensional Gravity
• Natural Inflation with Hidden Scale Invariance
• Inflation and reheating in scale-invariant scalar-tensor gravity
• The Neutrino Option
• Quantum Yang-Mills field theory
• Strongly coupled quantum field theory
• Induced Gravity I: Real Scalar Field
• Exact solutions of classical scalar field equations
• Induced Gravity II: Grand Unification
• Condition for confinement in non-Abelian gauge theories
• Conformal Realization of the Neutrino Option
• Global flow structure and exact formal transseries of the Gubser flow in kinetic theory
• Scalar field theory in the strong self-interaction limit
• Spectrum of Yang-Mills theory in 3 and 4 dimensions
• Confinement and Renormalization Group Equations in String-inspired Non-local Gauge Theories
• Strong coupling expansion for general relativity
• A theorem on the Higgs sector of the Standard Model
• Confinement in a three-dimensional Yang-Mills theory
• Infrared QCD
• On a novel evalutation of the hadronic contribution to the muon's $g-2$ from QCD
• The Higgs of the Higgs and the diphoton channel
• Confinement in QCD and generic Yang-Mills theories with matter representations
• Differential Dyson-Schwinger equations for quantum chromodynamics
• Yang-Mills Propagators and QCD
• Proof of triviality of $\lambda {\varphi }^4$ theory
• Nambu-Jona-Lasinio model correlation functions from QCD
• Dual perturbation expansion for a classical $\lambda {\varphi }^4$ field theory
• Quantum Yang--Mills Dark Energy
• Fate of False Vacuum in Non-perturbative Regimes
• Quark confinement in QCD in the 't Hooft limit
• Classical solutions of a massless Wess-Zumino model
• Mapping theorem and Green functions in Yang-Mills theory
• Some exact Green function solutions for non-linear classical field theories
• Dynamical generation of electroweak scale from the conformal sector: A strongly coupled Higgs via the Dyson--Schwinger approach
• A scalar potential from gauge condensation and its implications
• Generating the Electro-Weak Scale by Vector-like Quark Condensation