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

TL;DR

This paper introduces a non-perturbative mechanism for generating the electroweak scale through a conformally invariant scalar sector, using Dyson-Schwinger equations to analytically estimate the Higgs mass in a strongly coupled regime.

Contribution

It presents a novel analytical approach to estimate the electroweak scale and Higgs mass via Dyson-Schwinger equations in a conformal scalar sector, linking non-perturbative dynamics to scale generation.

Findings

Analytical expression for Higgs mass in strongly coupled regime.

Demonstration that the Higgs sector is essential for mass generation in the Standard Model.

Potential solutions to the gauge hierarchy problem through dynamical scale generation.

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.