Dynamical Generation of Electroweak Scale From the Conformal Sector: A Strongly Coupled Higgs via the Dyson–Schwinger Approach

A novel pathway to generate the electroweak (EW) scale via non-perturbative dynamics of a conformally invariant scalar sector at the classical level is proposed. A method is provided 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, an analytical result for the Higgs mass in the strongly coupled regime is found in terms of its quartic self interaction term and the cut-off scale of the theory. It is also shown 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. 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, is led by this analysis.