Non-perturbative Origin of Electroweak Scale via Higgs-portal: Dyson-Schwinger in Conformally Invariant Scalar Sector

Abstract

We investigate conformally extended Standard Model with a hidden scalar $\varphi$. It is shown that due to non-perturbative dynamics in the hidden sector, $\varphi$ develops a vacuum expectation value (vev) in the form of a mass gap which triggers the electroweak symmetry breaking (EWSB) and dynamically generates the SM Higgs boson mass. For estimating the non-perturbatively generated mass scale, we solve the hierarchy of Dyson-Schwinger Equations in form of partial differential equations using the exact solution known via a novel technique developed by Bender, Milton and Savage. We employ Jacobi Elliptic function as exact background solution and show that the mass gap that arises in the hidden sector can be transmuted to the EW sector, expressed in terms of Higgs-portal mixed quartic coupling $\beta$ and self interaction quartic coupling ${\lambda }_{\varphi }$ of $\varphi$. We identify the suitable parameter space where the observed SM Higgs boson can be successfully generated . Finally, we discuss how this idea of non-perturbative EW scale generation can serve as a new starting point for better realistic model building in the context of resolving the hierarchy problem in the Standard Model.

24 pages, 3 figures. Version accepted for publication in Fortschritte der Physik

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