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

TL;DR

The paper proposes a non-perturbative, scale-invariant route to generate the electroweak scale by coupling the Standard Model to a hidden scalar through a Higgs-portal interaction. It employs Dyson-Schwinger equations with exact Jacobi elliptic function backgrounds, following the Bender-Milton-Savage approach, to produce a mass gap in the hidden sector that transmits to the Higgs sector. Leading-gap analysis yields explicit expressions for the hidden and Higgs masses and demonstrates consistency with the observed Higgs mass within a viable parameter space, including a spectrum for hidden-sector states. This framework offers a non-perturbative alternative to naturalness problems and has potential implications for Higgs-portal dark matter and early-universe electroweak dynamics, while suggesting testable phenomenology in future experiments.

Abstract

We investigate conformally extended Standard Model with a hidden scalar $φ$. It is shown that due to non-perturbative dynamics in the hidden sector, $φ$ 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 $β$ and self interaction quartic coupling $λ_φ$ of $φ$. 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.

Figures (3)

• Figure 1: We show the evolution of the phion mass $M_\phi=m_0$ with respect to $\mu$ and the corresponding evolution of the Higgs boson mass $M_h$ (blue dots) with the value of the experimental Higgs boson mass and its error bar. We set $\beta=10^{-4}$, $\lambda_\phi=10^{-2}$, $\lambda_h=0.086$ and $v=0.246\ \textit{TeV}$. The model appears to be consistent with a wide range of $\mu$ values.
• Figure 2: Plot same as Fig.\ref{['fig1']} but as a function of $\lambda_\phi$ rather than $\mu$. It is seen that the consistency of the model is granted provided $\lambda_\phi$ is smaller enough. We assume $\mu=1.5\ TeV$.
• Figure 3: In this plot, the limit of mass (blue line) is seen to be below the red line for a large set of $\lambda_\phi<1$, in agreement with our discussion in the text. This grants the full consistency of the model. We set $\mu=1.5\ TeV$.