Non-perturbative Origin of the Electroweak Scale with Dyson-Schwinger: Fermionic Mass Gap and Higher-order Excitations

TL;DR

This paper demonstrates how non-perturbative dynamics in a fermion-scalar interaction can generate a mass gap that triggers electroweak symmetry breaking and produces the observed Higgs boson mass, using Dyson-Schwinger equations.

Contribution

It introduces a novel non-perturbative approach employing Dyson-Schwinger equations and Jacobi elliptic functions to explain the origin of the electroweak scale and Higgs mass.

Findings

Fermion sector develops a mass gap due to non-perturbative effects.

The mass gap can be transferred to the electroweak sector, generating the Higgs boson mass.

Identifies parameter space consistent with observed Higgs properties.

Abstract

We study interaction of a fermion field $\psi$ with a scalar field $\phi$ and analyze the spectrum of the theory obtained in this way. It is shown that due to non-perturbative dynamics in the hidden fermion sector, $\phi$ 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 fermion sector can be transmuted to the EW sector, expressed in terms of fermion mass and the $\phi$ self-quartic. We identify the suitable parameter space where the observed SM Higgs boson can be successfully generated .