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

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 .