A Flavor Change Study based on Dyson-Schwinger Equation

TL;DR

This paper investigates flavor change effects and symmetry breaking in a multi-flavor system using Dyson-Schwinger equations, proposing a novel perspective on the origin of fermion masses and the Higgs boson within this framework.

Contribution

It introduces a new approach to study flavor change and symmetry breaking via Dyson-Schwinger equations, linking Goldstone bosons to the Higgs mechanism.

Findings

Fermion masses are split according to symmetry breaking patterns.

Identifies Goldstone bosons with electric charges 0, 0, +1, -1, where one acts as the Higgs boson.

Provides a quark mass spectrum consistent with the symmetry breaking chain.

Abstract

We study the flavor change effects using the Dyson-Schwinger (DS) equation in a multi-flavor system. By taking the Electroweak interaction as perturbation into conditions, the $\text{SU(4)}_\text{L}\rightarrow\text{SU(2)}_\text{L}\otimes\text{SU(2)}_\text{L}\rightarrow\text{SO(2)}_\text{L}\otimes\text{SO(2)}_\text{L}$ symmetry breaking chain is studied. Under this symmetry breaking pattern fermion masses are split, and we can identify the fermions with different masses as different generations. Quark mass spectrum is then given. Meanwhile, there are a total of fifteen Goldstones but only four of them are independent. The Goldstones have electric charges $0$, $0$, $+1$, $-1$, respectively. One of them becomes pseudo-Nambu-Goldstone boson (pNGB) and gains a mass due to the Electroweak interaction perturbation. It can be identified as the Higgs boson. The other three Goldstones maintain massless and will be eaten by gauge bosons to give $W^\pm$ and $Z^0$ masses via Schwinger mechanism. Thus, the Goldstones can take the role of the Higgs boson.