An Electroweak-like Theory from Four Fermion Interactions

TL;DR

This paper proposes an electroweak-like theory derived from four-fermion interactions within a single lepton generation, where vector bosons emerge as fermion pair collective modes, mimicking gauge bosons in the Standard Model.

Contribution

It introduces a novel electroweak-like framework based on fermion pairs from four-fermion interactions, providing a new perspective on gauge boson emergence and chiral symmetry breaking.

Findings

Fermion pairs form vector bosons resembling $W^$, $Z$, and 0$.

Left-handed fermions couple to charged bosons, ensuring gauge invariance.

Z-like and 0-like bosons mediate weak interactions and electromagnetic interactions, respectively.

Abstract

An electroweak-like theory of a broken chiral symmetry that is constructed by the collective modes of fermion pairs from four fermion interactions of one lepton generation is presented. The products of Dirac spinors lead to the separation of the two chiral fermions to couple respectively with two different kinds of polarization states. Because of a broken vacuum, a fermion and an anti-fermion out of the four pair up to form vector bosons, which behave like gauge bosons, such as $W^\pm$, $Z$ and $\gamma$ in a group structure of $SU(2)_L\times U(1)_Y$. The pairing of spinors only allows left-handed fermions to interact with charged bosons to secure the gauge invariance, while, as desired, $Z$-like bosons mediate different weak forces for two chiral fermions and $\gamma$-like bosons interact freely with fermions.