Tetrions: a discrete approach to the standard model

TL;DR

This paper proposes a novel discrete mathematical framework using the binary tetrahedral group to explain fundamental features of the standard model, including chirality and fermion generations.

Contribution

It introduces a finite group-based approach to symmetry-breaking in the standard model, linking representation theory to particle physics phenomena.

Findings

Explains chirality of weak interaction via binary tetrahedral group

Accounts for three fermion generations using finite group representations

Highlights differences in mass generation mechanisms from standard model

Abstract

I show how the symmetry-breaking of a recently proposed embedding of the standard model of particle physics in $E_8$ can be explained in terms of the representation theory of the binary tetrahedral group. This finite group provides a link between various types of spin and isospin that can be exploited to `explain' the chirality of the weak interaction, and the existence of three generations of fermions. Two apparently small technical differences between the finite group model and the standard model turn out to have profound consequences for the ways in which the weak and strong forces create mass.