The Central Correlations of Hypercharge, Isospin, Colour and Chirality in the Standard Model

TL;DR

This paper explores the internal group structure of the Standard Model, revealing discrete and continuous correlations among hypercharge, isospin, colour, and chirality, and their implications for particle representations and symmetry breaking.

Contribution

It identifies the faithful internal group as a specific quotient involving discrete factors and analyzes the consequences of these correlations for Standard Model fields and parameters.

Findings

Discrete $ ext{Z}_2$-correlation between chirality and Lorentz properties

Discrete $ ext{Z}_2 imes ext{Z}_3$-correlation in the internal group structure

Continuous $ ext{U}(1)$-correlation between hyperisospin and chirality

Abstract

The correlation of the fractionally represented hypercharge group with the isospin and colour group in the standard model determines as faithfully represented internal group the quotient group ${\U(1)\x\SU(2)\x\SU(3)\over\Z_2\x\Z_3}$. The discrete cyclic central abelian-nonabelian internal correlation involved is considered with respect to its consequences for the representations by the standard model fields, the electroweak mixing angle and the symmetry breakdown. There exists a further discrete $\Z_2$-correlation between chirality and Lorentz properties and also a continuous $\U(1)$-external-internal one between hyperisospin and chirality.