Horizontal Symmetry: Bottom Up and Top Down

TL;DR

This paper explores the relationship between horizontal symmetry groups and fermion mixing, applying group theory to neutrino mixing and discussing symmetry choices for leptons and quarks.

Contribution

It establishes a group-theoretical connection between horizontal symmetry and fermion mixing, and compares dynamical and purely group-theoretical approaches.

Findings

A connection between $ ext{G}$ and neutrino mixing is demonstrated.

The dynamical theory favors certain stable mixing patterns.

$A_4$ is identified as the preferred symmetry for leptons.

Abstract

A group-theoretical connection between horizontal symmetry $\G$ and fermion mixing is established, and applied to neutrino mixing. The group-theoretical approach is consistent with a dynamical theory based on $U(1)\times \G$, but the dynamical theory can be used to pick out the most stable mixing that purely group-theoretical considerations cannot. A symmetry common to leptons and quarks is also discussed. This higher symmetry picks $A_4$ over $S_4$ to be the preferred symmetry for leptons.