A bottom-up analysis of horizontal symmetry

TL;DR

This paper reviews and extends a group-theoretical approach to derive horizontal symmetry from neutrino mixing, clarifies previous misunderstandings, and explores how these symmetries can fit fermion masses and mixings.

Contribution

It applies a method to compute vacuum alignments for $A_4$ and $S_3$, expanding the analysis of horizontal symmetries in neutrino physics.

Findings

Effective theories with these groups can fit all fermion masses and mixing parameters.

The method clarifies misunderstandings in the literature.

Constraints on dynamical models are identified.

Abstract

The group-theoretical method used to derive horizontal symmetry from neutrino mixing is reviewed and expanded. Some misunderstanding in the literature regarding the result is clarified. The method used previously to find vacuum alignments of $S_4$ is applied to compute those of $A_4$ and $S_3$. A study of effective theories based on these three groups shows that in each case there are just enough free parameters to fit all the masses and the remaining mixing parameters. This places constraint on dynamical models because effective theories are just dynamical models with the right-handed fermions integrated out. How quarks may fit into this scheme is briefly discussed.