Horizontal Symmetry from the Bottom Up

TL;DR

This paper reviews a method to derive horizontal symmetries from mixing matrices, applying it to leptonic and quark sectors, and discusses group-theoretic models like D4 to unify these symmetries.

Contribution

It introduces a general technique to extract horizontal symmetries from mixing matrices and explores their application to leptonic and quark mixing, including specific group examples.

Findings

Derived leptonic symmetry from tri-bimaximal mixing

Extended the method to variations of the mixing matrix

Discussed quark-lepton symmetry unification using D4 group

Abstract

A general method to derive horizontal symmetry from a mixing matrix is reviewed. The technique has been applied to deduce leptonic symmetry from the tri-bimaximal neutrino mixing matrix and three of its variations. The question of how the quark mixing can be accommodated within the leptonic symmetry group is discussed, including in this connection an example based on the group $D_4$.