The Horizontal Symmetry for Neutrino Mixing

TL;DR

This paper demonstrates that the finite group S_4, or its containing groups, uniquely explains the tri-bimaximal neutrino mixing pattern through a group-theoretical approach, linking symmetry to neutrino phenomenology.

Contribution

It identifies S_4 as the only finite group capable of producing tri-bimaximal mixing for all Yukawa couplings, providing a group-theoretical foundation for neutrino mixing models.

Findings

S_4 uniquely yields tri-bimaximal mixing.

The method links group theory to neutrino phenomenology.

Dynamical schemes can determine Higgs VEVs up to scale.

Abstract

We argue that the best way to determine horizontal symmetry is from neutrino mixing, and proceed to show that the only finite group capable of yielding the tri-bimaximal mixing for all Yukawa couplings is $S_4$, or any group containing it. The method used is largely group theoretical, but it can be implemented by dynamical schemes in which the Higgs expectation values introduced to break $S_4$ spontaneously are uniquely determined up to an unknown scale for each.