Theory of Neutrino Masses and Mixing

TL;DR

This paper explores the application of finite group symmetries, specifically S_4 and A_4, to neutrino mass models, illustrating how group theory informs lepton mixing patterns like tri-bimaximal mixing.

Contribution

It introduces the use of finite groups in neutrino physics, detailing character theory and tensor products, and presents a specific A_4-based model for lepton mixing.

Findings

Demonstrates the role of A_4 in modeling lepton mixing

Connects group representations to Yukawa couplings

Provides a concrete model for tri-bimaximal mixing

Abstract

We motivate the usage of finite groups as symmetries of the Lagrangian. After a presentation of basic group-theoretical concepts, we introduce the notion of characters and character tables in the context of irreducible representations and discuss their applications. We exemplify these theoretical concepts with the groups S_4 and A_4. Finally, we discuss the relation between tensor products of irreducible representations and Yukawa couplings and describe a model for tri-bimaximal lepton mixing based on A_4.