Theory of Neutrino Masses and 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.

23 pages, lecture presented at IV International Pontecorvo Neutrino Physics School, September 26 - October 6, 2010, Alushta, Crimea, Ukraine

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• Neutrino Mixing and the Axion-Gluon Vertex
• Matter Parity Violating Dark Matter Decay in Minimal SO(10), Unification, Vacuum Stability and Verifiable Proton Decay
• Non-Zero ${\theta }_{13}$ and ${\delta }_{CP}$ in a Neutrino Mass Model with $A_4$ Symmetry
• Fully constrained mass matrix: Can symmetries alone determine the flavon vacuum alignments?
• Non$-$zero ${\theta }_{13}$ and ${\delta }_{CP}$ phase with $A_4$ Flavor Symmetry and Deviations to Tri$-$Bi$-$Maximal mixing via $Z_2\times Z_2$ invariant perturbations in the Neutrino sector
• Singlet Fermion Assisted Dominant Seesaw with Lepton Flavor and Number Violations and Leptogenesis
• ${\text{TM}}_1$ neutrino mixing with $\sin {\theta }_{13}=\frac{1}{\sqrt{3}}\sin \frac{\pi }{12}$
• Non-zero ${\theta }_{13}$ and leptonic CP phase with $A_4$ Symmetry