Consequences of minimal seesaw with complex μτ antisymmetry of neutrinos

We review the application of non abelian discrete groups to the theory of neutrino masses and mixing, which is strongly suggested by the agreement of the Tri-Bimaximal mixing pattern with experiment. After summarizing the motivation and the formalism, we discuss specific models, based on A4, S4 and other finite groups, and their phenomenological implications, including lepton flavor violating processes, leptogenesis and the extension to quarks. In alternative to Tri-Bimaximal mixing the application of discrete flavor symmetries to quark-lepton complementarity and Bimaximal Mixing is also considered.

We review pedagogically non-Abelian discrete groups, which play an important role in the particle physics. We show group-theoretical aspects for many concrete groups, such as representations, their tensor products. We explain how to derive, conjugacy classes, characters, representations, and tensor products for these groups (with a finite number). We discussed them explicitly for \(S_N\), \(A_N\), \(T'\), \(D_N\), \(Q_N\), \(\Sigma(2N^2)\), \(\Delta(3N^2)\), \(T_7\), \(\Sigma(3N^3)\) and \(\Delta(6N^2)\), which have been applied for model building in the particle physics. We also present typical flavor models by using \(A_4\), \(S_4\), and \(\Delta (54)\) groups. Breaking patterns of discrete groups and decompositions of multiplets are important for applications of the non-Abelian discrete symmetry. We discuss these breaking patterns of the non-Abelian discrete group, which are a powerful tool for model buildings. We also review briefly about anomalies of non-Abelian discrete symmetries by using the path integral approach.