Tri-Bimaximal Neutrino Mixing and the Family Symmetry Z_7 x Z_3

TL;DR

This paper explores the use of the finite group Z_7 x Z_3 in neutrino flavor models, demonstrating its ability to produce tri-bimaximal mixing while accommodating quark and lepton hierarchies.

Contribution

It introduces the application of the Frobenius group Z_7 x Z_3 in neutrino mixing models, expanding the set of flavor symmetries used in particle physics.

Findings

Z_7 x Z_3 can generate tri-bimaximal neutrino mixing.

The model accommodates quark and charged lepton hierarchies.

Z_7 x Z_3 offers an alternative to S_4 and A_4 in flavor symmetry models.

Abstract

The Non-Abelian finite group PSL_2(7) is the only simple subgroup of SU(3) with a complex three-dimensional irreducible representation. It has two maximal subgroups, S_4 which, along with its own A_4 subgroup, has been successfully applied in numerous models of flavor, as well as the 21 element Frobenius group Z_7 x Z_3, which has gained much less attention. We show that it can also be used to generate tri-bimaximal mixing in the neutrino sector, while allowing for quark and charged lepton hierarchies.