Nonabelian discrete symmetries, fermion mass textures and large neutrino mixing

Abstract

Nonabelian discrete groups are an attractive tool to describe fermion masses and mixings. They have nonsinglet representations which seem particularly suitable for distinguishing the lighter generations from the heavier ones. Also, they do not suffer from the extra constraints a continuous group must obey, e.g. limits on extra particles. Some of the simplest groups are the nonabelian discrete subgroups of SO(3) and SU(2), the so called dihedral groups D n and dicyclic groups Q 2n , which both have only singlet and doublet representations. After studying which vacuum expectation value (VEV) directions of representations of dihedral and dicyclic groups preserve which subgroups, we construct a simple model based on the group Q 6 × Q 6 . The model reproduces the masses and mixings of all quarks and leptons, including neutrinos. It has a large mixing angle in the µ − τ neutrino sector, in accordance with the recent SuperKamiokande results, while keeping a small quark mixing in the bottom -charm sector. The reason is similar to the one found in the literature based on the SU(5) group: the large left handed mixing angle in the lepton sector corresponds to the large unphysical right handed in the down quark sector. The large mixing is also responsible for the different hierarchies of the two heaviest families in the up and down sector, and can be summarized as the order of magnitude relation: ms m b ∼ tan(θ µτ ) mc mt .

Structure of neutrino mass matrix and CP-violation

“…With increase of θ 12 , the amplitude of variations of µτ -block elements with σ (see (15)) decreases as c 2 12 . For maximal 1-2 mixing we get ∼ (30 − 35)% decrease in comparison with the best fit value of θ 12 .…”

“…Depending on the phase ρ, the contribution related to m 1 can suppress or enhance the amplitude of variations of the µτ -block elements with σ (see (15)). The extreme modifications are determined by…”

“…Then, to approach the fundamental theory one should find the mass matrix in the symmetry basis and at the corresponding symmetry scale. Both abelian (e.g., [5,6,7,8,9,10,11]) and non abelian (e.g., [12,13,14,15]) symmetries broken (spontaneously) at the various symmetry scales have been widely considered (see also the reviews [16,17]). In particular, the possibilities have been studied to identify the flavor symmetry scale with other known scales in the theory like the Grand Unification scale or the string scale.…”

Spontaneous breaking of gauge groups to discrete symmetries

“…However, as explained in [36,37], this irrep will actually break to the continuous subgroup P in (2). So we must look at the next lowest irrep with a trivial SU(2) singlet, the 7.…”

Large neutrino mixing and normal mass hierarchy: A discrete understanding

“…In section II we will comment on the present status of U (1) and Z n flavor symmetries in confronting neutrino oscillation data and in particular the large atmospheric mixing (see also [34]). To overcome at least some of the problems of Abelian symmetries and obtain greater predictiveness, a variety of non-Abelian symmetries have been used, both discrete [35,36,37,38] and continuous [39,40,41].…”