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 \times Q_6. The model reproduces the masses and mixings of all quarks and leptons, including neutrinos. It has a large mixing angle in the mu - tau 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: m_s/m_b \sim tan(theta_μτ) \sqrt{m_c/m_t}