Nonabelian discrete symmetries, fermion mass textures and large neutrino mixing

Nonabelian discrete groups are an attractive tool to describe fermion masse s 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 mus t obey, e.g. limits on extra, particles. Some of the simplest groups are th e 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 doub let representations. After studying which vacuum expectation value (VEV) di rections of representations of dihedral and dicyclic groups preserve which subgroups, we construct a simple model based on the group Q(6) X Q(6). The model reproduces the masses and mixings of all quarks and leptons, includin g neutrinos. It has a large mixing angle in the mu - tau neutrino sector, i n accordance: with the recent SuperKamiokande results, while keeping a smal l 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) similar to tan(theta(mu T)) root m(c)/m(t) . (C) 2000 Elsevier Science B.V , All rights reserved.