Abstract
We propose a model based on SU(3) family symmetry which leads to a successful description of quark and lepton masses and mixing angles including approximate bi-maximal mixing in the neutrino sector suitable for the LOW or quasi-vacuum solar solutions, with the atmospheric angle predicted to be accurately maximal due to the SU(3) symmetry. The model predicts a CHOOZ angle $\theta_{13}\sim |V_{ub}|.$ The SU(3) symmetry can also ensure the near degeneracy of squarks and sleptons needed to avoid large flavour changing neutral currents.
Highlights
The origin of fermion masses and mixing angles has been a long standing puzzle[1]
In this paper we shall show that a near maximal mixing angle may be a signal of an underlying non-Abelian family symmetry and demonstrate how vacuum alignment in such a model can lead to maximal mixing
In this paper we have constructed a model of fermion masses based on an SU(3) family symmetry
Summary
The origin of fermion masses and mixing angles has been a long standing puzzle[1]. Our determination of the mass matrices has been improved by new experimental information on both the quark and lepton sectors. Given that the third family of quarks and leptons is much heavier, and that the dominant contribution to FCNC comes from the light generations, early attempts to develop such theories considered the non-Abelian group SU(2) acting on the first two generations only[4] These theories do not offer an easy explanation for the near maximal neutrino mixing in the neutrino sector involving the second and third generations. In this paper we shall consider a particular class of SU(3) model which gives a successful description of quark masses and mixing angles, and simultaneously gives approximately bimaximal leptonic mixing with θ23 fixed to be almost maximal by a combination of SU(3) and vacuum alignment In both cases the origin of the mixing angles is controlled by the non-Abelian vacuum structure relating the second and third generations. The alignment of the < φ23 > VEVs is non-trivial and is the subject of a later section
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