Neutrino Mass Matrices in Models with Horizontal Symmetries

We have studied the most general neutrino mass matrices in models with SU(2) and SU(3) horizontal symmetries. Without going into the details of the models it is possible to write down the effective operators, which predict the structure of the Majorana neutrino mass matrices. Unlike other extensions of the standard model, the structure is now independent of the effective Yukawa couplings and depends entirely on the Higgs which gives mass to the other fermions. In the case of SU(3) symmetries the lowest dimensional operators are forbidden requiring a low mass scale for lepton number violation. The structure of fermion masses and mixing is not predicted in the standard model because all generations are treated similarly. All the fermion masses and mixing are free parameters, which are supposed to be determined by experiments. To eliminate this uncertainty and to understand the generation structure several approaches has been considered [1]. One such approach assumes that the fermions of different generations are related by some gauge symmetry group, called the horizontal symmetry [2]. The vacuum expectation values (vev) of the Higgs would then give us the structure of the fermion masses and mixing. So far most of the searches for physics beyond the standard model has met with negative results except for the neutrino sector. The neutrino mass is predicted to be zero in the standard model, but a solution to the atmospheric neutrino anomaly [3] has evidenced a nonvanishing mass for the neutrinos. This result has been supported by the solar neutrino results [4]. Even the Laboratory experiments started supporting this result predicting a neutrino mass and mixing required to explain the observed neutrino oscillations [5, 6]. The developments in the neutrino physics over the past few years have already established some possible structures for the neutrino mass matrix. Since the horizontal symmetric models are some of the possible extensions of the standard model, it is most natural to study the horizontal symmetries in the light of the recent results from neutrino physics. In this article we point out that it is possible to make some general comments about the neutrino masses and mixing in some of the models of gauged horizontal symmetries. We shall discuss the nonabelian SU(2)H , SU(3) V H and SU(3) V L H horizontal gauge symmetries, although our results could be generalized to other symmetries as well. We start with a brief introduction to the horizontal symmetries, we are going to discuss. We shall include the right handed neutrinos and their interactions while studying the neutrino masses. In the SU(2)H horizontal symmetry all the left and right handed fermions and antifermions transform