Phenomenological model combining flavor symmetry violation and lepton number violation in neutrino physics

We consider the neutrino sector where the right-handed neutrino is a Standard Model gauge singlet. In this framework new possibilities exist for generating mass terms because there is a new scale associated with the fact that the heavy neutrinos can have a Majorana mass that violates lepton number. We use the symmetry GSM x U(1) H x U(1)L where GSM is the Standard Model gauge group, U(1)H is the horizontal (or flavor) symmetry of Froggatt-Nielsen models and U(1)L is lepton number. In the model we have a scalar field SH, which is a singlet under GSM x U(1)L and carries horizontal charge which generates the mass and mixing angle hierarchies in the charged lepton and quark sectors of the Standard Model. In addition there is a pair of fields SHL and SHL that are Standard Model gauge group singlets and lepton number violating scalar fields with horizontal charge. The model we have falls into a class that implements an accidental Le - Lmu - Ltau symmetry which is broken perturbatively by the interactions of the Froggatt-Nielsen fields whose vacuum expectation values break the horizontal symmetry U(1)H. This results in a pseudo-Dirac form for the mixing between the electron neutrino and the maximally mixed state from the muon- and tau-neutrino sector. In order to be in agreement with the solar and atmospheric neutrino data we have implemented perturbations in our model which are consistent with GSM x U(1)H x U(1) L. The perturbations are implemented through the fields SH and S'H which admit interactions that are incompatible with the Le - Lmu - Ltau symmetry and, as a consequence, generate the necessary perturbations that make the model phenomenologically viable.