Anomaly-free flavor symmetry and neutrino anarchy

Abstract

We show that one can describe the quark and lepton masses with a single anomaly-free $U(1)$ flavor symmetry provided a single order one parameter is enhanced by roughly 4--5. The flavor symmetry can be seen to arise from inside the ${E}_{6}$ symmetry group in such a way that it commutes with the $\mathrm{SU}(5)$ grand unified gauge group. The scenario does not distinguish between the left-handed lepton doublets and hence is a model of neutrino anarchy. It can therefore account for the large mixing observed in atmospheric neutrino experiments and predicts that the solar neutrino oscillation data are consistent with the large mixing angle solution of matter-enhanced oscillations.