Large Mixing and Large Hierarchy Between Neutrinos with Abelian Flavor Symmetries

The experimental data on atmospheric and solar neutrinos suggest that there is near-maximal mixing between \nu_\mu and \nu_\tau but that their masses are hierarchically separated. In models of Abelian horizontal symmetries, mixing of O(1) generically implies that the corresponding masses are of the same order of magnitude. We describe two new mechanisms by which a large hierarchy between strongly mixed neutrinos can be achieved in this framework. First, a discrete Abelian symmetry can give the desired result in three ways: mass enhancement, mixing enhancement and mass suppression. Second, holomorphic zeros can give mass suppression.