Testing Leptonic SU(2) Horizontal Symmetry Using Neutrino Mixings

After some preliminary arguments suggesting that neutrino mixings with inverted mass pattern may be easier to understand within the framework of a local horizontal symmetry $SU(2)_H$ acting on leptons, we construct a specific model and analyze its implications and predictions. Within this class of models, there are two possible scenarios for neutrino mixings, one of which was discussed by us in a recent paper. In both cases, the smallness of $\Delta m^2_{\odot}/\Delta m^2_A$ is naturally obtained. In this paper, we show that for the second case, the horizontal symmetry leads to an experimentally testable relation between the neutrino parameters $U_{e3}$ and the ratio of solar and atmospheric mass difference squared i.e. $U^2_{e3} cos 2\theta_{\odot} = \frac{\Delta m^2_{\odot}}{2 \Delta m^2_A} + O(U^4_{e3})$. Taking the solar neutrino parameters inferred from present data at 99.7% confidence level, the above relation leads to a lower bound on $U_{e3}\geq 0.08$ and an allowed region in the $U_{e3}$ and $\frac{\Delta m^2_{\odot}}{2 \Delta m^2_A}$ space which can be testable in proposed long baseline experiments.