Résumé
Phys.Rev.D76:096007,2007 The smallness of the 1-3 lepton mixing angle$\theta_{13}$and of the neutrino mass-squared-difference ratio$\Delta m^2_{12}/\Delta m^2_{23}$can be understood as the departure from a common limit where they both vanish. We discuss in general the conditions for realizing the mass degeneracy of a pair of neutrinos and show that the vanishing of a CP violating phase is needed. We find that the discrete quaternion group Q of eight elements is the simplest family symmetry which correlates the smallness of$\Delta m^2_{12}$to the value of$\theta_{13}$ . In such a model we predict$0.12\lesssim \sin\theta_{13} \lesssim 0.2$if the ordering of the neutrino mass spectrum is normal, and$\sin\theta_{13}\lesssim 0.12$if it is inverted.