Partial mass-degeneracy and spontaneous CP violation in the lepton sector

Inspired by the small mass-squared difference measured in the solar neutrino oscillation experiments and by the testability, we suggest that a limit of the partial mass degeneracy, in which masses of the first two generation fermions are degenerate, may be a good starting point for understanding the observed fermion mass spectra and mixing patterns. The limit indicates the existence of a two-dimensional rotation symmetry, such as $O(2)$, $D_N$ and so on, in flavor space of the first two generations. We propose simple models for the lepton sector based on $D_N$ and show that the models can successfully reproduce the experimental data without imposing unnatural hierarchies among dimensionless couplings, although at least $10\%$ tuning is necessary in order to explain a large atmospheric mixing. It is especially found that the $Z_2$ subgroup of the $D_N$ symmetry plays an important role in understanding the smallness of the electron mass and $\theta_{13}^{\rm PMNS}$. We also discuss testability of the models by the future neutrinoless-double-beta-decay experiments and cosmological observations.