Predictive Framework with a Pair of Degenerate Neutrinos at a high scale

Abstract

Radiative generation of the solar scale $\Delta_{\odot}$ is discussed in the presence of leptonic CP violation. We assume that both the solar scale and $U_{e3}$ are zero at a high scale and the weak radiative corrections generate them. It is shown that all leptonic mass matrices satisfying these requirements lead to a unique prediction $\Delta_{\odot} \cos 2\theta_{\odot}\approx 4 \delta_\tau \sin^2 \theta_A |m_{ee}|^2$ for the solar scale in terms of the radiative correction parameter $\delta_\tau$, the physical solar (atmospheric) mixing angles $\theta_{odot} (\theta_A)$ and the Majorana neutrino mass $m_{ee}$ probed in neutrinoless double beta decay. This relation is independent of the mixing matrix and CP-violating phases at the high scale. The presence of CP-violating phases leads to dilution in the solar mixing angle defined at the high scale. Because of this, bi-maximal mixing pattern at the high energy leads to large but non-maximal solar mixing in the low-energy theory. An illustrative model with this feature is discussed.