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.

Comments: 15 pages, including a postscript figure