Predictive framework with a pair of degenerate neutrinos at a high scale

Abstract

Radiative generation of the solar scale Δ_⊙ 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 Δ_⊙cos2θ_⊙≈4δ_τsin²θ _A|m_ee|² for the solar scale in terms of the radiative correction parameter δ_τ, the physical solar (atmospheric) mixing angles θ_⊙ (θ_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.