Radiative Generation of the LMA Solution from Small Solar Neutrino Mixing at the GUT Scale

Abstract

We show that in see-saw models with small or even vanishing lepton mixing angle ${\theta }_{12}$, maximal ${\theta }_{23}$, zero ${\theta }_{13}$ and zero CP phases at the GUT scale, the currently favored LMA solution of the solar neutrino problem can be obtained in a rather natural way by Renormalization Group effects. We find that most of the running takes place in the energy ranges above and between the see-saw scales, unless the charged lepton Yukawa couplings are large, which would correspond to a large $\tan \beta$ in the Minimal Supersymmetric Standard Model (MSSM). The Renormalization Group evolution of the solar mixing angle ${\theta }_{12}$ is generically larger than the evolution of ${\theta }_{13}$ and ${\theta }_{23}$. A large enhancement occurs for an inverted mass hierarchy and for a regular mass hierarchy with $|m_2-m_1|\ll |m_2+m_1|$. We present numerical examples of the evolution of the lepton mixing angles in the Standard Model and the MSSM, in which the current best-fit values of the LMA mixing angles are produced with vanishing solar mixing angle ${\theta }_{12}$ at the GUT scale.

Comments: 10 pages, 6 figures; reference added, minor changes in the text; results unchanged; final version to appear in JHEP