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\nangle $\\theta_{12}$, maximal $\\theta_{23}$, zero $\\theta_{13}$ and zero CP\nphases at the GUT scale, the currently favored LMA solution of the solar\nneutrino problem can be obtained in a rather natural way by Renormalization\nGroup effects. We find that most of the running takes place in the energy\nranges above and between the see-saw scales, unless the charged lepton Yukawa\ncouplings are large, which would correspond to a large $\\tan \\beta$ in the\nMinimal Supersymmetric Standard Model (MSSM). The Renormalization Group\nevolution of the solar mixing angle $\\theta_{12}$ is generically larger than\nthe evolution of $\\theta_{13}$ and $\\theta_{23}$. A large enhancement occurs\nfor an inverted mass hierarchy and for a regular mass hierarchy with $|m_2 -\nm_1| \\ll |m_2 + m_1|$. We present numerical examples of the evolution of the\nlepton mixing angles in the Standard Model and the MSSM, in which the current\nbest-fit values of the LMA mixing angles are produced with vanishing solar\nmixing angle $\\theta_{12}$ at the GUT scale.\n