Are lepton flavor mixings in the democratic mass matrix stable against quantum corrections?

Abstract

We investigate whether the lepton flavor mixing angles in the so-called democratic type of mass matrix are stable against quantum corrections or not in the minimal supersymmetric standard model with dimension five operator which induces neutrino mass matrix. By taking simple breaking patterns of $S_3{}_L \times S_3{}_R$ or $O(3)_L \times O(3)_R$ flavor symmetries and the scale where democratic textures are induced as $O(10^{13})$ GeV, we find that the stability of the lepton flavor mixing angles in the democratic type of mass matrix against quantum corrections depends on the solar neutrino solutions. The maximal flavor mixing of the vacuum oscillation solution is spoiled by the quantum corrections in the experimental allowed region of $\tan β$. The large angle MSW solution is spoiled by the quantum corrections in the region of $\tan β> 10$. The condition of $\tan β\leq 10$ is needed in order to obtain the suitable mass squared difference of the small angle MSW solution. These strong constraints must be regarded for the model building of the democratic type of mass matrix