Democratic-type neutrino mass matrix

We consider the democratic-type neutrino mass matrix and show that this matrix predicts the atmospheric neutrino mixing to be almost maximal, $\sin^2 2\theta_{atm}>0.999$ as well as the large CP violation (the CP violation phase in the standard form is maximal $\delta=\pi/2$). We construct the $Z_3$ symmetric dimension five effective Lagrangian with two up-type Higgs doublets and show that this Lagrangian leads to the democratic neutrino mass matrix. Furthermore, we consider the restricted model with one up-type Higgs doublet and obtain the prediction, $0.87<\sin^2 2\theta_{sol}<8/9$.