Renormalization group effect and a democratic-type neutrino mass matrix

In our previous paper, we proposed the democratic-type neutrino mass matrix which gives interesting predictions, $\theta_{23}=-\frac{\pi}4$, $|\tan \theta_{12}|=\sqrt{2-3\sin^2 \theta_{13}}$ and $\delta=\frac {\pi}2$, where $\theta_{ij}$ is the mixing angle between mass eigenstates $\nu_i$ and $\nu_j$, and $\delta$ is the CP violation angle in the standard parameterization of mixing matrix. In this paper, we examined how predictions behave at $m_Z$ by assuming that they are given at the right-handed neutrino mass scale, $M_R$.