Dirac CP phase in the neutrino mixing matrix and the Froggatt-Nielsen mechanism with ${rm bf det} bf [M_ u]=0$

We discuss the Dirac CP violating phase $delta_{CP}$ in the Froggatt-Nielsen model for a neutrino mass matrix $M_ u$ imposing a condition ${rm det} [M_ u]=0$. This additional condition restricts the CP violating phase $delta_{CP}$ drastically. We find that the phase $delta_{CP}$ is predicted in the region of $pm (0.4- 2.9)$ radian, which is consistent with the recent T2K and NO$ u$A data. There is a remarkable correlation between $delta_{CP}$ and $sin^2theta_{23}$. The phase $delta_{CP}$ converges on $sim pm pi/2$ if $sin^2theta_{23}$ is larger than $0.5$. Thus, accurate measurements of $sin^2theta_{23}$ are important for a test of our model. The effective mass $m_{ee}$ for the neutrinoless double beta decay is predicted in the rage of $3.3-4.0$ meV.