Dirac CP phase in the neutrino mixing matrix and the Froggatt-Nielsen mechanism with $\det[M_\nu]=0$

We discuss the Dirac CP violating phase $\delta_{CP}$ in the Froggatt–Nielsen model for a neutrino mass matrix $M_\nu$ imposing a condition $\det\[M_\nu\]=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$\nu$A data. There is a remarkable correlation between $\delta_{CP}$ and $\sin^2\theta_{23}$. The phase $\delta_{CP}$ converges to $\sim\pi/2$ if $\sin^2\theta_{23}$ is larger than 0.5. Thus, the accurate measurement of $\sin^2\theta_{23}$ is important for a test of our model. The effective mass $m_{ee}$ for the neutrinoless double beta decay is predicted in the rage $3.3–4.0$ meV.

In Physics Letters B