Dirac CP phase in the neutrino mixing matrix and the Froggatt-Nielsen mechanism with $\mathbf{det}[{\mathbf{M}}_{\nu }]=0$

Abstract

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 on $\sim \pm \pi /2$ if ${\sin }^2{\theta }_{23}$ is larger than $0.5$. Thus, accurate measurements of ${\sin }^2{\theta }_{23}$ 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.

Comments: 12 pages, 9 figures