Neutrino mass matrices with one texture equality and one vanishing neutrino mass

In the light of latest data of neutrino oscillation experiments, we carry out a systematic investigation on the texture structures of Majorana neutrino mass matrix $M_{\nu }$, which contain one vanishing neutrino mass and an equality between two matrix elements. Among 15 logically possible patterns, it is found that for norm order ($m_3>m_2>m_1=0$) of neutrino masses only three of them are compatible with recent experimental data at the $3\sigma$ level, while for inverted order ($m_2>m_1>m_3=0$) two patterns is phenomenologically allowed. In the numerical analysis, we perform a scan over the parameter space of all viable patterns to get a large sample of scattering points. We present the implications of each allowed pattern for three mixing angles $({\theta }_{12},{\theta }_2,{\theta }_3)$, leptonic $CP$ violation and neutrinoless double-beta decay, predicting strong correlations between oscillation parameters. The theoretical realization of a concrete example is discussed in the framework of Froggatt-Nielsen mechanism.

Figure 1

The correlation plots for NO P4 pattern.

Figure 2

The correlation plots for NO P6 pattern.

Figure 3

The correlation plots for NO P12 pattern.

Figure 4

The correlation plots for IO P12 pattern.

Figure 5

The correlation plots for IO P13 pattern.