Parallel lepton mass matrices with texture and cofactor zeros

In this paper we investigate the parallel texture structures containing texture zeros in the charged lepton mass matrix $M_l$ and cofactor zeros in the neutrino mass matrix $M_{\nu }$. These textures are interesting since they are related to the $Z_n$ flavor symmetries. Using the weak basis permutation transformation, the 15 parallel textures are grouped as 4 classes (class I, II, III, and IV), with the matrices in each class sharing the same physical implications. Under the current experimental data, the classes I and III with inverted mass hierarchy and class II with normal mass hierarchy are phenomenologically acceptable. The correlations between some important physical variables are presented, which are essential for the model selection and can be tested by future experiments. The model realization is illustrated by means of $Z_4\times Z_2$ flavor symmetry.

Figure 1

The correlation plots for class I (IH). The blue horizontal bands represent the $1\sigma$ uncertainty in determination of ${\theta }_{12}$, ${\theta }_{23}$, and ${\theta }_{13}$, while they plus the green horizontal bands correspond to the $2\sigma$ uncertainty.

Figure 2

The correlation plots $({\theta }_{23},{\theta }_{12})$ and $({\theta }_{23},{\theta }_{13})$ for class I (NH). The horizontal and vertical lines, respectively, denote the $3\sigma$ upper and lower bounds of ${\theta }_{12}$ and ${\theta }_{23}$.

Figure 3

The correlation plots for class II (NH). The blue horizontal bands represent the $1\sigma$ uncertainty in determination of ${\theta }_{12}$, ${\theta }_{23}$, and ${\theta }_{13}$, while they plus the green horizontal bands correspond to the $2\sigma$ uncertainty.

Figure 4

The correlation plots $({\theta }_{23},{\theta }_{12})$ and $({\theta }_{23},{\theta }_{13})$ for class II (IH). The horizontal and vertical lines, respectively, denote the $3\sigma$ upper and lower bounds of ${\theta }_{12}$ and ${\theta }_{23}$.

Figure 5

The correlation plots for class III (IH). The blue horizontal bands represent the $1\sigma$ uncertainty in determination of ${\theta }_{12}$, ${\theta }_{23}$, and ${\theta }_{13}$, while they plus the green horizontal bands correspond to the $2\sigma$ uncertainty.

Figure 6

The correlation plots $({\theta }_{23},{\theta }_{12})$ and $({\theta }_{23},{\theta }_{13})$ for class III (NH). The horizontal and vertical lines, respectively, denote the $3\sigma$ upper and lower bounds of ${\theta }_{12}$ and ${\theta }_{23}$.