$S_4$ flavored $CP$ symmetry for neutrinos

A generalized $CP$ symmetry for leptons is presented where $CP$ transformations are part of an $S_4$ symmetry that connects different families. We study its implications for lepton mixings in a gauge model realization of the idea using a type II seesaw for neutrino masses. The model predicts maximal atmospheric mixing, nonzero ${\theta }_{13}$ and maximal Dirac phase ${\delta }_D=\pm \frac{\pi }{2}$.

Figure 1

Variation of ${\theta }_{13}$ as a function of the lightest neutrino mass. This scatter plot was generated using ${ϵ}_c>0$. There are points with ${ϵ}_c<0$ as well, corresponding to flipping the sign of the Dirac phase. However, they do not introduce any perceptible change.

Figure 2

The effective neutrino mass measured in neutrinoless double beta decay as a function of the lightest neutrino mass. As in Fig. 1, we have chosen ${ϵ}_c>0$ here.