An $S_4$ model inspired from self-complementary neutrino mixing

We build an $S_4$ model for neutrino masses and mixings based on the self-complementary (SC) neutrino mixing pattern. The SC mixing is constructed from the self-complementarity relation plus $delta_{rm CP}=-frac{pi}{2}$. We elaborately construct the model at a percent level of accuracy to reproduce the structure given by the SC mixing. After performing a numerical study on the models parameter space, we find that in the case of normal ordering, the model can give predictions on the observables that are compatible with their $3sigma$ ranges, and give predictions for the not-yet observed quantities like the lightest neutrino mass $m_1in [0.003,0.010]$ eV and the Dirac CP violating phase $delta_{rm CP}in[256.72^circ,283.33^circ]$.