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

TL;DR

This paper develops an $S_4$ flavor symmetry model based on self-complementary neutrino mixing, accurately reproducing observed mixing patterns and predicting specific ranges for the lightest neutrino mass and CP phase.

Contribution

It introduces a novel $S_4$ model inspired by self-complementary mixing, providing detailed predictions consistent with current data and specific forecasts for unmeasured parameters.

Findings

Model compatible with 3σ experimental ranges for normal ordering

Predicts lightest neutrino mass between 0.003 and 0.010 eV

Forecasts Dirac CP phase between 256.72° and 283.33°

Abstract

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 model's parameter space, we find that in the case of normal ordering, the model can give predictions on the observables that are compatible with their $3\sigma$ ranges, and give predictions for the not-yet observed quantities like the lightest neutrino mass $m_1\in [0.003,0.010]$ eV and the Dirac CP violating phase $\delta_{\rm CP}\in[256.72^\circ,283.33^\circ]$.