Atmospheric Neutrino octant from flavor symmetry

Abstract

The binary tetrahedral group ($T^{\prime }$) has provided the most successful flavor symmetry in understanding simultaneously the three mixing angles both for quarks in the CKM matrix and for neutrinos in the PMNS matrix. One prediction, invariant under leptonic CP violation, relates the atmospheric and reactor neutrino mixings ${\theta }_{32}$ and ${\theta }_{13}$, respectively. We study sedulously this relation using the latest neutrino data. It is natural to focus on the frustrating experimental octant ambiguity of ${\theta }_{32}$. We conclude that the flavor symmetry requires that ${\theta }_{32}$ is in the second octant ${\theta }_{32}>45^{\circ }$, not in the first one ${\theta }_{32}<45^{\circ }$, and eagerly await experimental confirmation of this prediction.