Second Octant Favored for Non-Maximal $θ_{23}$

Abstract

One of the most robust relationships predicted by binary tetrahedral ($T^{'}$) flavor symmetry relates the reactor neutrino angle $θ_{13}$ to the atmospheric neutrino angle $θ_{23}$, independently of $θ_{12}$. It has the form $θ_{13} = \sqrt{2} |\fracπ{4} - θ_{23}|$. When this prediction first appeared in 2008, $θ_{13}$ was consistent with zero and $θ_{23}$ with $π/4$. Non-zero $θ_{13}$ was established by Daya Bay in 2012. Non-zero $|\fracπ{4}-θ_{23}|$ is now favored by the NO$ν$A experiment and, for $θ_{23}$, the aforementioned $T^{'}$ relation selects the second octant ($θ_{23} > \fracπ{4}$) over the first octant ($θ_{23} < \fracπ{4}$). This analysis initially assumes CP conservation in the lepton sector, but leptonic CP violation is discussed and it is shown that this specific $T^{'}$ relationship is invariant.