Second Octant Favored for Non-Maximal $\theta_{23}$

Abstract

One of the most robust relationships predicted by binary tetrahedral ($T^{'}$) flavor symmetry relates the reactor neutrino angle $\theta_{13}$ to the atmospheric neutrino angle $\theta_{23}$, independently of $\theta_{12}$. It has the form $\theta_{13} = \sqrt{2} |\frac{\pi}{4} - \theta_{23}|$. When this prediction first appeared in 2008, $\theta_{13}$ was consistent with zero and $\theta_{23}$ with $\pi/4$. Non-zero $\theta_{13}$ was established by Daya Bay in 2012. Non-zero $|\frac{\pi}{4}-\theta_{23}|$ is now favored by the NO$\nu$A experiment and, for $\theta_{23}$, the aforementioned $T^{'}$ relation selects the second octant ($\theta_{23} > \frac{\pi}{4}$) over the first octant ($\theta_{23} < \frac{\pi}{4}$). 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.