Implications of the Super-K atmospheric data for the mixing angles ${\theta }_{13}$ and ${\theta }_{23}$

Abstract

A three-neutrino analysis of oscillation data is performed using the recent, more finely binned Super-K oscillation data, together with the CHOOZ, K2K, and MINOS data. The solar parameters, ${\Delta }_{21}$ and ${\theta }_{12}$, are fixed from a recent analysis, and ${\Delta }_{32}$, ${\theta }_{13}$, and ${\theta }_{23}$ are varied. We utilize the full three-neutrino oscillation probability and an exact treatment of the Earth's MSW effect with a castle-wall density. By including terms linear in ${\theta }_{13}$ and $\epsilon :={\theta }_{23}-\pi /4$, we find asymmetric errors for these parameters ${\theta }_{13}=-0.07_{-0.11}^{+0.18}$ and $\epsilon =0.03_{-0.15}^{+0.09}$. For ${\theta }_{13}$, we see that the lower bound is primarily set by the CHOOZ experiment while the upper bound is determined by the low energy $e$-like events in the Super-K atmospheric data. We find that the parameters ${\theta }_{13}$ and $\epsilon$ are correlated -- the preferred negative value of ${\theta }_{13}$ permits the preferred value of ${\theta }_{23}$ to be in the second octant, and the true value of ${\theta }_{13}$ affects the allowed region for ${\theta }_{23}$.

Comments: 15 pages, 13 figures, submitted to Phys. Rev. C