Implications of the Super-K atmospheric, long baseline, and reactor data for the mixing anglesθ13andθ23

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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 Earth's Mikheyev-Smirnov-Wolfenstein (MSW) effect with a castle-wall density. By including terms linear in $\theta${}13 and $\varepsilon${}:=$\theta${}23-$\pi${}/4, we find asymmetric errors for these parameters $\theta${}13=-0.07-0.11+0.18 and $\varepsilon${}=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 $\varepsilon${} are correlated\char22{}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.
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