We use a model, with no CP violation, of the world's neutrino oscillation data, excluding the LSND experiments, and search the full parameter space ($0\leq\theta_{ 12} \le \pi/2$; $-\pi/2 \le \theta_{ 13} \le \pi/2$; and 0\leq\theta_{ 23} \le \pi /2$) for the best fit values of the mixing angles and mass-squared differences. We find that the mixing angle $\theta_{ 13}$ is bounded by $-0.15<\theta_{ 13}<0.20$ with an absolute minimum at $\theta_{ 13}=0.12$ and a local minimum at $-0.04$. The importance of the negative $\theta_{ 13}$ region and this structure in the chi-square space has heretofore been overlooked because the factorization approximation commonly employed yields oscillation probabilities that are a function of $\sin^2\theta_{ 13}$.
Categories: nucl-th
