Global Neutrino Data Analysis and the Quest to Pin Down $\sin\theta_{13}$ in Different Mixing Matrix Parametrizations

Hints for sizable $\sin^2 \theta_{13}$ have been reported in earlier global neutrino oscillation data analyses as well as will be reported in this work, and quite recently by the Double Chooz experiment. However, as we enter the era of precision neutrino oscillation experiments, terms linear in $\sin\theta_{13}$ will no longer be negligible, and its sign would affect the extraction of other oscillation parameters. The sign of $\sin\theta_{13}$ also plays a crucial role in the determination of the CP-violating phase. In this work we show that by adopting an alternative parametrization for the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) mixing matrix, one already has a chance to infer the sign of each mixing angle in the conventional parametrization using existing global neutrino data. A weak preference for negative $\sin \theta_{13}$ is found. In particular, the solar data suggest that $\sin\theta_{13} > 0$ while all other data the opposite. This leads to the speculation on whether the Mikheyev-Smirnov-Wolfenstein (MSW) effect is responsible. In this work we found that in the new mixing matrix parametrization, the 68% CL constraints on the three mixing angles are comparable to those estimated in the conventional parametrization adopted in the literature. Owing to the strong correlations among the three mixing angles in the new parametrization, the advantages of doing the global neutrino oscillation analysis using data from past, current, and near future neutrino oscillation experiments shall become manifest.

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