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Hints for sizable $\sin^2 \theta_{13}$ have been reported in earlier globalneutrino 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 eraof precision neutrino oscillation experiments, terms linear in$\sin\theta_{13}$ will no longer be negligible, and its sign would affect theextraction of other oscillation parameters. The sign of $\sin\theta_{13}$ alsoplays a crucial role in the determination of the CP-violating phase. In thiswork we show that by adopting an alternative parametrization for thePontecorvo-Maki-Nakagawa-Sakata (PMNS) mixing matrix, one already has a chanceto infer the sign of each mixing angle in the conventional parametrizationusing 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 thespeculation on whether the Mikheyev-Smirnov-Wolfenstein (MSW) effect isresponsible. In this work we found that in the new mixing matrixparametrization, the 68% CL constraints on the three mixing angles arecomparable to those estimated in the conventional parametrization adopted inthe literature. Owing to the strong correlations among the three mixing anglesin the new parametrization, the advantages of doing the global neutrinooscillation analysis using data from past, current, and near future neutrinooscillation experiments shall become manifest.

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