On the determination of the leptonic CP phase

The combination of data from long-baseline and reactor oscillation experiments leads to a preference of the leptonic CP phase $δ_{\rm CP}$ in the range between $π$ and $2π$. We study the statistical significance of this hint by performing a Monte Carlo simulation of the relevant data. We find that the distribution of the standard test statistic used to derive confidence intervals for $δ_{\rm CP}$ is highly non-Gaussian and depends on the unknown true values of $θ_{23}$ and the neutrino mass ordering. Values of $δ_{\rm CP}$ around $π/2$ are disfavored at between $2σ$ and $3σ$, depending on the unknown true values of $θ_{23}$ and the mass ordering. Typically the standard $χ^2$ approximation leads to over-coverage of the confidence intervals for $δ_{\rm CP}$. For the 2-dimensional confidence region in the ($δ_{\rm CP},θ_{23}$) plane the usual $χ^2$ approximation is better justified. The 2-dimensional region does not include the value $δ_{\rm CP} = π/2$ up to the 86.3\% (89.2\%)~CL assuming a true normal (inverted) mass ordering. Furthermore, we study the sensitivity to $δ_{\rm CP}$ and $θ_{23}$ of an increased exposure of the T2K experiment, roughly a factor 12 larger than the current exposure and including also anti-neutrino data. Also in this case deviations from Gaussianity may be significant, especially if the mass ordering is unknown.

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