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_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_CP is highly non-Gaussian and depends on the unknown true values of θ₂₃ and the neutrino mass ordering. Values of δ_CP around π/2 are disfavored at between 2σ and 3σ, depending on the unknown true values of θ₂₃ and the mass ordering. Typically the standard χ² approximation leads to over-coverage of the confidence intervals for δ_CP. For the 2-dimensional confidence region in the (δ_CP,θ₂₃) plane the usual χ² approximation is better justified. The 2-dimensional region does not include the value δ_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_CP and θ₂₃ 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.