On the determination of the leptonic CP phase

Abstract: The combination of data from long-baseline and reactor oscillation experiments leads to a preference of the leptonic CP phase $\delta_{\rm CP}$ in the range between $\pi$ and $2\pi$. 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 $\delta_{\rm CP}$ is highly non-Gaussian and depends on the unknown true values of $\theta_{23}$ and the neutrino mass ordering. Values of $\delta_{\rm CP}$ around $\pi/2$ are disfavored at between $2\sigma$ and $3\sigma$, depending on the unknown true values of $\theta_{23}$ and the mass ordering. Typically the standard $\chi^2$ approximation leads to over-coverage of the confidence intervals for $\delta_{\rm CP}$. For the 2-dimensional confidence region in the ($\delta_{\rm CP},\theta_{23}$) plane the usual $\chi^2$ approximation is better justified. The 2-dimensional region does not include the value $\delta_{\rm CP} = \pi/2$ up to the 86.3\% (89.2\%)~CL assuming a true normal (inverted) mass ordering. Furthermore, we study the sensitivity to $\delta_{\rm CP}$ and $\theta_{23}$ 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.