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 ${\delta }_{\mathrm{CP}}$ 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 ${\delta }_{\mathrm{CP}}$ is highly non-Gaussian and depends on the unknown true values of ${\theta }_{23}$ and the neutrino mass ordering. Values of ${\delta }_{\mathrm{CP}}$ 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 ${\delta }_{\mathrm{CP}}$. For the 2-dimensional confidence region in the (${\delta }_{\mathrm{CP}},{\theta }_{23}$) plane the usual ${\chi }^2$ approximation is better justified. The 2-dimensional region does not include the value ${\delta }_{\mathrm{CP}}=\pi /2$ up to the 86.3\% (89.2\%)~CL assuming a true normal (inverted) mass ordering. Furthermore, we study the sensitivity to ${\delta }_{\mathrm{CP}}$ 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.

25 pages, 12 figures. Matches version which is to appear in JHEP. New appendix with the first anti-neutrino results from T2K is added

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• Neutrino Oscillation Physics Potential of the T2K Experiment
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• Revisiting fermion mass and mixing fits in the minimal SUSY $SO(10)$ GUT
• A View of Neutrino Studies with the Next Generation Facilities
• Revisiting T2KK and T2KO physics potential and ${\nu }_{\mu }$ - ${\bar{\nu }}_{\mu }$ beam ratio