# On the determination of the leptonic CP phase

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## Abstract

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 *θ* _{23} 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 *θ* _{23} and the mass ordering. Typically the standard *χ* ^{2} approximation leads to over-coverage of the confidence intervals for *δ* _{CP}. For the 2-dimensional confidence region in the (*δ* _{CP}, *θ* _{23}) plane the usual *χ* ^{2} 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 *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.

## Keywords

Neutrino Physics CP violation## Notes

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**Open Access**This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.