Reassessing the sensitivity to leptonic CP violation

TL;DR

This paper critically examines the standard statistical methods used to assess neutrino experiments' sensitivity to leptonic CP violation, revealing deviations from expected distributions in low-sensitivity scenarios and clarifying the impact of degeneracies.

Contribution

It provides an explicit calibration of the test statistic for neutrino CP violation sensitivity, highlighting when Wilk's theorem applies and when deviations occur due to experimental limitations.

Findings

Deviations from chi-squared distribution occur in low-sensitivity setups.

High-sensitivity experiments tend to conform to chi-squared distribution.

Sign degeneracies influence the test statistic distribution.

Abstract

We address the validity of the usual procedure to determine the sensitivity of neutrino oscillation experiments to CP violation. An explicit calibration of the test statistic is performed through Monte Carlo simulations for several experimental setups. We find that significant deviations from a $\chi^2$ distribution with one degree of freedom occur for experimental setups with low sensitivity to $\delta$. In particular, when the allowed region to which $\delta$ is constrained at a given confidence level is comparable to the whole allowed range, the cyclic nature of the variable manifests and the premises of Wilk's theorem are violated. This leads to values of the test statistic significantly lower than a $\chi^2$ distribution at that confidence level. On the other hand, for facilities which can place better constraints on $\delta$ the cyclic nature of the variable is hidden and, as the potential of the facility improves, the values of the test statistics first become slightly higher than and then approach asymptotically a $\chi^2$ distribution. The role of sign degeneracies is also discussed.