Statistical interpretation of sterile neutrino oscillation searches at reactors

TL;DR

This paper develops a new statistical framework for analyzing sterile neutrino oscillation data from reactors, revealing that traditional methods overestimate significance levels, and applies it to real experimental data.

Contribution

It introduces an asymptotic distribution for the log-likelihood in neutrino experiments, correcting the statistical interpretation of sterile neutrino hints.

Findings

Reveals Wilks' theorem does not hold for neutrino oscillation data.

Provides a new method for accurate significance estimation.

Applies the framework to Neutrino-4 data, reducing the significance from 3.2σ to 2.6σ.

Abstract

A considerable experimental effort is currently under way to test the persistent hints for oscillations due to an eV-scale sterile neutrino in the data of various reactor neutrino experiments. The assessment of the statistical significance of these hints is usually based on Wilks' theorem, whereby the assumption is made that the log-likelihood is $\chi^2$-distributed. However, it is well known that the preconditions for the validity of Wilks' theorem are not fulfilled for neutrino oscillation experiments. In this work we derive a simple asymptotic form of the actual distribution of the log-likelihood based on reinterpreting the problem as fitting white Gaussian noise. From this formalism we show that, even in the absence of a sterile neutrino, the expectation value for the maximum likelihood estimate of the mixing angle remains non-zero with attendant large values of the log-likelihood. Our analytical results are then confirmed by numerical simulations of a toy reactor experiment. Finally, we apply this framework to the data of the Neutrino-4 experiment and show that the null hypothesis of no-oscillation is rejected at the 2.6\,$\sigma$ level, compared to 3.2\,$\sigma$ obtained under the assumption that Wilks' theorem applies.