Regular Article - Theoretical Physics
Statistical interpretation of sterile neutrino oscillation searches at reactors
Instituto de Física Teórica UAM/CSIC, Universidad Autónoma de Madrid, Calle Nicolás Cabrera 13-15, 28049, Madrid, Spain
2 Instituto de Física Corpuscular UV/CSIC, Parque Científico, Calle Catedrático José Beltrán 2, 46980, Paterna, Spain
3 Physics Department, Center for Neutrino Physics, Virginia Tech, Blacksburg, USA
4 Institut für Astroteilchenphysik, Karlsruher Institut für Technologie (KIT), 76021, Karlsruhe, Germany
Accepted: 16 December 2020
Published online: 2 January 2021
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 -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 level, compared to 3.2 obtained under the assumption that Wilks’ theorem applies.
© The Author(s) 2020
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