Abstract: Neutrinos exist in one of three types or 'flavours'-electron, muon and tau neutrinos-and oscillate from one flavour to another when propagating through space. This phenomena is one of the few that cannot be described using the standard model of particle physics (reviewed in ref. (1)), and so its experimental study can provide new insight into the nature of our Universe (reviewed in ref. (2)). Neutrinos oscillate as a function of their propagation distance (L) divided by their energy (E). Therefore, experiments extract oscillation parameters by measuring their energy distribution at different locations. As accelerator-based oscillation experiments cannot directly measure E, the interpretation of these experiments relies heavily on phenomenological models of neutrino-nucleus interactions to infer E. Here we exploit the similarity of electron-nucleus and neutrino-nucleus interactions, and use electron scattering data with known beam energies to test energy reconstruction methods and interaction models. We find that even in simple interactions where no pions are detected, only a small fraction of events reconstruct to the correct incident energy. More importantly, widely used interaction models reproduce the reconstructed energy distribution only qualitatively and the quality of the reproduction varies strongly with beam energy. This shows both the need and the pathway to improve current models to meet the requirements of next-generation, high-precision experiments such as Hyper-Kamiokande (Japan)(3) and DUNE (USA)(4). Electron scattering measurements are shown to reproduce only qualitatively state-of-the-art lepton-nucleus energy reconstruction models, indicating that improvements to these particle-interaction models are required to ensure the accuracy of future high-precision neutrino oscillation experiments.

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.

Abstract: Heavy neutral leptons are predicted in many extensions of the Standard Model with massive neutrinos. If kinematically accessible, they can be copiously produced from kaon and pion decays in atmospheric showers, and subsequently decay inside large neutrino detectors. We perform a search for these long-lived particles using Super-Kamiokande multi-GeV neutrino data and derive stringent limits on the mixing with electron, muon and tau neutrinos as a function of the long-lived particle mass. We also present the limits on the branching ratio versus lifetime plane, which are helpful in determining the constraints in non-minimal models where the heavy neutral leptons have new interactions with the Standard Model.