Neutrino physics is one of the rare sectors of the modern physics, where there are experimental discrepancies with the Standard Model (SM) with statistical significance exceeding 5 sigmas. Oscillations between 3 active neutrinos are already well established experimentally and measured with percent precision. This settles a minimal extension of SM, which introduces massive neutrinos. This paper reviews the current experimental situation in the search for an effect which is well beyond SM. Three groups of anomalies could be considered: an appearance anomaly, which occurs when accelerator experiments find an excess of electron neutrino observed in the mainly muon neutrino beam; a gallium anomaly, when a shortage of neutrinos from a radioactive source is observed in gallium-based neutrino detection experiments; a reactor antineutrino anomaly, when a shortage of reactor antineutrinos is observed. A possible explanation of all these anomalies could be neutrino oscillation to a new, so-called sterile, state with mass 1 eV, giving oscillations with characteristic L/E 1 m/MeV.
Igor Alekseev (Mon,) studied this question.