ar X iv : h ep - p h / 99 07 48 5 v 1 2 6 Ju l 1 99 9 Four - neutrino mixing

It is shown that only two four-neutrino schemes are compatible with the results of all neutrino oscillation experiments. These two schemes have a mass spectrum composed of two pairs of neutrinos with close masses separated by the “LSND gap” of the order of 1 eV. Talk presented at the Xth International School “PARTICLES and COSMOLOGY”, 19–25 April 1999, Baksan Valley, Kabardino-Balkaria, Russia, KIAS-P99067, hep-ph/9907485. The investigation of neutrino properties is considered today as one of the most exciting fields of research in high-energy physics. It has received a stupendous boost from the evidence in favor of neutrino oscillations discovered recently in the Super-Kamiokande experiment [1, 2]. The main Super-Kamiokande evidence in favor of neutrino oscillations consists in the observation of an up–down asymmetry of high-energy μ-like events generated by atmospheric neutrinos: Aμ ≡ (Dμ − Uμ)/(Dμ + Uμ) = 0.311± 0.043± 0.01 [2] . (1) Here Dμ and Uμ are, respectively, the number of downward-going and upward-going events, corresponding to the zenith angle intervals 0.2 < cos θ < 1 and −1 < cos θ < −0.2. Since the fluxes of high-energy downward-going and upward-going atmospheric neutrinos are predicted to be equal with high accuracy on the basis of geometrical arguments (see [3]), the SuperKamiokande evidence in favor of neutrino oscillations is model-independent and provides a definite confirmation of the indications in favor of oscillations of atmospheric neutrinos found in the Super-Kamiokande experiment itself [1, 2, 4] and in other experiments through the measurement of the ratio of μ-like and e-like events (Kamiokande, IMB, Soudan 2 [5]) and through the measurement of upward-going muons produced by neutrino interactions in the rock below the detector (MACRO [6]). Large νμ ⇆ νe oscillations of atmospheric neutrinos are excluded by the absence of a up–down asymmetry of high-energy e-like events generated by atmospheric neutrinos and detected in the Super-Kamiokande experiment (Ae = 0.036± 0.067 ± 0.02 [1]) and by the negative result of the CHOOZ long-baseline ν̄e disappearance experiment [7]. Therefore, the atmospheric neutrino anomaly consists in the disappearance of muon neutrinos and can be explained by νμ → ντ and/or νμ → νs oscillations (here νs is a sterile neutrino that does not take part in weak interactions). Other indications in favor of neutrino oscillations have been obtained in solar neutrino experiments (Homestake, Kamiokande, GALLEX, SAGE, Super-Kamiokande [8]) and in the LSND experiment [9]. The flux of electron neutrinos measured in all five solar neutrino experiments is substantially smaller than the one predicted by the Standard Solar Model [10] and a comparison of the data of different experiments indicate an energy dependence of the solar νe suppression, which represents a rather convincing evidence in favor of neutrino oscillations (see [11]