Neutrino Masses and Mixing one Decade from Now

We review the status of neutrino masses and mixings in the light of the solar and atmospheric neutrino data. The result from the LSND experiment is also considered. We discuss the present knowledge and the expected sensitivity to the neutrino mixing parameters in the simplest schemes proposed to reconcile these data some of which include a light sterile neutrino in addition to the three standard ones. 1 1 Indications for Neutrino Mass: Two–Neutrino Analysis Neutrinos are the only massless fermions predicted by the Standard Model. This seemed to be a reasonable assumption as none of the laboratory experiments designed to measure the neutrino mass have found any positive evidence for a non-zero neutrino mass. However, the confidence on the masslessness of the neutrino is now under question due to the important results of underground experiments, starting by the geochemical experiments of Davis and collaborators till the more recent Gallex, Sage, Kamiokande and Super– Kamiokande (SK) experiments (1; 2; 3). Altogether they provide solid evidence for the existence of anomalies in the solar and the atmospheric neutrino fluxes which could be explained by the hypothesis of neutrino oscillations which requires the presence of neutrino masses and mixings. Particularly relevant has been the recent confirmation by the SK collaboration (3) of the 1 Talk given at the ICFA/ECFA Workshop ”Neutrino Factories based on Muon Storage Rings, ν-FACT99”, Lyon, July 1999. Preprint submitted to Elsevier Preprint 18 April 2008 atmospheric neutrino zenith-angle-dependent deficit which strongly indicates towards the existence of νμ conversion. Together with these results there is also the indication for neutrino oscillations in the ν̄μ → ν̄e channel by the LSND experiment (4). We first review our present knowledge of the present experimental status for the different evidences and present the results of the different analysis in the framework of two–neutrino oscillations.