Neutrino physics is nowadays receiving more and more attention as a possible source of information for the long-standing problem of new physics beyond the Standard Model. The recent measurement of the third mixing angle theta13 in the standard mixing oscillation scenario encourages us to pursue the still missing results on leptonic CP violation and absolute neutrino masses. However, several puzzling measurements exist, which deserve an exhaustive evaluation. The NESSiE Collaboration has been setup to undertake a definitive experiment to clarify the muon disappearance measurements at small L/E, which will be able to put severe constraints to any model with more than the three-standard neutrinos, or even to robustly measure the presence of a new kind of neutrino oscillation for the first time. Within the context of the current CERN project, aimed to revitalize the neutrino field in Europe, we will illustrate the achievements that can be obtained by a double muon-spectrometer system, with emphasis on the search for sterile neutrinos.
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