Tensions in several phenomenological models grew with experimental results on neutrino/antineutrino oscillations at Short-Baseline (SBL) and with the recent, carefully recomputed, antineutrino fluxes from nuclear reactors. At a refurbished SBL CERN-PS facility an experiment aimed to address the open issues has been proposed [1], based on the technology of imaging in ultra-pure cryogenic Liquid Argon (LAr). Motivated by this scenario a detailed study of the physics case was performed. We tackled specific physics models and we optimized the neutrino beam through a full simulation. Experimental aspects not fully covered by the LAr detection, i.e. the measurements of the lepton charge on event-by-event basis and their energy over a wide range, were also investigated. Indeed the muon leptons from Charged Current (CC) (anti-)neutrino interactions play an important role in disentangling different phenomenological scenarios provided their charge state is determined. Also, the study of muon appearance/disappearance can benefit of the large statistics of CC muon events from the primary neutrino beam. Results of our study are reported in detail in this proposal. We aim to design, construct and install two Spectrometers at NEAR and FAR sites of the SBL CERN-PS, compatible with the already proposed LAr detectors. Profiting of the large mass of the two Spectrometers their stand-alone performances have also been exploited.
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