  The NESSiE experiment is designed to perform an accurate measurement of
muon-neutrino disappearance at small L/E, in order to severely constrain models
with more than three-standard neutrinos, or even determine for the first time
the presence of a new kind of neutrino oscillation. NESSiE is a Short-Baseline
experiment with magnetic spectrometers at two different sites on the
FNAL-Booster neutrino beam. The experiment would allow to definitively solve
the existing tension of the muon-neutrino disappearance result with the
appearance and disappearance "anomalies" at eV mass scale, by spanning one more
order of magnitude in the mixing angle between standard and sterile neutrinos.
We demonstrate that this project constitutes the most robust and fast way to
unambigously study the neutrino physics at that scales.
