  Standard model of particle physics fails to explain neutrino oscillations,
dark matter and baryon asymmetry of the Universe. All these problems can be
solved with three sterile neutrinos added to the model. Quite remarkably, if
sterile neutrino masses are well below the electroweak scale, this modification
--- Neutrino Minimal Standard Model (nuMSM) --- can be tested experimentally.
We discuss a new experiment on search for decays of GeV-scale sterile
neutrinos, which in the framework of the nuMSM are responsible for the
matter-antimatter asymmetry generation and for the active neutrino masses. If
lighter than 2 GeV, these particles can be produced in decays of charm mesons
generated by high energy protons in a target of a proton beam-dump experiment,
and subsequently decay into light SM particles. In order to fully explore this
sector of the nuMSM, the new experiment requires data obtained with at least
10^{20} incident protons on target (achievable at CERN SPS in the future), and
a big volume detector constructed from a large amount of identical single
modules, with a total sterile neutrino decay length of few kilometers. The
preliminary feasibility study for the proposed experiment shows that it has
sensitivity which may either lead to the discovery of new particles below the
Fermi scale --- right-handed partners of neutrinos --- or rule out see-saw
sterile neutrinos with masses below 2 GeV.
