High-intensity proton beams impinging on a fixed target or beam dump allow to probe new physics via the production of new weakly-coupled particles in hadron decays. The CERN SPS provides opportunities to do so with the running NA62 experiment and the planned SHiP experiment. Reconstruction of kaon decay kinematics (beam mode) allows NA62 to probe for the existence of right-handed neutrinos and dark photons with masses below 0.45 GeV. Direct reconstruction of displaced vertices from the decays of new neutral particles (dump mode) will allow NA62 and SHiP to probe right-handed neutrinos with masses up to 5 GeV and mixings down to several orders of magnitude smaller than current constraints, in regions favoured in models which explain at once neutrino masses, matter-antimatter asymmetry and dark matter.
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