Heavy Neutral Leptons from kaon decays in the SHiP experiment
  We calculate the signal rate of hypothetical heavy neutral leptons (HNL or
sterile neutrinos) from kaon decays expected in the framework of the SHiP
experiment. The kaons are produced in the hadronic shower initiated in the
beam-dump mode by 400 GeV protons from CERN SPS. For a sufficiently light HNL
(when the decays are kinematically allowed) we find kaon decays to be a
noticeably richer source of HNL as compared to $D$-meson decays adopted in
previous studies of the HNL phenomenology at SHiP. In particular, SHiP is
capable of fully exploring the central part of the kinematically allowed region
of the HNL mass and mixing with electron and muon neutrinos down to the lower
cosmological bound. The latter is associated with HNL decays in the early
Universe to energetic products rescattering off and thus destroying light
nuclei produced at the primordial nucleosynthesis. A consistency of the HNL
model with smaller mixing would require either a hierarchy -- much larger
mixing of all the HNL with tau neutrino -- or non-standard cosmology and new
ingredients in the HNL sector, closing the room for the minimal non-seesaw type
I model with sterile neutrinos lighter than kaons.
