  We study an effective theory beyond the standard model (SM) where either of
two additional gauge singlets, a Majorana fermion and a real scalar,
constitutes all or some fraction of dark matter. In particular, we focus on the
masses of the two singlets in the range of O(10) MeV-O(10) GeV, with a neutrino
portal interaction which plays important roles not only in particle physics but
also in cosmology and astronomy. We point out that the dark matter abundance
can be thermally explained with (co)annihilation, where the dark matter with a
mass greater than 2 GeV can be tested in future lepton colliders, CEPC, ILC,
FCC-ee and CLIC, in the light of the Higgs boson invisible decay. When the
gauge singlets are lighter than O(100)MeV, the interaction can affect the
neutrino propagation in the universe due to its annihilation with the cosmic
background neutrino into the gauge singlets. Although can not be the dominant
dark matter in this case, the singlets are produced by the invisible decay of
the Higgs boson at a rate fully within the reach of the future lepton
colliders. In particular, a high energy cutoff of cosmic-ray neutrino, which
may account for the non-detection of Greisen-Zatsepin-Kuzmin (GZK) neutrinos or
non-observation of Glashow resonance, can be set. Interestingly, given the
cutoff and the mass (range) of the WIMP, a neutrino mass can be "measured"
kinematically.
