We suggest a hybrid seesaw model where relatively light right-handed neutrinos give no contribution to neutrino mass matrix due to a special symmetry. This allows their Yukawa couplings to the standard model particles to be relatively strong, so that the standard model Higgs boson can decay dominantly to a left- and a right-handed neutrino, leaving another stable right-handed neutrino as cold dark matter. In our model neutrino masses arise via the type-II seesaw mechanism, the Higgs triplet scalars being also responsible for the generation of the matter-antimatter asymmetry via the leptogenesis mechanism.
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