A neutral fermion without the ordinary active-neutrino weak gauge couplings. Mixing can still let it interact or decay. Its possible dark-matter role depends on lifetime, production and free streaming, rather than on Majorana character alone.
A right-handed neutrino can transform as under colour, weak isospin and hypercharge. It has no direct Standard Model gauge coupling, but may mix with active neutrinos. Sterility under the low-energy group does not imply sterility under an enlarged unbroken gauge group.
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A sterile neutrino is a hypothetical type of neutrino that does not interact via the standard weak interactions like the three known types of neutrinos: electron neutrinos, muon neutrinos, and tau neutrinos. Instead, sterile neutrinos are proposed to interact only through gravity and possibly via mixing with active neutrinos, making them "sterile" because they do not participate in the weak force.