Comment on “A New Dark Matter Candidate: Non–thermal Sterile Neutrinos”

I point out that the sterile neutrinos suggested as candidates for “cool” Dark Matter will decay through their mixing with light neutrinos. This leads to an upper bound of about 200 keV on the mass of the sterile neutrinos, but might facilitate their detection. Recently Shi and Fuller proposed [1] a new kind of Dark Matter candidate: a sterile neutrino, with small but non–vanishing mixing with the ordinary neutrinos. The idea is that a large pre–existing lepton asymmetry stored in light neutrinos can be converted into an asymmetry of massive sterile neutrino through a thermal resonance. Since low–energy neutrinos would be converted first, the resulting relic neutrinos are less energetic (“cooler”) than thermal relics of the same mass would be. This mechanism requires [1] a lepton asymmetry ∆L> ∼10 −3 and a mixing angle between active and sterile neutrinos sin 2θ > ∼ 10 . One then obtains the desired relic density for mνs ∼ 1 keV · (0.1/∆L). An explicit particle physics model along these lines has been constructed by Chun and Kim [2]. Here the sterile “neutrino” is the axino, which mixes with ordinary neutrinos through R–parity violating interactions. These studies seem to have overlooked the simple fact that the mixing with ordinary, light neutrinos allows the sterile neutrino to decay into three light neutrinos through the exchange of a virtual Z boson. The total decay width of the sterile neutrino is then found to be Γ(νs → 3ν) = Γ(μ − → e−νμν̄e) · sin 2 θeff · (