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Observational limits on the high-energy neutrino background have been used to place general constraints on dark matter that annihilates only into standard model particles.
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There is also a constraint on “secret” self-interactions of neutrinos, coming from the observed invisible width of the Z Z boson: M. S. Bilenky and A. Santamaria, arXiv:hep-ph/9908272. However, this constaint turns out to be that the ν ν ¯ ν ν ¯ \nu\bar{\nu}\nu\bar{\nu} operator be as weak or weaker than the SM Fermi coupling G F G_{F} . In contrast, the dark matter operator χ χ ¯ ν ν ¯ \chi\bar{\chi}\nu\bar{\nu} is already of weak strength, so the loop-induced ν ν ¯ ν ν ¯ \nu\bar{\nu}\nu\bar{\nu} operator obtained by “squaring” χ χ ¯ ν ν ¯ \chi\bar{\chi}\nu\bar{\nu} and integrating out the χ \chi and χ ¯ \bar{\chi} would be much smaller
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T.E. Jeltema and S. Profumo, arXiv:0805.1054
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