See links here, here, here, here and here. The hard fact is: massive right handed neutrinos don’t contribute much to weak interactions because of their immense mass, but do interact with gravity unlike massless left handed neutrinos. I can’t understand why dark matter in the form of massive right handed neutrinos isn’t already considered a confirmed fact, based on experimental evidence of neutrino flavor mixing! (See my discussion of massive right handed neutrino lifespan evidence below.)
Right handed neutrinos are implied by neutrino flavor mixing data and the see-saw mechanism for neutrino mass: left handed neutrinos are massless, right handed neutrinos are massive, so the small apparent (“observed”) masses of neutrinos are an average over time for oscillations between the briefly-existing massive right-handed neutrinos (which, due to their large mass, have a short mean-free-path before transforming back into massless left-handed neutrinos in the vacuum) and the longer-existing (massless) left handed neutrinos, which can only undergo weak interactions!
The (large) mass of right-handed neutrinos makes them couple to the gravity field, not only the weak interaction; but the lack of mass of left-handed neutrinos ensures that those merely couple to the weak force, not gravity. This asymmetry in couplings for the two kinds of neutrinos is responsible for the small observable apparent mass of neutrinos, which is simply a time-average superposition between both of the states. I don’t understand how anyone can accept the model for neutrino oscillation between between left and right handed states, if they don’t accept that both states have at least one interaction (i.e. Standard Model weak charge) in common, so I disagree strongly with Peter Woit’s statement that right-handed massive neutrinos don’t undergo weak (or any other S.M.) interactions:
Right-handed neutrino fields fit naturally into the SM pattern of fundamental fields, but with zero SU(3)xSU(2)xU(1) charges. That such fields have something to do with dark matter looks more promising than the SUSY or axion proposals of introducing a new and different sector of fields. – Woit
I disagree that right-handed neutrinos need to have a lack of weak charge: their short life (due to their mass) reduces the effective weak charge of right-handed neutrinos, simply because they aren’t there for long, as compared to left-handed neutrinos! So I very much prefer Professor Matt Strassler’s far more cautiously-worded comment about right handed neutrinos:
… the dark matter particles are kind of like neutrinos — they’re fermions, like neutrinos, and they are connected to neutrinos in some way, though they aren’t as directly affected by the weak nuclear force. [Emphasis added to key words.]
The fact that the right-handed neutrinos “aren’t as directly affected by the weak nuclear force” as left-handed neutrinos is simply down to their short-lifetime due to their immense mass.
The lifetime for spontaneously produced particles of mass m in vacuum is only h-bar/(mc^2) seconds, whereas left handed neutrinos are massless and therefore have an effectively infinite lifetime, and so they remain unchanged until they undergo a weak interaction with either a flavour-changing, massive, short-lived right-handed neutrino in the vacuum, or else a Standard Model weak charge.
Since the massive Standard Model charges that form ordinary matter are long lived (not spontaneous pair-production short-life particles in the vacuum), their weak charge cross-sections are more apparent, simply because they last far than those of massive right-handed neutrinos, a simple fact that apparently appears so “facile” to some highly technical dudes, that no effect is made to grasp it at all!