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Q&A

Is it possible to create a beam of non-relativistic neutrinos?

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Neutrinos have extremely low masses, and it's quite easy for them to reach high energies and speeds. As such, it almost always makes sense to treat a neutrino as being relativistic. I've been doing some reading on non-relativistic neutrinos, with kinetic energies of $\lesssim$ 1 meV. These would interact even less with matter than ordinary neutrinos; for example, the threshold for producing inverse beta decay is 1.8 MeV. The only non-relativistic neutrinos currently known to be produced naturally are from the cosmic neutrino background (C$\nu$B), which is redshifted enough for its neutrinos to have a temperature of $\sim$1.95 K and speeds of only several hundred kilometers per second. Therefore, I'm interested in the possibility of producing non-relativistic neutrinos on Earth. Is it possible?

I know that existing neutrino beams produce neutrinos through pion decay (see here for some general history). Proton-proton collisions produce other baryons, including pions and kaons. The charged pions can be aligned by a magnetic field, producing a beam. The pions then decay into muons and muon neutrinos: $$\pi^-\to\mu^-+\bar\nu_{\mu},\quad\pi^+\to\mu^++\nu_{\mu}$$ The muons can be blocked, allowing the muon neutrinos and antineutrinos to continue on to their target.

The problem is, these neutrinos have way too much energy, and clearly continue through the Earth unimpeded until they reach a detector. This makes me think that it's not a great idea to try to create non-relativistic neutrinos in a particle accelerator: The beams need to have a lot of energy to ensure a significant number of proton-proton collisions, but this also means that the decay products have a lot of energy. Assuming my logic is correct (and it could be wrong), we would need another way. Is it possible to create some sort of beam of non-relativistic neutrinos on Earth, or, as I'm increasingly of the opinion, is this simply completely impossible?

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Any mechanism for generating a neutrino beam starts with a way to generate neutrinos, and there is only one underlying means right now: weak decay (including beta decay in radioactive nuclides).

These are three body processes (at tree level) which means that they generate a non-trivial distribution of energies for the products. Being light the neutrino(s) always have a energy distribution that goes to a large fraction of energy available from the decay on one end and to zero on the other. So you can get a few low energy neutrinos just by collecting a large sample of things that decay by weak processes.

But that's not a beam. To make a beam, you have to control the direction.

Conventional beams rely on Lorentz focussing meaning that the progenitors must have a large Lorentz factor, so those beams are necessarily significantly relativistic. You can't make your low energy beam that way.

All is not (yet) lost. Neutrinos are fermions, so they have spin. And they have the unusual property that all are left-handed and anti-neutrinos are all right-handed (in the standard model which we know is wrong in some ways about neutrinos; the jury is still out on this being a actual unbreakable rule or just very strong).

If we had a low energy decay where the mother had a non-trivial angular momentum and could prepare the mother sample in a highly polarized state we could generate direction preference for the neutrino.

On the angular distribution I'm just guessing, but I would expect that this is not a strong preference: more like the simplest directional antennas (the energy goes into one half of space) then something that you would normally term a "beam".

So that's something, but not great. It's not very focussed and it won't be mono-energetic.

And it gets worse. Due to weak universality, decays with a small amount of energy available (which we want to keep the neutrino energies low) will have a longer half-life. So we need a bigger sample and will have a harder time keeping it polarized.

Will you settle for "kinda a beam and very low intensity"?

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