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Would it be theoretically possible for a high energy neutrino and another high energy anti-neutrino to annihilate into a boson?
Which boson(s) would be possible theoretically?
- one or more photons ?
- the Higgs boson ?
- Z boson ?

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I think it would be helpful if the answers include expressions for the cross sections for the various processes. – Count Iblis Jul 21 '14 at 17:12
up vote 9 down vote accepted

The neutrino and the anti-neutrino can annihilate to create a $Z$ boson. But the mass of the $Z$ boson is around $90$ GeV, so in order to create such a boson, the neutrinos need to be high energetic.

Theoretically, a Higgs boson could be created as well, but for that an even larger amount of energy is needed, since the Higgs boson is heavier than the $Z$ boson. Moreover, the coupling of the Higgs to the neutrinos is extremely small. The Higgs boson's coupling is proportional to the mass of the neutrinos. Neutrinos are known to have a non-vanishing mass but a very small one. Because of the very low mass, the coupling is also very small. This is not a process that likely is going to be observed in an experiment.

On the other hand, the creation of photons is not possible at all. Photons couple to electric charge. Neutrinos are neutral, hence no coupling to photons.

Maybe even more interesting than a neutrino-antineutrino annihilation would be the observation of a neutrino-neutrino annihilation. If neutrinos are their own antiparticles, we call them Majorana neutrinos (otherwise they are called Dirac neutrinos).

We don't know if neutrinos are Majorana or Dirac. If we would observe a neutrino-neutrino annihilation, it would be a clear sign that neutrinos are Majorana. But neutrino experiments are notoriously difficult to carry out. The only experiment that I know of that is looking for a neutrino-neutrino annihilation, is the neutrinoless double $\beta$ decay.

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Photons can be produced (e.g. the Z boson couples to charged stuff, or neutrinos couple directly to Ws). Of course such amplitudes are probably ridicolous. – fqq Jul 21 '14 at 15:02
Sorry, I accidentally approved an edit, now reverted. But the edit questions whether "If we would observe a neutrino-neutrino annihilation, it would be a clear sign that neutrinos are Majorana" should end with Dirac. I think not. – innisfree Jul 21 '14 at 16:25
Are annihilations into W$^0$ bosons specifically forbidden? – Emilio Pisanty Jul 21 '14 at 17:18
Majorana is correct. Thanks for reverting the edit. If there would exist a physical $W^0$, neutrinos could couple to it. – pfnuesel Jul 21 '14 at 19:05
I'm confused. I thought W0 = Z. – Joshua Jul 21 '14 at 19:59

Yes, the Z boson can decay into a neutrino and anti-neutrino, and the process you describe is just the time reverse of this.

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Z boson can decay to a neutrino-antineutrino pair. Your this process is the reverse of the decay.

Direct combination to photon(s) is impossible, because photons don't interact weakly, and neutrinos don't interact electromagnetic.

Direct combination to Higgs were (IMHO) possible, because it doesn't contradict to a preservation law, but I think it has an extreme low cross section.

AFAIK in supernova explosions, the neutrino annihilation has an important part in the processes.

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Were you thinking of neutrino absorption? I've seen estimates that layer of matter just outside the core in a supernova collapse is dense enough to absorb ~10% of the neutrino flux produced within the core itself; but don't recall seeing anything about neutrino annihilation before. – Dan Neely Jul 21 '14 at 18:53

But also we have to note that photon pair creation through neutrino anti-neutrino annihilation is possible at higher orders in perturbation theory (starting at the one-loop level with the exchange of charged leptons and $W^\pm$ vector boson). This process has indeed very small cross section because of the loop integral suppression factor.

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A remark: if neutrinos were massless, even at higher order annihilation of $\nu+\bar{\nu} \to \gamma \gamma$ would be forbidden. The reason is related to the Yang-Landau theorem which states that spin 1 object cannot decay into 2 photons. Since with massless neutrinos, helicity is equivalent to chirality and only left-handed neutrino and right-handed antineutrino interact, the system $\nu + \bar{\nu}$ would form a spin 1 object, hence the interdiction. Now, since neutrinos have mass, there should be a possibility that the chiral $\bar{\nu}_R$ is a helicity $\bar{\nu}_L$ forming a spin 0 system – Paganini Jan 11 at 13:42
I agree with you concerning this. But we know that neutrinos have a tiny mass which would made the process possible. Also I was thinking about box diagrams. Thanks @Paganini for the remark. – Adil Jueid Jan 11 at 13:45

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