# Neutrino annihilation and bosons

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?
• 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

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.

• 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
• The $W^0$ boson from the $W$ triplet is not the same as the $Z$ boson. Neither masses nor couplings are correct. The $Z$ boson is a linear combination of $W^0$ and the singlet state $B^0$. Specifically: $Z = -\sin{\theta_W} B^0 + \cos{\theta_W} W^0$, where $\theta_W$ is the Weinberg angle. – pfnuesel Jul 21 '14 at 20:10
• @pfnuesel I think your statement about the Higgs coupling to neutrinos is imprecise. First of all, the Higgs coupling to neutrinos has nothing to do with the fact that the Higgs is much heavier than neutrinos. Second, how do we know that the corresponding coupling is small? We don't even known the mechanism responsible for neutrino's mass. If it was a simple Yukawa interaction, then you would be right. But remember that a right-handed neutrino has never been observed in nature. – Melquíades Jul 22 '14 at 14:51
• The coupling of the Higgs is proportional to the neutrino mass, not to the Higgs mass, I improved my answer to make this more clear. And yes, we don't know the mechanism how the neutrinos receive mass. I simply assumed it's the same Yukawa coupling as for other elementary particles. – pfnuesel Jul 22 '14 at 15:46
• @Michael (past and present) Why don't you ask a new question then? – pfnuesel Oct 19 '18 at 17:29

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

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.

• 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 '16 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 '16 at 13:45

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.

• 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 Is Fiddling By Firelight Jul 21 '14 at 18:53