I Can Neutrinos Be Their Own Anti-Particles?

[mifcvm]

If the neutrino has zero charge, can it be its own anti-particle? If they are the same particle, can they annihilate?
Or are they different particles?
In addition, I read that annihilation would violate one of the conservation laws of the standard model (leptonic number)... How does this happen?

 

[ChrisVer]

If the neutrino has zero charge, can it be its own anti-particle?

In some theories yes, the neutrinos are their own antiparticles (see for example Majorana neutrinos). But still you would need right-handed neutrinos and left-handed antineutrinos for that (which could potentially exist but not interact with the weak interactions).

If they are the same particle, can they annihilate?

Yes, they could potentially annihilate and you would have processes like the neutrinoless double-beta decay. Searches for those decays in nuclei that are unstable to double beta decays have not found anything significant (they only set limits).

In addition, I read that annihilation would violate one of the conservation laws of the standard model (leptonic number)... How does this happen?

Again think of the neutrinoless double beta decay, you would have the production of 2 beta particles out of nowhere (and without neutrinos to account for the lepton number conservation). Your lepton number would go from 0 to (-)2...
https://en.wikipedia.org/wiki/Double_beta_decay#/media/File:Double_beta_decay_feynman.svg

 

[mfb]

A neutrino has zero electric charge. Electric charge is not the only quantum number particles have.

It is possible that they are their own antiparticles, experiments cannot rule out (or confirm) that yet. It would mean neutrinos are Majorana fermions.
If they are, the lepton numbers as we usually define them are not conserved quantities any more. Neutrinoless double beta decay would become possible, the search for this decay is one of the main methods how this is studied.

 

[Orodruin]

But still you would need right-handed neutrinos and left-handed antineutrinos for that (which could potentially exist but not interact with the weak interactions).

This is not correct. Majorana neutrinos do not require the existence of right-handed neutrinos. The most basic example of this being the type-II seesaw model where the Weinberg operator is generated when integrating out a scalar triplet instead of singlet fermions.