The difference of neutrino and anti-neutrino? If Majorana

Accidently

People say that if neutrinos are Majorana particles, they are "identical to their anti particle". But anti neutrinos are obviously different from neutrinos. They produce anti-leptons rather than leptons in the scattering process. So the only difference I can image is the helicity, however that is not Lorentz invariant.......

Severian

Well, that is the point. Do neutrinos "produce anti-leptons rather than leptons in the scattering process"? This is not clear. The problem is that they are so unreactive that one cannot produce them and decay them within the same experiment. You either produce them through weak interactions (eg [tex]e^{-} \rightarrow W^{-} \nu_{e}[/tex]) or detect them (e.g. neutrino detectors like superK). To see whether they have the properties of particles and antiparticles simultaneously you need to do both.

Neutrinoless bouble beta decay experiments should tell us once and for all. There you have both because you have two vertices involving neutrinos. One vertex can only happen if it is a neutrino, and the other can only happen if it is an anti-neutrino. So a non-zero result means it must be both at once.

In other words, a Majorana neurtino violates lepton number.

Edit: I don't see what is wrong with that latex :(

Accidently

I think people can both produce and detect neutrino beams. For example, people are doing long base line neutrino oscillation experiments in which neutrinos are produced in the accelerators or reactors, say from muon decay (muon -> muon neutrino + electron + anti electron neutrino) and detected via the weak interaction (in this case muons and positions [rather than anti-muon and electron] would be produced in the target, usually miles away from the neutrino source).

The same situation in the solar neutrino oscillation experiments: in the water tank of SNO/SuperK electrons are produced.

Also, people want find CP violation in the neutrino sector by comparing the transition rate of neutrino and anti-neutrino, e.g. a very recent paper: [hep-ex/0612047] If neutrinos were Majorana type (neutrinos are also anti-neutrinos), how could people detect that?

Accidently

my understanding is there should be a helicity flip in the lepton number violation process (say neutrinoless double beta decay) induced by the neutrino majorana mass. however, that is easy to realize for a virtual particle whereas difficult for a real relativistic particle.

however i do not know if that is true and how to describe that.

RobtO

As I understand it, a Majorana neutrino will look like an antineutrino in some reference frames. So, yes, it is the helicity that makes the difference, and, right, it is not Lorentz invariant.

Severian

Any mass term will flip the helicity - that is what mass terms do. So for a massive particle, helicity is not a good quantum number. Think of it this way: the helicity is the spin in the direction of motion, so all I need to do to change the helicity is go faster than the particle. Then the direction of motion (relative to me) changes, and the helicity flips.

I can only not do that if the particle is travelling at the speed of light (because I can't overtake it). And to go at the speed of light it needs to be massless. So helicity is only a good quantum number for massless particles.

Accidently

Thank you guys for answering my question. I just read a paper talking about lepton number processes. They mention the helicity flip rate is of (m/E)^2 in the limit of m << E. And that is why we cannot verify the Majorana property of neutrinos in neutrino oscillation experiments. But in this case, I was wondering why people do not consider this helicity flip rate in the neutrinoless double beta decay (0vbb) experiments? coz the energy running in the internal neutrino line should be quite larger than neutrino mass, and that should supress the rate of 0vbb.

Is that because such flip rate is not valid for virtual particles? Or has been considered in some sense?