# The difference of neutrino and anti-neutrino? If Majorana

• Accidently
In summary, people are discussing whether neutrinos have the properties of particles and antiparticles simultaneously. If neutrinos are Majorana particles, they would have the property of being "identical to their anti particle", but that is not the case because anti neutrinos are obviously different. The problem is that neutrinos are so unreactive that one cannot produce them and decay them within the same experiment. So either one produces them through weak interactions or detects them. For CP violation in the neutrino sector, people are looking for a helicity flip in the lepton number violation process, but that is difficult to realize for a real relativistic particle.
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...

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 $$e^{-} \rightarrow W^{-} \nu_{e}$$) 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 :(

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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?

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.

Accidently said:
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...
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.

Accidently said:
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.

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 traveling 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.

Severian said:
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 traveling 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.

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?

## 1. What is the difference between a neutrino and an anti-neutrino?

Neutrinos and anti-neutrinos are both subatomic particles that have no electric charge. However, they differ in their quantum spin, with neutrinos having a spin of 1/2 and anti-neutrinos having a spin of -1/2. They also differ in their interactions with other particles, with neutrinos only interacting through the weak nuclear force and anti-neutrinos interacting through both the weak nuclear force and the electromagnetic force.

## 2. How are neutrinos and anti-neutrinos related to each other?

Neutrinos and anti-neutrinos are related through a process called "neutrino oscillation", where a neutrino can spontaneously change into an anti-neutrino and vice versa. This phenomenon is possible because neutrinos and anti-neutrinos are actually two different states of the same particle, known as a "neutrino flavor".

## 3. What is a Majorana neutrino?

A Majorana neutrino is a theoretical type of neutrino that is its own antiparticle. This means that a Majorana neutrino and a Majorana anti-neutrino are indistinguishable from each other. This is in contrast to the more commonly known Dirac neutrinos, where neutrinos and anti-neutrinos are distinct particles.

## 4. How do we know if a neutrino is a Majorana particle?

One way to determine if a neutrino is a Majorana particle is through a process called "neutrinoless double beta decay". In this process, a nucleus decays into a different nucleus by emitting two electrons and no anti-neutrinos. If this process is observed, it would confirm that neutrinos are Majorana particles.

## 5. What are the implications of a neutrino being a Majorana particle?

If a neutrino is indeed a Majorana particle, it would have significant implications for our understanding of particle physics and the universe. It would also have implications for the search for dark matter, as Majorana neutrinos could potentially make up a portion of dark matter. Additionally, understanding the nature of Majorana neutrinos could help us understand why there is more matter than antimatter in the universe.

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