Majorana Neutrinos: Evidence of Particle vs. Antiparticle?

[Malamala]

Hello! I don't know much about this topic so I am sorry if my question is silly. As far as I understand if neutrinos are Majorana particles, one consequence is that neutrinos are their own antiparticles. This can be observed, for example, in neutrinoless double beta decay. However, if we take the following reaction: $$\nu+p\to e^++n$$ we know from experiment that when $\nu$ is what we identify as an antineutrino the reaction is observed, but when $\nu$ is what we call a neutrino, the reaction doesn't take place. If the neutrino and antineutrino were the same particles, shouldn't both reaction take place equally often? Isn't this a clear evidence that neutrino is not its own antiparticle and hence not a Majorana particle? Of course I am missing something but I am not sure what. Can someone enlighten me please? Thank you!

 

[mfb]

The process would be possible but extremely unlikely, suppressed by the small mass of the neutrino relative to its energy. What we call antineutrino would be a neutrino with opposite helicity*, and due to the small mass the two are nearly independent even if neutrinos are Majorana particles.

*I hope I remember that correctly

 

[Malamala]

The process would be possible but extremely unlikely, suppressed by the small mass of the neutrino relative to its energy. What we call antineutrino would be a neutrino with opposite helicity*, and due to the small mass the two are nearly independent even if neutrinos are Majorana particles.

*I hope I remember that correctly

Sorry, I am a bit confused. If the neutrino and anti neutrino would be the exactly same particle, wouldn't the reaction rates be the same, as they are the same particle? Why would we get a further suppression for one over the other?

 

[mfb]

They are the same particle but they are arriving at your proton in different states.

It's a bit similar to light which has two polarizations. Same particle (photons), but you can have systems that let one polarization pass and not the other.

 

[Malamala]

They are the same particle but they are arriving at your proton in different states.

It's a bit similar to light which has two polarizations. Same particle (photons), but you can have systems that let one polarization pass and not the other.

Oh, I think I understand. But why don't we have the same argument for neutrinoless double beta decay? In principle we would need at one vertex a LH neutrino and at the other a RH antineutrino (in order for them to interact weakly). Given that they are the same particle (i.e. same line in a Feynman diagram), they can't be both LH and RH at the same time. So shouldn't neutrinoless double beta decay not take place by the same argument that the above reaction doesn't take place?

 

[vanhees71]

http://www.maria-laach.tp.nt.uni-siegen.de/downloads/files/2016/Mertens-2016-2.pdf