If neutrinos are their own antimatter

[zincshow]

This article on Majorana particles:
http://news.yahoo.com/hunt-source-matter-continues-130052152.html

If neutrinos are their own antimatter partners, it could help explain a fundamental mystery of the universe: Why matter exists at all.

and

If the predictions of the Standard Model — the dominant theory of particle physics that explains subatomic particles — were correct, "you'd expect to produce equal amounts of matter and antimatter"

How is it that a neutrino property (own anti-particle? maybe no anti-particle?) causes more matter to be produced then antimatter?

 

[ChrisVer]

I am not sure whether what that article says is correct or not.
The main thing with the neutrinoless double beta decay is that in fact you have a production of the extra two electrons...and only... neutrinos annihilate with itself so you have a lepton number violation (2 neutrons for example will give 2 protons and 2 electrons as a final result)...
Of course I am not so into that idea- because I think the matter-antimatter asymmetry should have happened before the formation of nuclei, especially heavy nuclei which seem to be subject in the double beta decays (Germanium for example) with reasonable amount of lifetimes...

 

[Matterwave]

I think it would only "help to explain" this, not really explain it very much if you ask me. Neutrinos and anti-neutrinos being the "same" particle really means that they are different helicity states of one another (technically, since neutrinos do have some mass, it should be different spin states, but neutrinos are so light it's not a huge sin, phenomenologically speaking, to regard them as mass less in many cases). The neutrinos would simply be the left-handed helicity states and the anti-neutrinos would be the right handed ones.

It is a known fact that the weak force is left-handed biased. It violates parity conservation by preferring left handed interactions. In this way, I suppose, one might argue that the matter-anti-matter disproportion could be partly due to the left-handed nature of the weak force (a property that is already explained in the standard model). But, and someone chime in here if I'm wrong (which I very well might be!), this wouldn't really help us for the particles which we DO KNOW are NOT Majorana in nature.

 

[Chronos]

The original article can be found here: http://arxiv.org/abs/1402.6956, Search for Majorana neutrinos with the first two years of EXO-200 data. Baryon asymmetry [an excess of matter] can be produced as a consequence of CP [charge parity] violations. This have been observed for quarks, but, not for neutrinos until about a year ago by the T2k collaboration - re: http://t2k-experiment.org/2013/07/n...on-neutrinos-transform-to-electron-neutrinos/

 

[Bill_K]

The original article can be found here: http://arxiv.org/abs/1402.6956, Search for Majorana neutrinos with the first two years of EXO-200 data. Baryon asymmetry [an excess of matter] can be produced as a consequence of CP [charge parity] violations. This have been observed for quarks, but, not for neutrinos until about a year ago by the T2k collaboration - re: http://t2k-experiment.org/2013/07/n...on-neutrinos-transform-to-electron-neutrinos/

Sorry, I don't get your remark about the T2K result, which seems to have nothing to do with Majorana neutrinos, baryon asymmetry or CP violation.

It just reports oscillations from muon neutrinos to electron neutrinos. How is this any different from the OPERA experiment, which observed the oscillation of muon neutrinos to tau neutrinos?

 

[kurros]

I think it would only "help to explain" this, not really explain it very much if you ask me. Neutrinos and anti-neutrinos being the "same" particle really means that they are different helicity states of one another (technically, since neutrinos do have some mass, it should be different spin states, but neutrinos are so light it's not a huge sin, phenomenologically speaking, to regard them as mass less in many cases). The neutrinos would simply be the left-handed helicity states and the anti-neutrinos would be the right handed ones.

It is a known fact that the weak force is left-handed biased. It violates parity conservation by preferring left handed interactions. In this way, I suppose, one might argue that the matter-anti-matter disproportion could be partly due to the left-handed nature of the weak force (a property that is already explained in the standard model). But, and someone chime in here if I'm wrong (which I very well might be!), this wouldn't really help us for the particles which we DO KNOW are NOT Majorana in nature.

I am unclear what you are talking about. First, yes, as you say, the "different helicity" state thing makes no sense, because neutrinos are massive, and a lorentz boost can change their helicity, but not their "anti"-ness. You then say that "really" we should talk about their spin state, but this makes no sense either; I presume you are thinking of their chirality, since you talk about the weak force and handedness later on.

However, chirality makes no sense here either. A Majorana fermion can be thought of as a superposition of both a left-chiral Weyl fermion and a right-chiral Weyl fermion. You need both of them to satisfy the Majorana condition and allow you to write down a Majorana mass.

The Majorana condition means that literally the antiparticle is the same thing as the particle. So really, there aren't any antineutrinos if neutrinos are Majorana. They are all just the same particle.

There is, however, something I am confused about, and maybe this is what you are talking about. There is of course a difference between the flavour and mass eigenstates of neutrinos. The Majorana neutrinos are the mass eigenstates, if neutrinos are Majorana, but I don't know that this means the flavour eigenstates are also Majorana, or if that even makes sense. The flavour eigenstates may just be described in terms of the Weyl fermions, so that it makes sense to talk about their "anti-particles" being the opposite chirality Weyl fermion, but that these things both mix together in the mass eigenstate.

Anyone know a good reference? I found this one explaining basic things about Majorana fermions http://arxiv.org/pdf/1006.1718v2.pdf, but it doesn't have any details about what happens in the Standard Model.

 

[Bill_K]

There is of course a difference between the flavour and mass eigenstates of neutrinos. The Majorana neutrinos are the mass eigenstates, if neutrinos are Majorana, but I don't know that this means the flavour eigenstates are also Majorana, or if that even makes sense. The flavour eigenstates may just be described in terms of the Weyl fermions, so that it makes sense to talk about their "anti-particles" being the opposite chirality Weyl fermion, but that these things both mix together in the mass eigenstate.

For this reason it's better to talk about a Majorana mass rather than a Majorana particle.

The right-handed flavor states are the ones that are sterile wrt the electroweak interaction, and invariant wrt the electroweak symmetry, so they are the states that can have Majorana masses M. The mass eigenstates are mixtures of both left- and right-handed states.

In the seesaw model, M >> m_D, the Dirac mass, so the mixing angle is very small, and the light eigenstate is predominantly left-handed, while the predominantly sterile eigenstate is very massive.

 

[dauto]

For this reason it's better to talk about a Majorana mass rather than a Majorana particle.

The right-handed flavor states are the ones that are sterile wrt the electroweak interaction, and invariant wrt the electroweak symmetry, so they are the states that can have Majorana masses M. The mass eigenstates are mixtures of both left- and right-handed states.

In the seesaw model, M >> m_D, the Dirac mass, so the mixing angle is very small, and the light eigenstate is predominantly left-handed, while the predominantly sterile eigenstate is very massive.

Yes, and that massive particle may decay into either leptons or anti-leptons (plus other particles). If there is enough CP violation an excess of leptons (leptogenesis) may occur and depending on how heavy the Majorana neutrinos really are, that may happen early enough in the Big Bang that spharelons may still be active converting the excess leptons into excess baryons hence the statement of how that whole thing may be relevant to understanding baryogenesis.

 

[Orodruin]

Sorry, I don't get your remark about the T2K result, which seems to have nothing to do with Majorana neutrinos, baryon asymmetry or CP violation.

It just reports oscillations from muon neutrinos to electron neutrinos. How is this any different from the OPERA experiment, which observed the oscillation of muon neutrinos to tau neutrinos?

Together with the reactor neutrino oscillation results for θ₁₃, the T2K experiment gives a very weak preference for the CP violating Dirac phase of the PMNS matrix being pi/2. Since this is a Dirac CP-violating phase, it has nothing to do with Majorana neutrinos per se and cannot be directly related with the baryon asymmetry through, e.g., leptogenesis. However, it is related to CP violation in the lepton sector, just as the CP violating phase in the CKM gives CP violation in the quark sector.

T2K actually adds information on the mixing parameters, unlike OPERA which essentially only confirmed what we already knew from atmospheric oscillation experiments by explicitly confirming that nu_mu actually oscillate into nu_tau.

 

[zincshow]

... However, chirality makes no sense here either. A Majorana fermion can be thought of as a superposition of both a left-chiral Weyl fermion and a right-chiral Weyl fermion. You need both of them to satisfy the Majorana condition and allow you to write down a Majorana mass.

The Majorana condition means that literally the antiparticle is the same thing as the particle. So really, there aren't any antineutrinos if neutrinos are Majorana. They are all just the same particle...

So, in this model, a neutrino should be thought of as a single particle alternating in 2 states, left-chiral and right-chiral. It is this "superposition" that gives the neutrino a small but real mass.

 

[zincshow]

For this reason it's better to talk about a Majorana mass rather than a Majorana particle.

The right-handed flavor states are the ones that are sterile wrt the electroweak interaction, and invariant wrt the electroweak symmetry, so they are the states that can have Majorana masses M. The mass eigenstates are mixtures of both left- and right-handed states.

In the seesaw model, M >> m_D, the Dirac mass, so the mixing angle is very small, and the light eigenstate is predominantly left-handed, while the predominantly sterile eigenstate is very massive.

Does the seesaw model mean the neutrino is alternating between a electron-neutrino, a muon-neutrino, a tau-neutrino?

If a neutrino alternates between these states does that mean the mass of the three different neutrinos are the same?

 

[Bill_K]

Does the seesaw model mean the neutrino is alternating between a electron-neutrino, a muon-neutrino, a tau-neutrino?

If a neutrino alternates between these states does that mean the mass of the three different neutrinos are the same?

Do you understand the difference between "superposition" and "alternating"? Schrodinger's cat is in a superposition of alive and dead, but that does not mean he alternates back and forth!

In any model of massive neutrinos there will be a mass matrix, the PMNS matrix. The basis states are the flavor states (electron, muon, tau). Neutrino mixing follows from the presence of off-diagonal terms in this matrix. The neutrino mass states are the three different eigenstates of the matrix.

If the neutrinos are Majorana, you also have to consider mixing between the conjugate states, and instead of a 3x3 matrix you have a 6x6 matrix to diagonalize, and there will be six different masses. Specifically in the seesaw model the eigenstates are predominantly left- and right-handed and the right-handed states are very massive.

 

[zincshow]

Do you understand the difference between "superposition" and "alternating"? Schrodinger's cat is in a superposition of alive and dead, but that does not mean he alternates back and forth! ...

I used the word alternating only in the sense that when you measure it is one or the other, not to imply its state before the measurement.

 

[Orodruin]

In any model of massive neutrinos there will be a mass matrix, the PMNS matrix. The basis states are the flavor states (electron, muon, tau). Neutrino mixing follows from the presence of off-diagonal terms in this matrix. The neutrino mass states are the three different eigenstates of the matrix.

If the neutrinos are Majorana, you also have to consider mixing between the conjugate states, and instead of a 3x3 matrix you have a 6x6 matrix to diagonalize, and there will be six different masses. Specifically in the seesaw model the eigenstates are predominantly left- and right-handed and the right-handed states are very massive.

A bit of nomenclature: The PMNS matrix is not the neutrino mass matrix, but the leptonic equivalent to the CKM matrix, i.e., it diagonalizes the neutrino mass matrix.

Furthermore, there is no direct need to go to a 6x6 mass matrix for having Majorana neutrinos, this is simply the case for the type I seesaw. At low energies, the only d=5 operator that you can write down with SM fields is the Weinberg operator, which after EW symmetry breaking gives the 3 left-handed SM neutrinos a Majorana mass. The Weinberg operator may result from the type I seesaw, but there are also other possible UV completions such as introducing a heavy SU(2) triplet scalar (type II seesaw) or a triplet fermion (type III).

To answer zincshows question: No, the seesaw mechanism does not directly imply oscillations although it does allow for them. It would in principle be possible to obtain just diagonal matrices. It would however require that the Yukawas were diagonalizable in the same basis as the right-handed neutrino mass matrix.

 

[Bill_K]

A bit of nomenclature: The PMNS matrix is not the neutrino mass matrix, but the leptonic equivalent to the CKM matrix, i.e., it diagonalizes the neutrino mass matrix.

You're right, of course. Thanks for the correction.

 

[Matterwave]

I am unclear what you are talking about. First, yes, as you say, the "different helicity" state thing makes no sense, because neutrinos are massive, and a lorentz boost can change their helicity, but not their "anti"-ness. You then say that "really" we should talk about their spin state, but this makes no sense either; I presume you are thinking of their chirality, since you talk about the weak force and handedness later on.

However, chirality makes no sense here either. A Majorana fermion can be thought of as a superposition of both a left-chiral Weyl fermion and a right-chiral Weyl fermion. You need both of them to satisfy the Majorana condition and allow you to write down a Majorana mass.

The Majorana condition means that literally the antiparticle is the same thing as the particle. So really, there aren't any antineutrinos if neutrinos are Majorana. They are all just the same particle.

There is, however, something I am confused about, and maybe this is what you are talking about. There is of course a difference between the flavour and mass eigenstates of neutrinos. The Majorana neutrinos are the mass eigenstates, if neutrinos are Majorana, but I don't know that this means the flavour eigenstates are also Majorana, or if that even makes sense. The flavour eigenstates may just be described in terms of the Weyl fermions, so that it makes sense to talk about their "anti-particles" being the opposite chirality Weyl fermion, but that these things both mix together in the mass eigenstate.

Anyone know a good reference? I found this one explaining basic things about Majorana fermions http://arxiv.org/pdf/1006.1718v2.pdf, but it doesn't have any details about what happens in the Standard Model.

Sorry I did not see this thread for a while. If a neutrino is indeed Majorana in nature, you will indeed be able to transform a neutrino into an anti-neutrino by performing a Lorentz boost. I have no idea what you're talking about with the rest of your post. Weyl fermions are eigenstates of helicity. As Neutrinos are not massless, they are not Weyl in nature. They are either Dirac or Majorana.

Mass eigenstates are just that, they are states which diagonalize the vacuum Hamiltonian. The flavor eigenstates are eigenstates of the weak interaction Hamiltonian. That these two sets of eigenstates are not identical with each other is the origin of flavor transformation.