# Majorana neutrinos

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What do you look for? In the above quoted paper there's a review about different models of Dirac and Majorana neutrinos.

The appealing feature of Majorana neutrinos, i.e., Weyl spinors vs. Dirac spinors, is that although Majorana neutrinos have a mass (and at least 2 of the 3 known neutrino flavors should have mass due to the observed mixing), there are only left-handed (chirality -1) neutrinos and no right-handed ones as in the Dirac case.

The notion that Majorana neutrinos with mass were "their own antiparticles" indeed doesn't make much sense, because there's no conserved lepton number any more which could distinguish between particles and antiparticles. Nevertheless the consequence of this is that there's the possibility of "neutrino-less double ##\beta## decay", if the neutrinos are Majorana particles, and that's why this is the key observable to empirically demonstrate this. So far, there's neither evidence for nor a clear exclusion of neutrino-less double-##\beta## decay. So the question whether neutrinos are Majorana or Dirac fermions is undecided.

ohwilleke
Mentor
What do you look for?
When a neutrino hits a neutron, it produces a proton and an electron. When an antineutrino hits a proton, it produces a positron and a neutron. Individually, there is no problem with pure Majorana neutrinos participating in these reactions, as long as we don't mind violating lepton number.

However, in the experiments @Vanadium 50 describes, a neutrino source produces a beam that is fired into a target containing both protons and neutrons; and as he describes it, the source can be made to produce a beam that only produces electrons when fired into the target (indicating that only the neutron reaction above is happening) or a beam that only produces positrons when fired into the same target (indicating that only the proton reaction above is happening).

The question is, if neutrinos are pure Majorana fermions, how is it that possible? If neutrinos are pure Majorana fermions, it should be impossible to make a source that can produce a beam that only produces electrons, or only produces positrons, when fired into a target that contains both protons and neutrons; in any such target, both reactions described above should happen with any neutrino beam, because the neutrinos have no way of distinguishing the neutron reaction from the proton reaction.

ohwilleke and vanhees71
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I'm not sure, whether the sensitivity of neutrino experiments of this kind is high enough to exclude that both reactions happen. Though, if this were the case I'd say that then the question were settled in favor of Dirac fermions, and then nobody would ask anymore, whether the neutrinos could be Majorana fermions.

Note that at the level you can neglect the neutrino masses there's no difference between Majorana and Dirac fermions within the standard model, i.e., there are only left-handed neutrinos and right-handed antineutrinos.

Now you have three possibilities to introduce masses:

-pure Dirac mass terms and conserved lepton number; then you have "sterile" right-handed neutrinos since the mass terms mix in the right-handed parts of the Dirac fields, which however don't participate in the weak interaction. Then the neutrino mass eigenstates carry lepton number +1 and the anti-neutrinos lepton number -1 and are thus distinguishable

-pure Majorana mass terms; then lepton number is not conserved and there are only left-handed fields in the game (left-handed Weyl fermions), i.e., there are no "sterile" right-handed neutrinos

-both Majorana and Dirac mass terms; then lepton number is not conserved and you have sterile right-handed neutrinos.

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ohwilleke
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I'm not sure, whether the sensitivity of neutrino experiments of this kind is high enough to exclude that both reactions happen.
It should be easy: the charges of the reaction products are opposite, so they bend in opposite directions in a magnetic field and can easily be distinguished. As I understand it, that's how the detectors in experiments like MINOS work.

malawi_glenn and vanhees71
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But if it were so easy, why are then the searches for neutrinoless double-##\beta## decay are still pursued? I guess @Vanadium 50 can answer this much better than I.

ohwilleke
Gold Member
Or put differently, how does a Majorana neutrino know that if it was made by antileptons, it should hit protons and make antileptons, and if it was made by leptons, it should hit neutrons and make leptons? That seems to be what happens to the neutrinos in the experiments @Vanadium 50 was describing.

As for whether it makes sense to describe Majorana neutrinos as "their own antiparticle", I believe the generally taken meaning is "it is impossible to regard the particle as either matter or antimatter because there is no way to distinguish those possibilities." (Or as you put it, "there's no conserved lepton number any more which could distinguish between particles and antiparticles"). It does not follow that if a particle has no matter or antimatter properties, then it does not make sense to describe it as its own antiparticle, that is simply what the term is taken to mean. By your reasoning, the phrase "is its own antiparticle" would be itself fundamentally meaningless, because what particle that is its own antiparticle could possibly have attributes that could distinguish matter from antimatter? So there is no point in defining a phrase such that it becomes meaningless, just assume the usage that does mean something (can annihilate with identical versions of itself).

weirdoguy
Staff Emeritus
At this point, this is sounding like a personal opinion masquerading as authoritative, and worse, being used as a kind of club to dismiss discussion of this very interesting topic, among "non-experts" who can hope for no more than a "glimmer of understanding."

Again, disrespectful, unhelpful, uncollegial and beneath you. Thar's third time,

I point out that only one of us has actually done these kinds of experiments.

Gold Member
Again, disrespectful, unhelpful, uncollegial and beneath you. Thar's third time,
Well it's certainly the third time you've said that, but that's the only thing I can agree with.
I point out that only one of us has actually done these kinds of experiments.
And I point out that, despite that fact, you have still not answered the important question: How can Majorana neutrinos made by antileptons be restricted to generating antileptons in a detector? That is the question we need the answer to, so if you don't know, then just say that.

ETA: Let me be very clear that I do respect your extensive knowledge of particle physics, and I do appreciate your willingness to share it on a forum. I'm sure you have other things to do, yet you choose to take time to explain things here, which is fundamentally a generous act. That's not what I'm talking about, I'm talking about the way you have tried to steer this thread away from useful inquiry into the issue of "under what circumstances can neutrinos be their own antiparticles, within the constraints of what has already been observed about them, and what is the generally taken meaning of that expression." But it really doesn't matter who said what when in this thread, because it has all come down to the question I just stated, also posed above by @PeterDonis. That is where the inquiry has led us, and the only real payoff we can get at this point is the answer to that question.

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weirdoguy
Gold Member
I had thought, maybe inaccurately connecting dots that shouldn't be connected, that a Majorana neutrino can come in a left-parity neutrino and a right-parity anti-neutrino form, and that the reason that we say that it is its own antiparticle is that with all other Standard Model fermions you have four possibilities:

Left parity particle, right parity particle, left parity antiparticle, and right parity antiparticle,

while in the case of a neutrino, you collapse those four combinations into two:

left parity particle and right parity antiparticle - which is indistinguishable from having a left parity particle and a right parity particle, and no antiparticles.

I also had understood, perhaps wrongly, that a left parity particle could transition to a right parity particle in some kind of interaction related to the Higgs mechanism (by which quarks, antiquarks, charged leptons, charged antileptons, W+ bosons, W- bosons, Z bosons, and Higgs bosons get their rest masses in the Standard Model) in some fashion.

I thought that transitions of the same particle from left parity to right parity and back were what drove the Higgs mechanism (seemingly implied, e.g., here, although I've seen more explicit illustrations to that effect)

Hence, in such a transition, a left parity neutrino could convert to a right parity neutrino (perhaps improperly called an antineutrino), which is why Majorana neutrinos don't conserve lepton number.

In contrast, in a Dirac neutrino scenario you have a left parity neutrino and a right parity antineutrino and one can't transition into the other, which is great for explaining that neutrinos and antineutrinos are different in their interactions with protons/neutrons due to lepton number conservation.

But, in the Dirac neutrino case, I had thought that this screws up the Higgs mechanism that requires transitions between a left parity and right parity fermion, and transitions between a left parity and right parity antifermion - which would necessitate sterile neutrinos because W and Z bosons don't interact with right handed particles or left handed antiparticles, neutrinos don't have electromagnetic charge, and neutrinos don't have strong force color charge (so they would interact only via gravity and Higgs mechanism related parity transitions).

Also, for some reason I've never really understood, the usual proposal is that the sterile counterparts of weak force interacting Dirac neutrinos (a.k.a. active neutrinos), unlike the parity counterparty of every other SM fermion which has the same mass regardless of its parity or matter/antimatter status, should have a different mass than the active neutrinos of opposite parity in a see saw mechanism.

Along the same lines it also isn't entirely obvious why Dirac and Majorana mass generation mechanism are the only options for neutrino mass.

Why can't we theorize that neutrinos acquire mass in some third way, call it "Wilma mass" or "Zappa mass" the conserves lepton number in some manner that does not require that there be a sterile neutrino - e.g. through W boson or Z boson interactions?

This would seem to be a rather modest theoretical tweak compared to creating a whole new set of three sterile neutrinos with three new mass parameters of their own and some sort of mixing parameters.

If you are making up new physics with new rules of physics solely to explain neutrino mass anyway, why not do it in some other fashion than the Dirac mass and Majorana mass options that we know and love (or know and hate)?

What do I have right? Where have I gone astray?

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Mentor
Please read post #37. It is a good summary of the basics of neutrinos and addresses pretty much all of the issues you raise.

ohwilleke and vanhees71
Gold Member
All except for the conclusion of that post, which was:
"So we're left with two possibilities:
1. We see antineutrinos, more or less as expected.
2. Our understanding of stellar collapse is grossly wrong (no neutronization), and QM is wrong, and SR is wrong, and all three are wrong in just the right way to conspire to give a signal that looks exactly like expected."

That does not seem to be borne out by the rest of this thread. Instead, we appear to have a third possibility, which is what the thread has been about from the start:
3. We think we were seeing antineutrinos, but actually there is no meaningful difference between neutrinos and antineutrinos, so we were actually seeing the versions of this Majorana particle that stem from creation by left- and right-handed leptons, which can only (for reasons we don't yet seem clear on in the thread) go on to create either left- or right-handed leptons in the detector, rarely crossing over.

The fact that reasonable people are searching for evidence of this situation clearly establishes that we might not be seeing "antineutrinos" when we thought we were, and this requires no significant modification to stellar collapse theory, QM, nor SR, nor any special conspiracies to have fooled us all this time. Instead, our mistake would have been to get carried away with conservation of lepton number, so we decided to associate the handedness of the lepton that created it with handedness of the neutrino via the usual particle/antiparticle dichotomy that we are used to, which ends up not being meaningful for it. We may then also conclude that we had no easy way to spot our mistake, until (if) we detect neutrinoless double beta decay at a rate associated with a Majorana particle expectation.

This possibility exhibits the crucial feature that distinguishes science from pretty much everything else we see around us: openmindedness.

Mentor
our mistake would have been to get carried away with conservation of lepton number
The open question in this thread, regarding the neutrino experiments like MINOS and Majorana neutrinos, has nothing to do with getting carried away with conservation of lepton number. As I said in post #107, individually, if we accept violation of lepton number conservation, there is no problem with the reactions, and indeed that seems to be the common belief among physicists. Nobody is arguing that Majorana neutrino models are impossible because they violate lepton number conservation; everybody seems to accept that yes, that's a consequence and that's just how it is.

The problem is that our ability to tune the neutrino source so that leptons of only one charge get produced in the detector (electrons or positrons, but not both) does not seem to be consistent with a Majorana neutrino model--on such a model, electrons and positrons should be produced in the detector in roughly equal numbers no matter what we do to the neutrino source. The alternatives here seem to me to be these:

(1) My description above of the experimental results is wrong; electrons and positrons are in fact produced in roughly equal numbers in these experiments, no matter what is done with the neutrino source. However, some other factor involved, which has not been explained, prevents us from detecting this.

(2) A Majorana neutrino model can in fact explain the results as I have described them above. If that is in fact the case, I would expect to find at least a rough theoretical model showing how this can be done somewhere in the literature, but so far I have not found one, nor even any hint that anyone thinks there should be one.

(3) There is a big disconnect between two communities in neutrino physics: those who take it as a routine fact that we can tune sources to produce either only neutrinos, or only antineutrinos, on demand, and think of the two as distinct particles; and those who take it as a routine fact that Majorana neutrinos are a real theoretical possibility and look for experiments (different from the ones the first group gets its routine facts from) to explore it.

ohwilleke and vanhees71
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I point out that only one of us has actually done these kinds of experiments.
That's true, and it's why I have asked you if you know of a mathematical model that explains how the experimental results you described can be consistent with a Majorana neutrino model. In terms of the alternatives I just described in post #117, it seems like you think alternative (2) is obvious, but it's not obvious to me, and if it is obvious to you, it would be helpful to get at least a brief explanation of why.

ohwilleke and vanhees71
Gold Member
The open question in this thread, regarding the neutrino experiments like MINOS and Majorana neutrinos, has nothing to do with getting carried away with conservation of lepton number. As I said in post #107, individually, if we accept violation of lepton number conservation, there is no problem with the reactions, and indeed that seems to be the common belief among physicists. Nobody is arguing that Majorana neutrino models are impossible because they violate lepton number conservation; everybody seems to accept that yes, that's a consequence and that's just how it is.
Saying "carried away by Lepton conservation" is by no means a claim that Majorana neutrino models are impossible, so I don't understand the connection you are drawing there. Indeed, I am saying the opposite-- "getting carried away by Lepton conservation" is another way of saying "rejecting Majorana neutrino models without experimental justification." This is because, any time we demand that neutrinos be either particles or antiparticles in a distinguishable way, we are making it so we can attach a lepton number to them based on the handedness of leptons they produce (indeed, we saw @Vanadium 50 make precisely that suggestion above). That's the "carried away" part, equal to rejecting the Majorana possibility without cause.

The alternatives here seem to me to be these:

(1) My description above of the experimental results is wrong; electrons and positrons are in fact produced in roughly equal numbers in these experiments, no matter what is done with the neutrino source. However, some other factor involved, which has not been explained, prevents us from detecting this.
That possibility seems ruled out by what @Vanadium 50 has said.
(2) A Majorana neutrino model can in fact explain the results as I have described them above. If that is in fact the case, I would expect to find at least a rough theoretical model showing how this can be done somewhere in the literature, but so far I have not found one, nor even any hint that anyone thinks there should be one.
I agree, this must be the situation and it is odd that it is so difficult to understand how it would work. I don't know enough about the neutrino constraints, but one idea would be to say Majorana neutrinos preserve the handedness of the lepton that made them when they go to make leptons, but not doing it by being either particles or antiparticles, they do it in some other way.

Adding to this sense is that I got the impression from the seesaw mechanism that the low-mass neutrinos are the ones that couple to the weak force while the high-mass ones are sterile, so that would be kind of the trick right there: Majorana neutrino fields could involve some kind of simultaneous superposition of left/right and particle/antiparticle such that the low-mass particles they generate can couple to the weak force without being either a particle or an antiparticle, and the high-mass particles are sterile. So if the weak force is looking for credentials like "|left>|particle>" or "|right>|antiparticle>", the Majorana neutrinos pass the test by being "|left>|particle>+|right>|antiparticle>", and the transformation left-->right and particle-->antiparticle leaves them invariant (which is what is meant by "is its own antiparticle"). If so, then the way they "remember" the handedness of what made them would need to have something to do with the difference between that wavefunction and a mixture of "|left>|particle>" and "|right>|antiparticle>". In short, it would have to matter whether there was a + in the superposition or a -. We know the regular Dirac "|left>|particle>" states interact with neutrons to make leptons, and the "|right>|antiparticle>" interact with protons to make antileptons, so we just need a way for the + or - in the Majorana superposition to do the same thing. One way to do that would be to set it up so the sign controlled whether the neutron or proton interactions suffer destructive interference. I don't know how that could be done, but it's just one possible suggestion for a way that a particle that was its own antiparticle could still "remember" whether it was made by a lepton or an antilepton.

(And I note in this scheme, the transformation left-->right and particle-->antiparticle would induce a change in the sign of the wavefunction, so that would have to be an ignorable difference somehow, maybe it doesn't work but it has the spirit of how a particle could do it. We note that if we look at the neutrino beams we have today, and imagine doing left-->right and particle-->antiparticle for the entire apparatus, we produce no contradiction in the observed behavior if Majorana neutrinos transform into the identical particle.)
(3) There is a big disconnect between two communities in neutrino physics: those who take it as a routine fact that we can tune sources to produce either only neutrinos, or only antineutrinos, on demand, and think of the two as distinct particles; and those who take it as a routine fact that Majorana neutrinos are a real theoretical possibility and look for experiments (different from the ones the first group gets its routine facts from) to explore it.
We have certainly seen that people manipulating accelerator beams like to think of them as being beams of neutrinos or antineutrinos, because this works for them to do so. That's a very different issue as to whether or not it is actually correct or required. So I would say the answer looks very much like "both (2) and (3)," but it's not necessarily a disconnect, so much as one group deciding to commit to a certain essentially philosophical stance, and the other group saying "not so fast-- you don't really know that." Or maybe: "you are making a distinction that seems to work to make, but we might end up showing it does not actually exist." An analogy could be the aether in physics in the late 1800s.

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vanhees71
Mentor
"getting carried away by Lepton conservation" is another way of saying "rejecting Majorana neutrino models without experimental justification."
The point I was making is that I don't see anyone doing that. @Vanadium 50 doesn't seem to be; he explicitly said the experimental results he describes are consistent with a Majorana neutrino model (though he hasn't explained how that can be the case).

vanhees71
Staff Emeritus
Majorana neutrinos violate lepton number. But the degree of violation in accelerator experiments is tiny - part in a billion, part in a trillion, whatever. In 0νββ decay, the violation is significant (changes lepton number by 2) but the rates are low if Majorana, zero if Dirac.

vanhees71
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2022 Award
Majorana neutrinos violate lepton number. But the degree of violation in accelerator experiments is tiny - part in a billion, part in a trillion, whatever. In 0νββ decay, the violation is significant (changes lepton number by 2) but the rates are low if Majorana, zero if Dirac.
Exactly, and because of this indeed today the question whether neutrinos are Majorana or Dirac particles is undecided. To decide it by simply looking at production of charged leptons by scattering of neutrinos seems hopeless and the neutrino-less-double-##\beta## decay is ultra challenging but presumably the only chance to decide the question.

Mentor
Maybe this helps to clarify precisely the issues with phenomenology referred to above
I don't see anything in that paper that addresses the issue I described in post #117 (and in earlier posts as well).

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I thought we were still discussing the issue discussed in #107.

Mentor
the degree of violation in accelerator experiments is tiny
"Tiny" as in "none has yet been measured", correct? I.e., this is an experimental constraint.

If you are saying that theoretically, the violation in accelerator experiments done to date is expected to be tiny for Majorana neutrinos, that is what I don't understand; I described the issue in post #117 (and in earlier posts). In terms of lepton number violation, with Majorana neutrinos, it seems like the violation of lepton number conservation in the experiments you described earlier in the thread should be huge: even with a source that generates neutrinos with all leptons (for example, from decays of ##\pi^-## mesons to muons, ##\mu^-##) or all antileptons (for example, from decays of ##\pi^+## mesons to antimuons, ##\mu^+##), with a target that contains roughly equal numbers of protons and neutrons, the detector should detect roughly equal numbers of leptons and antileptons. But that doesn't seem to be what is observed.

vanhees71
Gold Member
The problem is that our ability to tune the neutrino source so that leptons of only one charge get produced in the detector (electrons or positrons, but not both) does not seem to be consistent with a Majorana neutrino model--on such a model, electrons and positrons should be produced in the detector in roughly equal numbers no matter what we do to the neutrino source.
Whether neutrinos are Dirac or Majorana (or massless in a different world), the coupling structure in the weak sector is always such that you have a left-chiral Weyl field coupling to leptons, and the charge conjugate of that Weyl field coupling to anti-leptons. This determines what interactions happen, and at this stage there is no lepton number violation.
Now the two Weyl fields are either combined into a Majorana field, or you add an additional right-handed field and build a Dirac field out of those, and the two fields you have combined end up in the mass term together.
So if the mass term is Majorana, you have terms in the propagator that mix between these two* (in terms of the Weyl fields the term is more a "vertex with two legs", see for example here https://arxiv.org/abs/2012.09882). There you have the lepton number violation, but the terms are proportional to the neutrino masses, so any violation of lepton number is suppressed by those.

Edit: * what I mean here by "the two" is "the field interacting with leptons" and "the field interacting with anti-leptons"

dextercioby, malawi_glenn and vanhees71
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the coupling structure in the weak sector is always such that you have a left-chiral Weyl field coupling to leptons, and the charge conjugate of that Weyl field coupling to anti-leptons
I agree the weak couplings involve only left-chiral Weyl fields and their charge conjugates, but I don't think it's quite as simple as you describe. In particular, I don't think it helps with the issue I described, because Weyl fields don't propagate by themselves. What propagates from the source to the target in the experiments that have been described are mass eigenstates.

Suppose, for example, that we have set the source to produce neutrinos--for example, suppose the source is NuMi at Fermilab and we've selected the mode where the neutrinos come from decay of positive pions and kaons, which produce antimuons ##\mu^+## and muon neutrinos, i.e., neutrinos described by left-handed Weyl fields. (Note that this is not the same as the coupling you describe--the antimuons and muon neutrinos are both outgoing from the reaction, and no leptons are coming in, so they must have opposite lepton numbers since this is a Standard Model, lepton number conserving process.)

But what propagates from the source to the target is not just the left-handed Weyl field, but a mass eigenstate. The question is, which mass eigenstate?

If it's a Dirac mass eigenstate that propagates from the source to the target, then it's easy to understand why, at the target, only electrons are produced, even though the target contains roughly equal numbers of protons and neutrons. A Dirac mass eigenstate couples the left-handed neutrino to a right-handed neutrino, which has no weak couplings, so the only possible interaction at the target is the coupling of the left-handed neutrino to an electron (which happens when the neutrino hits a neutron and turns it into a proton).

But if it's a Majorana mass eigenstate that propagates from the source to the target, then we have a left-handed neutrino coupled to a right-handed antineutrino, and both of those have weak couplings. So at the target, both interactions are possible: left-handed neutrino to electron (along with neutron to proton) and right-handed antineutrino to positron (along with proton to neutron), and with a target having roughly equal numbers of protons and neutrons, we should expect to observe roughly equal numbers of electrons and positrons. But that's not what we observe, so it seems like observations in these experiments should rule out a Majorana mass.

Gold Member
But if it's a Majorana mass eigenstate that propagates from the source to the target, then we have a left-handed neutrino coupled to a right-handed antineutrino, and both of those have weak couplings. So at the target, both interactions are possible: left-handed neutrino to electron (along with neutron to proton) and right-handed antineutrino to positron (along with proton to neutron).
Yes, as I said the propagator mixes the two fields in the Majorana case. But only proportional to the neutrino mass. When you say
we should expect to observe roughly equal numbers of electrons and positrons
you did not just assume
a target having roughly equal numbers of protons and neutrons
but also that the mixing in the propagator produced an equal mixing of the two neutrino fields, which is not true.
In principle lepton number violation is possible in this kind of scenario, for example by observing ##\mu^- \to e^+## conversion (+ nuclear conversions to make charges work out), see e.g. https://arxiv.org/abs/2110.07093. But all these effect are suppressed by the small neutrino masses.

(Note that this is not the same as the coupling you describe--the antimuons and muon neutrinos are both outgoing from the reaction, and no leptons are coming in, so they must have opposite lepton numbers since this is a Standard Model, lepton number conserving process.)
Probably, what I meant was that you have left- and right-handed doublets and that determines the coupling structure and hence possible interactions/decays.

weirdoguy and vanhees71
Mentor
the propagator mixes the two fields in the Majorana case. But only proportional to the neutrino mass
Ah, I see. So if the source is producing muon neutrinos, we would only expect a fraction of antineutrinos at the target proportional to the mixing rate in the propagator and the time of propagation. Which for the experiments we have been discussing will be too small to measure. But in principle, if we could measure it, finding it would be a way of showing the existence of Majorana masses for neutrinos (since Dirac masses would not produce such effects no matter how long the propagation time).

weirdoguy, malawi_glenn and vanhees71
Gold Member
Yes, my understanding is that neutrino-less double beta-decay is your better bet in most scenarios.

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The flavor eigenstate is a superposition of the mass eigenstates, and what propagates is this superposition. You can only detect the reaction of this propagating state with your detector material, and this interaction is again governed by the weak-interaction vertices, and that's why there's some probability to detect the neutrino which started as an electron neutrino as a neutrino of another flavor. That's neutrino mixing, and occurs no matter whether the neutrinos are Majorana or Dirac fermions.

Your second paragraph is also right of course, but that's just lepton-number violation, which necessarily occurs for Majorana neutrinos.
Ah, I see. So if the source is producing muon neutrinos, we would only expect a fraction of antineutrinos at the target proportional to the mixing rate in the propagator and the time of propagation. Which for the experiments we have been discussing will be too small to measure. But in principle, if we could measure it, finding it would be a way of showing the existence of Majorana masses for neutrinos (since Dirac masses would not produce such effects no matter how long the propagation time).
The flavor-mixing matrix mixes the flavors (left-handed with left-handed and right-handed with right-handed), mass terms mix the left-handed and right-handed parts of the field.

Gold Member
The point I was making is that I don't see anyone doing that. @Vanadium 50 doesn't seem to be; he explicitly said the experimental results he describes are consistent with a Majorana neutrino model (though he hasn't explained how that can be the case).
I quoted just above the text that inspired that phrase. Again:
"So we're left with two possibilities:
1. We see antineutrinos, more or less as expected.
2. Our understanding of stellar collapse is grossly wrong (no neutronization), and QM is wrong, and SR is wrong, and all three are wrong in just the right way to conspire to give a signal that looks exactly like expected."
That seems literally the definition of demanding there be a difference between neutrinos and antineutrinos, because nothing else makes any sense. If that statement is no longer @Vanadium 50 's position, I'm glad that the thread has produced some progress there. But above all, I agree that "who said what when" is of no great consequence, what we need to understand is how Majorana neutrinos could be completely consistent with all current observations, while not exhibiting any distinction between neutrinos and antineutrinos, historically analagous to how the absence of an aether was completely consistent with all observations circa 1887.

vanhees71
Gold Member
2022 Award
Let me summarize it again. I hope I get it right.

For Majorana neutrinos the only difference between "neutrinos" and "antineutrinos" is the chirality. Neutrinos are left-handed and antineutrinos are right-handed. There are no other "charge-like" quantities like lepton number. In other words: For Majorana neutrinos the charge-conjugate of the left-handed neutrino is the right-handed neutrino and vice versa. Since there's no "lepton number" there's also no lepton-number conservation.

For Dirac neutrinos there are independent left- and right-handed components and they carry lepton number as a "charge-like quantity", and neutrinos and antineutrinos are distinguished by opposite lepton numbers. The right-handed neutrinos (left-handed anti-neutrinos) are "sterile", i.e., non-interacting.

Whether neutrinos are Majorana or Dirac particles is not yet empirically decided, i.e., all data are consistent with both Majorana or Dirac neutrinos.

The lepton-number violations in the case of Majorana neutrinos are small due to the smallness of the neutrino masses.

A very concise treatment is in the Book

S. Bilenky, Introduction to the Physics of Massive and Mixed Neutrinos, 2nd Ed., Springer (2018)

dextercioby, ohwilleke, Dr.AbeNikIanEdL and 2 others
Staff Emeritus
and as he describes it, the source can be made to produce a beam that only produces electrons when fired into the target (indicating that only the neutron reaction above is happening) or a beam that only produces positrons when fired into the same target (indicating that only the proton reaction above is happening).

The question is, if neutrinos are pure Majorana fermions, how is it that possible?
First, it's not just as "He describes it". I showed the data, and provided a pointer to a collectgioon of references..

But if neutrinos are Majorana, a neutrino beam is one of pure left handed chirality (not helicity - not polarization) and an anti-neutrino beam is one of pure right handed chirality

Staff Emeritus
Let me summarize it again. I hope I get it right.
You did, but...
For Majorana neutrinos the charge-conjugate of the left-handed neutrino is the right-handed neutrino and vice versa. Si
I don't think this is right. Go back to the Weyl fields:

$$C | \psi_L> = \overline{\psi_L} \neq \psi_R$$

I would say it is nothing uncer C or at least sterile.

Staff Emeritus
But in principle, if we could measure it, finding it would be a way of showing the existence of Majorana masses for neutrinos (since Dirac masses would not produce such effects no matter how long the propagation time).
Yes, but this is hard.

A "pure neutrino beam" is limited to about 99% purity, and there is an anti-corrleation between intensity and purity so most real beams don't do even this well.

Mentor
if neutrinos are Majorana, a neutrino beam is one of pure left handed chirality (not helicity - not polarization) and an anti-neutrino beam is one of pure right handed chirality
But if neutrinos have non-zero masses, there is no such thing--at least not once the beam has propagated for any appreciable time from the source compared to the mixing rate given by its mass. The mass term mixes left-handed and right-handed fields, whether it's Dirac or Majorana.

Mentor
this is hard.
Agreed. I'm just trying to make sure I'm clear about all of the possibilities allowed by the model, including ones that are extremely hard to detect in actual experiments.

Mentor
That seems literally the definition of demanding there be a difference between neutrinos and antineutrinos
I think the point that @Vanadium 50 has been trying to get across in this connection is that this business of "particle" vs. "antiparticle" is not that simple.

Consider the basic weak interaction lepton doublet in the Standard Model (looking just at the first generation for simplicity, having multiple flavors doesn't change anything in what I'm about to say). It's a doublet of the left-handed electron and the left-handed electron neutrino. But what do these terms actually refer to? They refer to two-component Weyl spinors. The "left-handed electron" Weyl spinor is actually a left-handed electron/right-handed antielectron (positron), and the "left-handed electron neutrino" Weyl spinor is actually a left-handed electron neutrino/right-handed electron antineutrino.

In both cases, which "particle" you describe the spinor as depends on which interaction you are looking at and how it is oriented in spacetime. For example, the "beta decay" interaction has both the "electron" and the "electron neutrino" lines as outgoing lines, so we describe the outgoing electron as a "left-handed electron" and the outgoing neutrino as a "right-handed electron antineutrino". But the interaction that produces the electrons detected in the experiments we've been discussing has the neutrino line as an incoming line, not an outgoing line, so we describe it as a left-handed electron neutrino. But in both cases, it's the same interaction (same Feynman diagram vertex) involving the same Weyl spinors.

In other words, at the level of single Weyl spinors, it doesn't even make sense to differentiate "particles" and "antiparticles"--they're just different ways of looking at the same 2-component Weyl spinor.

So why do we say that the electron is not its own antiparticle? Because the "electron" we actually observe in experiments is not just one 2-component Weyl spinor. It's two of them put together, i.e., a Dirac spinor. In the Standard Model there is, in addition to the "left-handed electron/right-handed positron" 2-component Weyl spinor (part of the weak doublet I described above), a "right-handed electron/left-handed positron" 2-component Weyl spinor, which is a weak singlet--it has no weak interaction couplings. So the "electron" we actually observe is a mixture of the "left-handed electron" component of the weak doublet "electron" Weyl spinor, and the "right-handed electron" component of the weak singlet "electron" Weyl spinor. And the "positron" we actually observe is a mixture of the "right-handed antielectron" component of the weak doublet and the "left-handed antielectron" component of the weak singlet. These are distinct "particles"; we can't invoke what we said above about Weyl spinors and "particles" vs. "antiparticles" because we aren't dealing with a single Weyl spinor; we are dealing with a pair of them coupled by a Dirac mass term.

If neutrino masses are pure Majorana masses, OTOH, then there is no weak singlet "right-handed electron neutrino/left-handed electron antineutrino" 2-component Weyl spinor. (Or at least, there is no reason to include one in the model.) The Majorana mass term couples the two components of the same Weyl spinor. So the "neutrino" we actually observe in experiments would just be one 2-component Weyl spinor, and what we said above about Weyl spinors and "particles" vs. "antiparticles" would apply to it.

The reason why the target in the experiments we've been discussing can still "tell" what kind of neutrinos it is seeing is that the source produces (with a small inaccuracy that we can ignore here) either pure left-handed neutrinos or pure right-handed neutrinos, and because neutrino masses are so small, the amount of "change of handedness" due to the mass term is too small to produce any detectable results at the target. So at the target we can still treat the beam as containing either all left-handed or all right-handed neutrinos, and the two possible interactions each require opposite handedness: the "produces electrons" interaction requires left-handed neutrinos, and the "produces positrons" interaction requires right-handed neutrinos.

And even if we find that neutrinos only have Majorana masses so that they "are their own antiparticles", they are still 2-component Weyl spinors with a left-handed and a right-handed component, and interactions that can distinguish between handedness can distinguish between the components. (Or, to put it in terms of a previous question you posed, the additional degree of freedom that lets these interactions discriminate between the neutrinos is chirality, not particle vs. antiparticle.)