I Majorana Neutrinos: Different Physics than Oscillation

[PeterDonis]

Is not a paper.

I don't mean the website that was originally linked. I mean the paper that was linked in post #22.

 

[PeterDonis]

we are talking about "people" at Fermilab (https://neutrinos.fnal.gov/types/antineutrinos/ ) (my bold):

Since an actual paper has been posted (post #22), it would be much better to use that as a reference. @Vanadium 50 is perfectly correct that that web page is not a good reference for a PF discussion. It contains no math and is not a scientific treatment, it's just a basic description.

 

[Ken G]

Since an actual paper has been posted (post #22), it would be much better to use that as a reference. @Vanadium 50 is perfectly correct that that web page is not a good reference for a PF discussion. It contains no math and is not a scientific treatment, it's just a basic description.

Normally I would agree, but here we have @Vanadium 50 stating : "How can one say "the neutrino is its own antipartiocle" (and its not, no matter how many people repeat ity here)"
So at issue in that claim is not the theory of neutrinos, it is a claim about "how can one say" something. Ergo, I gave examples of how one can say it, by saying it in a public forum, as they did. What I found so erroneous, and rather impolite, was the clear implication that the words "neutrino is its own antiparticle" was somehow from from "people on here." So that falsehood had to be dismissed.

 

[Vanadium 50]

because you chose to define them that way.

My definition is perfectly consistent with the standard one.

But the real issue is, if the Majorano Collaboration detects neutrinoless double beta decay, will anyone even bother to use the term "antineutrino" ever again?

Of course they will. I could zip out to Fermilab today and tell them to switch from neutrino mode to antineutrino mode and back again (well, if there wasn't a vacuum leak at the moment,) and the detectors would see negative leptons, then positive leptons, then negative leptons again.

You simply cannot take statements intended for the general public and treat them as rigorous scientific truths. If I told you that I read in My First Book of Stars (not a real book) that stars come in all sizes, shapes and colors, so there must exist somewhere a green cubical star that fits in my pocket, what would you say?

 

[Ken G]

My definition is perfectly consisten with the standard one.

You're dodging the real question: Do you think that if the Majorana Collaboration is successful in demonstrating that neutrinos are Majorana fermions, there will not be a good reason to retire the term "antineutrino"? That's the part that is not clear from your argument, because I can't see, given the language they use, why they would not find that an appropriate approach.

Of course they will. I could zip out to Fermilab today and tell them to switch from neutrino mode to antineutrino mode and back again (well, if there wasn't a vacuum leak at the moment,) and the detectors would see negative leptons, then positive leptons, then negative leptons again.

Correction, you could tell them to switch from detecting those various types of leptons. It is only you that are calling that "neutrino mode" or "antineutrino mode", based on your earlier tautology. Again, the real question is, would they have any reason to keep to your terminology here, or just retire the phrase "antineutrino" altogether? That is the question you have not answered. I don't say that you haven't got a good reason for your opinion, merely that you have not justified that opinion yet. That would be where the real insight would come from, not tautological definitions.

 

[PeterDonis]

The definition I picked does not even distinguish between mass and flavor eigenstates.

You talked about actual leptons coming out of actual processes that are detected in the lab. Don't those processes normally involve a specific flavor of lepton? If so, it would seem like they should also involve a specific flavor of neutrino.

Perhaps a more specific description of some of the processes you had in mind would help.

 

[PeterDonis]

at issue in that claim is not the theory of neutrinos, it is a claim about "how can one say" something.

I would take "how can one say" as a figure of speech. The claim @Vanadium 50 is making, as I understand it, is a claim about actual neutrinos that are involved in actual processes measured in labs like Fermilab. He is saying that such processes always produce specific charged leptons--positive or negative. They never produce equal mixtures of both charges. And he is claiming that, according to the theory of neutrinos, if neutrinos were their own antiparticles, those processes would always produce equal mixtures of both charges of leptons, not just one charge.

 

[PeterDonis]

if the Majorana Collaboration is successful in demonstrating that neutrinos are Majorana fermions

As I read the paper I linked to in post #22, it might not be that simple. The Majorana Collaboration is looking for evidence of neutrinoless beta decay. That would imply that there is a Majorana mass term in the Lagrangian, but the paper gives at least one theoretical model in which there are both Majorana and Dirac mass terms. (This model is described as a "toy model" because it only has one generation and does not include anything except neutrinos and W particles, but I don't see anything in the paper that rules out the possibility that a more sophisticated model along the same lines might not be true of actual neutrinos.) So the observation of neutrinoless beta decay would not necessarily show that neutrinos are purely Majorana fermions; it could still be the case that there are distinct neutrinos and antineutrinos.

 

[Ken G]

I would take "how can one say" as a figure of speech. The claim @Vanadium 50 is making, as I understand it, is a claim about actual neutrinos that are involved in actual processes measured in labs like Fermilab. He is saying that such processes always produce specific charged leptons--positive or negative. They never produce equal mixtures of both charges. And he is claiming that, according to the theory of neutrinos, if neutrinos were their own antiparticles, those processes would always produce equal mixtures of both charges of leptons, not just one charge.

That's what I don't understand. The Cerenkov detectors that detected SN 1987A neutrinos were of the type you describe-- able to detect leptons of either charge. But they don't produce equal mixtures, because the targets are different-- to get an electron, the target is a neutron, to get a positron, the target is a proton. In the standard model, if we hit water with equal fluxes of neutrinos and antineutrinos, we expect more positrons, and indeed we get more positrons. If neutrinos are their own antiparticle, then we also expect more positrons, which we also see.

As for the detectors in Fermilab, if what @Vanadium 50 means by "antineutrino mode" is that the detectors are set up to detect negative leptons, then yes, they will detect negative leptons-- whether the neutrinos are of Dirac or Majorana type. So I am still not seeing any contradiction from the possibility that neutrinos are their own antiparticle.

 

[Ken G]

As I read the paper I linked to in post #22, it might not be that simple. The Majorana Collaboration is looking for evidence of neutrinoless beta decay. That would imply that there is a Majorana mass term in the Lagrangian, but the paper gives at least one theoretical model in which there are both Majorana and Dirac mass terms. (This model is described as a "toy model" because it only has one generation and does not include anything except neutrinos and W particles, but I don't see anything in the paper that rules out the possibility that a more sophisticated model along the same lines might not be true of actual neutrinos.) So the observation of neutrinoless beta decay would not necessarily show that neutrinos are purely Majorana fermions; it could still be the case that there are distinct neutrinos and antineutrinos.

Yes, it would only be one step in the path toward their objective of deciding if neutrinos are their own antiparticles or not. It is rare that a single observation is a "slam dunk." So yes, that result would not yet be enough to retire the term "antineutrino", but the issue here is merely that this remains a possibility in the future-- without holding to @Vanadium 50 's claim:
"Our underdstanding 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."

In essence, my participation in this thread has parallel purposes: to learn a lot about neutrinos, and to assist forumgoers in retaining their open minds that we might have a lot to learn about neutrinos, including that they could be their own antiparticles, without having to put the rest of physics on its ear. Perhaps the first purpose will end up completely supplanting the second, but that has as yet not occurred.

 

[Vanadium 50]

You talked about actual leptons coming out of actual processes that are detected in the lab. Don't those processes normally involve a specific flavor of lepton?

Sure, but it's irrelevant to whether its a neutrino (yields a negative lepton) or antineutrino (yields a positive one), I'm trying to minimize complications.

I'm also trying to minimize yeahbuts. If I wrote "muon antineutrino", the peanut gallery would all chime in "mass and flavor eigenstates are not the same". Which, while true, is not necessary for this discussion.

 

[malawi_glenn]

I think theoritsts (like me) and experimentalists (like Vanadium) have different definitions of neutrino and antineutrino.

To me, an antiparticle is a particle whos state is returned after application of C, P and T transformations. Nothing more, nothing less. If that resulting state is the same as the state before the application of those operators, it is "it's own antiparticle".

One must also be careful when reading papers and articles. When you read "They detected neutrinos from SN1987A" they could be referring to $\nu$ and/or $\bar \nu$. Same when you read about say Higgs discovery that one decay channel is into four muons. Experts in the field knows that this is nonsense, Higgs can not decay in to four muons, but rather two muons and two anti-muons. But it is (for good and bad) standard lingo.

but the paper gives at least one theoretical model in which there are both Majorana and Dirac mass terms. (This model is described as a "toy model" because it only has one generation and does not include anything except neutrinos and W particles, but I don't see anything in the paper that rules out the possibility that a more sophisticated model along the same lines might not be true of actual neutrinos.)

There are papers which have all three generations, and the full SM.

 

[vanhees71]

Let's take a strep back. After some thought, I think the best terminology is to define a neutrino as one that produces a (negative) lepton after a interaction (technically, a charged current interaction) and an anti-neutrino as one that produces a (positive) anti-lepton after a interaction.

Indeed, given neutrino oscillations, that's the only way you can make sense of neutrinos at all. Only the asymptotic free mass eigenstates would have a "particle interpretation", but these cannot be detected, because all you can observe is the outcome of some interaction of the neutrinos with the detector material, and these detect flavor eigenstates due to the nature of the weak interaction.

 

[vanhees71]

I think theoritsts (like me) and experimentalists (like Vanadium) have different definitions of neutrino and antineutrino.

To me, an antiparticle is a particle whos state is returned after application of C, P and T transformations. Nothing more, nothing less. If that resulting state is the same as the state before the application of those operators, it is "it's own antiparticle".

"Particles" are asymptotic free mass eigenstates by definition. The mass eigenstates of neutrinos can, however, not be detected, because you can detect neutrinos only by interactions with some detector material and measuring the produced particles, among them the charged leptons or anti-leptons, i.e., the flavor eigenstates. In this sense we never detect neutrinos as "particles". That's also what's behind neutrino-oscillation measurements: You measure at one place, which neutrino flavor was produced and at the other place, which neutrino flavor is detected.

All this has little to do with the question, whether there are Majorana mass terms or not in the correct description of neutrinos. That's why experiments look for, e.g., neutrino-less double $\beta$ decay, which would indicate that there are such Majorana mass terms. So far no such events have been found though. So it's still an open question.

 

[malawi_glenn]

"Particles" are asymptotic free mass eigenstates by definition

Yeah that is also an aspect of QFT that complicate things when we try to discuss these kinds of matters ;)

 

[Ken G]

I think theoritsts (like me) and experimentalists (like Vanadium) have different definitions of neutrino and antineutrino.

Yet you don't go around disparaging "people here" for repeating language used by those at Fermilab, correct? (Besides, the issue here is not your personal definitions, it is whether or not the general canon will, or will not, include the term "antineutrino" if neutrinos are found to be Majorana fermions. Are you saying theorists would retire the term but experimentalists would continue using it? I really don't think we'd have such a Tower of Babel.)

To me, an antiparticle is a particle whos state is returned after application of C, P and T transformations. Nothing more, nothing less. If that resulting state is the same as the state before the application of those operators, it is "it's own antiparticle".

So does a Majorana fermion return to its state after CPT transformation?

 

[Ken G]

Indeed, given neutrino oscillations, that's the only way you can make sense of neutrinos at all. Only the asymptotic free mass eigenstates would have a "particle interpretation", but these cannot be detected, because all you can observe is the outcome of some interaction of the neutrinos with the detector material, and these detect flavor eigenstates due to the nature of the weak interaction.

So the same question shall be put to you: if neutrinos are demonstrated by experiment to be Majorano fermions, will the community retire the term "antineutrino" on grounds that it contains zero value, or will they retain the term any time an antilepton is produced? That I believe is the question that carries the insight here, whichever is the answer.

 

[Ken G]

Indeed, given neutrino oscillations, that's the only way you can make sense of neutrinos at all.

You make a nice point that what we call "neutrinos" (the flavor eigenstates) don't formally fall under the definition of particle, but this is not directly related to the common fact that we need to wait for the outcome of an experiment to be able to talk about its constituent stages. All that simply stems from Bell's theorem and the problems with local realism. If a photon does not even "carry with it" its own polarization in all situations, then we should not be surprised that any particles does not "carry with it" its own identity at all stages of an experiment. But that's not the issue here, the issue is whether or not there is any value in distinguishing neutrinos and antineutrinos at all, not how we would do it.

the asymptotic free mass eigenstates would have a "particle interpretation", but these cannot be detected, because all you can observe is the outcome of some interaction of the neutrinos with the detector material, and these detect flavor eigenstates due to the nature of the weak interaction.

Yet even in situations that are not challenges to local realism, we do conceptualize hypothetical states all the time. In Faraday rotation, a linearly polarized photon passing through a plasma with a line-of-sight magnetic field will have its polarization rotated. The photon is never in a state of circular polarization, yet a nice way to conceptualize what is happening is to imagine the photon as being in a superposition of circular polarizations with different propagation speeds. This would be true even if all we had were ways of measuring linear polarization. Note that in such a situation, we would still be able to imagine photons that were circularly polarized, as a useful conceptual device, even without the means for a circular polarization to be an outcome of an experiment. So what my question is driving at is, if neutrinos were Majorana fermions, would there be any value in the "antineutrino" conceptualization, independent of any issues of how to define it or measure it?

 

[malawi_glenn]

Are you saying theorists would retire the term but experimentalists would continue using it?

We do not go around and say "Z boson is its own antiparticle" all day long either.

After all, it is the physics that matters, not what we call things - just as with Pluto and planets.

if neutrinos are demonstrated by experiment to be Majorano fermions, will the community retire the term "antineutrino" on grounds that it contains zero value, or will they retain the term any time an antilepton is produced?

I think you mean "should" here, not will - because we have no time machines.

So does a Majorana fermion return to its state after CPT transformation?

A pure majorana fermion would yes, that is why we call it "its own antiparticle".

 

[Ken G]

We do not go around and say "Z boson is its own antiparticle" all day long either.

Hang on, we do say the "photon is its own antiparticle." Maybe not "all day long", but we do say it. Are you saying the situation is different with the Z boson? I mean, can it annihilate with another one or not?

After all, it is the physics that matters, not what we call things - just as with Pluto and planets.

Not at all like Pluto and the planets, the logic does not hold. Your syllogism is, if words don't really matter in regard to Pluto and the planets, then words never matter. I know you don't think that. After all, we're on a forum right now-- and what are we using to communicate? Words! So they don't matter, this is the point of a forum?

I think you mean "should" here, not will - because we have no time machines.

The device here is "if and when it is discovered that neutrinos are Majorana fermions, what will we do." It's asking for a prediction.

A pure majorana fermion would yes, that is why we call it "its own antiparticle".

Careful now, who is "we"? I think you'd better let @Vanadium 50 speak for themself, given that they suggested we define antineutrinos by anything that produces a negative lepton-- and no particle that is defined that way could ever be its own antiparticle.

 

[Vanadium 50]

You talked about actual leptons coming out of actual processes that are detected in the lab. Don't those processes normally involve a specific flavor of lepton? If so, it would seem like they should also involve a specific flavor of neutrino.

I tried to avoid getting into the question of mass vs. flavor eigenstates. Neutrinos are leptons, anti-neutrinos are anti-leptons. Yes, we can go into mroe detail and talk about individual flavors, but I deliberately avoided doing this.

 

[Vanadium 50]

I think you'd better let @Vanadium 50 speak for themself,

And yet you then jumped in and put some words in my mouth., Please don;t do that. hat's disrepsectful, unhelpful, unbcollegial and beneath you.

 

[Ken G]

And yet you then jumped in and put some words in my mouth., Please don;t do that. hat's disrepsectful, unhelpful, unbcollegial and beneath you.

I put no words in your mouth, it was exactly what you said. You suggested defining antineutrinos by any neutrino that makes an antilepton, is that not just what you said? And does it not immediately follow that by this definition, a neutrino is not its own antiparticle, even if it is a pure Majorano fermion? What is clear from the thread is terms like "is its own antiparticle", and "the particle and antiparticle are the same thing" do not have a consensus interpretation. This is precisely the reason I reframed the question some time ago, yet without any answer from anyone so far:

If neutrinos are established as being Majorana fermions, will there still be value in the term "antineutrino", and if so, what? (And the related question, will the term antineutrino be retired?)

 

[Vanadium 50]

that is why we call it "its own antiparticle".

I am trying to get us away from that woolly language.

I don't want people thinking a beam ofgneutrinos and a beam of antineutrinos are the same thing. That is experimentally not the case: I can run the current in the neutrino horn and get positive leptons in the detector, and then switch the current direction and now get negative leptons in the detector. This is not theory - this is an observed fact.

That's why I went through all the rigamarole of Weyl spinors.

 

[PeterDonis]

I can run the current in the neutrino horn and get positive leptons in the detector, and then switch the current direction and now get negative leptons in the detector. This is not theory - this is an observed fact.

Can you be more specific about which experiment this refers to? The only specific experiment you've referred to so far is the Cowan Reines experiment, which used a nuclear reactor as the neutrino source and so could not choose what kind of neutrinos were being detected--it was whatever kind were being emitted by the nuclear reactions in the reactor. What you're describing here seems like a neutrino source where we can choose what kind of neutrinos it emits at will.

 

[malawi_glenn]

Careful now, who is "we"? I think you'd better let @Vanadium 50 speak for themself

I meant "that is why particle physicsists in general write that pure majorana fermions are their own antiparticle". You should be able to read this in any quantum field theory textbook.

Hang on, we do say the "photon is its own antiparticle." Maybe not "all day long", but we do say it. Are you saying the situation is different with the Z boson? I mean, can it annihilate with another one or not?

What I meant is that we do not make a "fuzz" about the photon, the higgs, or the Z boson being their own antiparticles (whatever that means). Is there any value to you, the fact that those particles are their own antiparticle? To me, its not at all important. What is important to me is that if neutrinos are not pure Dirac, we have a strong case for beyond the standard model physics - there are more things to be discovered after this :)

what are we using to communicate? Words!

I can write down equations for you if you prefer that, after all - the language of physics is math. It would be better I think if we just said "the quantum field is transformed back to itself after successive CPT-transformations" ;) Or just, "pure Dirac fermion", "pure Majorana fermion" or "pseudo-Dirac fermion". Or, just stick with the Weyl spinors...

The device here is "if and when it is discovered that neutrinos are Majorana fermions, what will we do."

Ok now I understand better what you meant by that.

 

[malawi_glenn]

What you're describing here seems like a neutrino source where we can choose what kind of neutrinos it emits at will.

Perhaps this https://lbnf-dune.fnal.gov/how-it-works/neutrino-beam/

You basically create (charged) pions which decays to muon and neutrino. The pions can be deflected using an electromagnet. In this way you can get a beam of neutrinos from $\pi^+$ and from $\pi^-$ separetely, and thus one can measure if there is any difference between those beam compositions and interactions.

 

[PeterDonis]

Perhaps this https://lbnf-dune.fnal.gov/how-it-works/neutrino-beam/

You basically create (charged) pions which decays to muon and neutrino. The pions can be deflected using an electromagnet. In this way you can get a beam of neutrinos from $\pi^+$ and from $\pi^-$ separetely, and thus one can measure if there is any difference between those beam compositions and interactions.

Yes, this is very helpful, thanks!

 

[PeterDonis]

You basically create (charged) pions which decays to muon and neutrino.

This would be a weak interaction decay conserving lepton number, correct? So if we're getting positive pions, those would decay into positive muons (antimuons, lepton number -1) and muon neutrinos (lepton number +1), whereas if we're getting negative pions, those would decay into negative muons (lepton number +1) and muon antineutrinos (lepton number -1), correct?

 

[Ken G]

What I meant is that we do not make a "fuzz" about the photon, the higgs, or the Z boson being their own antiparticles (whatever that means). Is there any value to you, the fact that those particles are their own antiparticle? To me, its not at all important.

I never asked "is it a fuss if neutrinos are their own antiparticle," I asked, "if neutrinos are pure Majorano fermions, will there be any value in the term antineutrino, or will the term be retired." No one has yet answered that, even the person who said that there is no possible way that neutrinos are their own antiparticle.

What is important to me is that if neutrinos are not pure Dirac, we have a strong case for beyond the standard model physics - there are more things to be discovered after this :)

Yes of course, that is the exciting physics here. But to understand the significance to the lexicon, we need the answer to the question I have posed so many times now.

I can write down equations for you if you prefer that, after all - the language of physics is math.

Actually, the language of physics is the language we find in physics books, and that is not all math. Words matter, that's why we are literally using them right now. Why do I have to justify the importance of words just to get a fairly straightforward question answered?

 

[PeterDonis]

if neutrinos are pure Majorano fermions, will there be any value in the term antineutrino, or will the term be retired.

Does the Majorana Collaboration have anything to say about this? At any rate they would seem to be the ones in the best position to give an argument for the "just retire the term" position.

 

[PeterDonis]

if neutrinos are pure Majorano fermions

I'm not sure if this is even a possibility. It seems to be established that the Standard Model could be expanded to accommodate a Majorana mass for neutrinos, but I'm not sure whether it could accommodate neutrinos only having a Majorana mass. (If nothing else, one would have to explain why the standard Higgs mechanism doesn't give neutrinos Dirac masses, even though left-handed neutrinos, at least, are weak isospin doublets with the charged leptons.)

 

[PeterDonis]

This paper looks like a more detailed treatment of the Majorana neutrino question by a Fermilab physicist:

https://arxiv.org/pdf/0903.0899.pdf

There's an item in this paper that I'm not sure I understand. Fig. 1 in the paper shows the Feynman diagram that is expected to dominate neutrinoless beta decay. The accompanying text notes that each vertex has to conserve lepton number; that means the neutrino coming out of the left vertex has to be an antineutrino (since it's created along with an electron), but the neutrino going into the right vertex has to be a neutrino (since it gets converted to an electron). Hence, according to the text, the diagram cannot happen unless the neutrino is its own antiparticle, so the same particle can participate in both vertices.

But if the neutrino is its own antiparticle, wouldn't its lepton number have to be zero? And if that is the case, wouldn't both vertices then violate lepton number conservation? And wouldn't that then undermine the argument that led to the inference that the left vertex has to emit an antineutrino whereas the right vertex has to absorb a neutrino?

 

[Ken G]

Does the Majorana Collaboration have anything to say about this? At any rate they would seem to be the ones in the best position to give an argument for the "just retire the term" position.

Yes I agree. Their paper (https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.130.062501 ) does not speak directly to the issue of neutrinos being their own antiparticle, instead they focus on violation of lepton number conservation, but the violation can be a rare thing. Their interest is in the creation of a matter universe, because they say: "Neutrinoless double-beta decay (0νββ) is a hypothetical nuclear process involving the unbalanced creation of two new matter particles but no antimatter [1–5]. This lepton number-violating process is predicted generically by many grand-unification theories, as well as by leptogenesis [6], a leading explanation of why the Universe is matter dominated."

So from that statement alone, it seems like they would only need lepton numbers to be rarely unconserved, and not necessarily enough to notice in the experiments @Vanadium 50 is talking about. Reasoning from that, it would seem that what the Majorana Collaboration is really saying is that neutrinos could behave like Majorana fermions a small fraction of the time, and that might be enough to explain how our universe got to be matter. Yet much of their other language seems to focus on neutrinos acting like Majorana fermions essentially all the time, i.e., being Majorana fermions. So it's difficult to understand language like: (https://enapphysics.web.unc.edu/research/majorana/ ) "If observed, 0νββ implies that the neutrino is its own antiparticle, and therefore a Majorana fermion.” So that's why I'm asking the question of whether the term "antineutrino" still has value even neutrinos are found to Majorana fermions. I don't at present understand why the argument @Vanadium 50 is presenting has not already completely ruled out that possibility, because if a neutrino made by a negative lepton "remembers that" well enough that it can only then make a negative lepton the vast majority of the time, it's quite clearly an antineutrino.

Perhaps the term "Majorana fermion" is being generalized to "occasionally shows Majorana characteristics", and "is its own antiparticle" is being generalized to "can occasionally annihilate with another like itself". But if so, then they are between a rock and a hard place-- they need the neutrinos to usually act like Dirac fermions to agree with what @Vanadium 50 is saying, but they need them to be Majorana just often enough to give their experiment a chance of detecting neutrinoless double-beta decay. That's a lot harder to justify than testing if they are Majorana fermions.

It is starting to sound like, neutrinos are not really particles because they are not mass eigenstates, but they can be thought of as superpositions of particles; and they are not really their own antiparticles but they might be superpositions of particles that are their own antiparticles, combined with those that (mostly) are not.

 

[Ken G]

We can delve deeper into the thinking of the Majorana Collaboration. At https://enapphysics.web.unc.edu/research/majorana/ , they reveal their main motivations:

"First, the neutrino mass is over a million times smaller than the mass of other particles that make up matter. If the neutrino is a Dirac particle, there is no natural explanation for this. However, if neutrinos are Majorana particles, a simple theory called the “see-saw mechanism” can account for their tiny mass.

Second, we live in a universe composed almost entirely of matter, but the big bang produced equal amounts of matter and antimatter. Where did all the antimatter go? The neutrino acting as its own antiparticle could help explain how matter came to dominate over antimatter – and therefore, how we are able to exist at all."

Unfortunately, that first one only muddies the waters. I can see how the second one might apply if neutrinos are mostly a superposition of Dirac fermions, and only a little Majorana, but the first one seems to require they be mostly Majorana, since how else could it explain their small mass? But if they are mostly Majorana, then how does a beam of them made from negative leptons know to make negative leptons? It sounds like having one's cake and eating it too.

 

[Ken G]

I'm not sure if this is even a possibility. It seems to be established that the Standard Model could be expanded to accommodate a Majorana mass for neutrinos, but I'm not sure whether it could accommodate neutrinos only having a Majorana mass. (If nothing else, one would have to explain why the standard Higgs mechanism doesn't give neutrinos Dirac masses, even though left-handed neutrinos, at least, are weak isospin doublets with the charged leptons.)

Yes I see your point, reflected in @Vanadium 50 's argument as well, but you see the issue with the first quote I gave above from the Majorana Collaboration. If they want to explain the tiny neutrino mass, and they say that Dirac fermions have no natural explanation there, they must be relying pretty heavily on the Majorana characteristics. How does a tiny Majorana mass term account for a tiny total mass?

The quote from the Majorana Collaboration goes on:
"However, if and only if the neutrino is its own antiparticle, it is possible for the two neutrinos to “cancel,” leaving behind only the electrons. Thus, observing 0νββ would provide conclusive evidence that the neutrino is a Majorana particle. Unfortunately, this process is incredibly rare – the half-life of the decay is over a billion times longer than the age of the universe."

So there is the issue I mentioned above-- they are looking for a rare rate that they think they can estimate, but how could they estimate it if they don't know how strong the Majorana elements are? They don't imply the rate is rare because the particles are mostly Dirac in nature, they imply it's just a rare rate. So it sounds like they actually looking for a doubly rare rate, and they don't even know how to estimate it, but they are hoping it lives just below the level where we would have seen lepton number violation in regular neutrino-type beams.

 

[PeterDonis]

How does a tiny Majorana mass term account for a tiny total mass?

In at least one version of the seesaw mechanism, as I understand it, the Majorana mass is tiny and the Dirac mass is very large, so there are two sets of neutrinos, a set of very light ones (which are the ones we have detected) and a set of very heavy ones (which we haven't detected yet). I don't know how much of the potential parameter space of such theories the LHC results have ruled out.

 

[Ken G]

Here is a recent paper on the Dirac vs. Majorana issue as it relates to dipole moments:
https://lss.fnal.gov/archive/2022/pub/fermilab-pub-22-663-t.pdf
What is interesting in this paper is that once again, they do not seem to be talking about mostly Dirac with some tiny Majorana aspect, they are literally talking about particles that have antiparticles, vs. particles that are their own antiparticles. For example, they say:
"We find that a next-generation experiment two orders of magnitude more sensitive to the neutrino electromagnetic moments via νµ elastic scattering may discover that the neutrino electromagnetic moments are nonzero if the neutrinos are Dirac fermions. Instead, if the neutrinos are Majorana fermions, such a discovery is ruled out by existing solar neutrino data, unless there are more than three light neutrinos."

They add to this either/or perspective:
"It is well known that diagonal dipole moments for Majorana fermions are forbidden and hence these only have transition dipole moments. Dirac fermions, instead, are allowed to have both diagonal and transition dipole moments."

But then there is the cryptic:
"We also discuss how Majorana neutrinos can “mimic” Dirac neutrinos in the presence of new light neutral fermions."
Could this "mimicking" include acting to preserve lepton number most of the time? I'm speculating, but they do say:
"If the neutrinos are Majorana fermions, one can mimic the Dirac case by adding more neutrino mass eigenstates."
So although what they mean by "the Dirac case" is strictly about the dipole moment, one cannot help but wonder if one can connect negative leptons to negative leptons using particles that are their own antiparticles if one simply embeds the lepton number information into additional degrees of freedom such as additional mass eigenstates. What's to stop a Majorana neutrino from being able to annihilate with an identical particle, yet still "know" it came from a negative lepton? Then it would be its own antiparticle, so it would not strictly be an "antineutrino", yet it would mimic an antineutrino based on its memory of the lepton it is associated with.

I presume the issue is clarified in the sources referred to when they say:
"In recent years, there have been many efforts connecting these constraints to the parameters of the Lagrangian (see, for example, [6, 7, 15–25]). In most of these studies, special attention was dedicated to the Majorana-neutrino hypothesis." Surely, no one would dedicate so much effort to an idea that was obviously contradicted by simple neutrino beams, so I think they must have ways to conceptualize neutrinos as pure Majorana fermions, yet still equip them with the ability to "remember" which type of lepton they came from.

 

[Ken G]

In at least one version of the seesaw mechanism, as I understand it, the Majorana mass is tiny and the Dirac mass is very large, so there are two sets of neutrinos, a set of very light ones (which are the ones we have detected) and a set of very heavy ones (which we haven't detected yet). I don't know how much of the potential parameter space of such theories the LHC results have ruled out.

Interesting, but that would still imply that the neutrinos we are detecting are pure Majorana neutrinos, so would need to have some way of knowing what type of lepton they came from, while still showing the CPT symmetry of a particle that is its own antiparticle. I'm wondering if the pro-Majorana folks have a trick up their sleeve that we are overlooking.

 

[PeterDonis]

that would still imply that the neutrinos we are detecting are pure Majorana neutrinos

Not necessarily. In the seesaw mechanism, as I understand it, the actual physical neutrinos (the ones we detect in detectors) are neither the pure Majorana ones nor the pure Dirac ones; they are combinations of them.

 

[Ken G]

Not necessarily. In the seesaw mechanism, as I understand it, the actual physical neutrinos (the ones we detect in detectors) are neither the pure Majorana ones nor the pure Dirac ones; they are combinations of them.

Well that brings us back to the original issue, if the neutrino beam experiments force neutrinos to be mostly Dirac-type, or if they could still be essentially pure Majorana. I think the quotes I just gave make it pretty clear that there are still a lot of neutrino experts that think neutrinos could be essentially pure Majorana (after all, that paper was talking about dipole moment matrices that have zero diagonal elements, not diagonal elements that are a tiny bit smaller than you'd expect, etc.). Yet of course they know about the beam experiments, so it seems to me there must be a way that a neutrino that is flat out "its own antiparticle" (based on ability to annihilate, CPT symmetry, etc.) can still create mostly only negative leptons if it came from negative leptons. It must therefore come from some property other than lepton number, that is the possibility we have not taken into account.

 

[Vanadium 50]

Can you be more specific about which experiment this refers to?

Lots and lots. MINOS did it, and before that CCDR did it, and it goes all the way back to the CERN Wide-Band-Beam in the 70's and early 80's, and experiments like CDHS. Van der Meer invented the horn in the 1960's.

Here is one table from the latest Review of Particle Properties:

You can get a slightly more comprehensive view by looking at the experiments who have results on the top and bottom lines. (Also note that the nu cross-section is larger than nubar, in contrast to some claims made upthread)

 

[PeterDonis]

there must be a way that a neutrino that is flat out "its own antiparticle" (based on ability to annihilate, CPT symmetry, etc.) can still create mostly only negative leptons if it came from negative leptons

I looked through the "Publications" section of the Majorana Collaboration website in the hope of finding a paper that dealt with any proposed theoretical basis for such a possibility, but couldn't find one.

 

[PeterDonis]

Lots and lots.

Are all of these experimental results possible if neutrinos are pure Majorana fermions (i.e., no Dirac masses, just Majorana masses)? It doesn't seem like they would be, since pure Majorana fermions can't have a meaningful lepton number, but these results certainly seem to indicate that neutrinos do. Unless there is some other mechanism involved, but I'm not sure what it could be, and so far I've found no discussion of any such thing in the literature I've looked at.

 

[Ken G]

Exactly my question as well. I think the answer must be "yes", given all the work being done on Majorana neutrinos, but I don't know the mechanism proposed to essentially "hide" a lepton number like that.

 

[Ken G]

You can get a slightly more comprehensive view by looking at the experiments who have results on the top and bottom lines. (Also note that the nu cross-section is larger than nubar, in contrast to some claims made upthread)

Not sure what "upthread" statement is being referenced, but is it not apparent that the cross-sections could be different (here by a factor remarkably close to 2) if it is true that the target of what is being called a neutrino is a neutron, and the target of what is being called an antineutrino is a proton? So if you are implying that a different cross section requires a different neutrino, I would point to the differing target. What seemed more telling is your point that one does not see both of those reactions happening for a given beam of neutrinos, which would seem to require that if they are Majorana neutrinos, they need internal degrees of freedom that are not lepton number. But that would seem to be all they would need.

 

[malawi_glenn]

This would be a weak interaction decay conserving lepton number, correct? So if we're getting positive pions, those would decay into positive muons (antimuons, lepton number -1) and muon neutrinos (lepton number +1), whereas if we're getting negative pions, those would decay into negative muons (lepton number +1) and muon antineutrinos (lepton number -1), correct?

In the context of the standard model (pure Dirac-neutrinos) yes.

"if neutrinos are pure Majorano fermions, will there be any value in the term antineutrino, or will the term be retired." No one has yet answered that

I thought you could read between the lines in my posts. "No" (if you ask me or basically every theoretician, what experimentalists would call things - I do not know).

 

[Ken G]

Thanks for your answer, at least we have one theorist who would say that, and a claim that most any theorist would. I'm not sure if the implied separation between theorists and experimentalists is really valid though, it would be pretty strange for experimentalists to see value in a term that theorists don't. But if we take it as likely that there is not value in the term "antineutrino" if neutrinos are pure Majorana particles, we now have the issue of whether or not neutron beam experiments have already ruled that out. It looks like the answer to that has to be "no, otherwise not so many people would still be doing research on neutrinos as pure Majorana particles." Combining those two conclusions takes us all the way back to the beginning of the thread: we do not know that neutrinos are not their own antiparticles, and it would not invalidate a long list of everything else we know if they were. But we still have to understand how all that can be consistent with @Vanadium 50 's point that neutrino beams built from antileptons tend to only produce antileptons in the detectors, there has to be a way for Majorana neutrinos to pull off that trick.

 

[malawi_glenn]

at least we have one theorist who would say that, and a claim that most any theorist would.

I base this on the analogy that we do not speak of "antiphotons", "anti-Z" nor "anti-higgs".

 

[vanhees71]

I tried to avoid getting into the question of mass vs. flavor eigenstates. Neutrinos are leptons, anti-neutrinos are anti-leptons. Yes, we can go into mroe detail and talk about individual flavors, but I deliberately avoided doing this.

The point is that this is not yet unanimously decided for neutrinos. Whether they are Majorana or Dirac particles is subject of active research, e.g., by the search for neutrinoless double $\beta$-decay. For a pretty comprehensive review on Majorana vs. Dirac neutrinos, see

https://arxiv.org/abs/1412.3320v1