I Majorana Neutrinos: Different Physics than Oscillation

[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.