I Majorana Neutrinos: Different Physics than Oscillation

[Ken G]

Here's another question that might shed light on that one. The first paper that @vanhees71 cited above noted that Dirac neutrinos are the general class that includes both Majorana and Weyl type, but Weyl type only applies for massless neutrinos, though they can be regarded as building blocks for Majorana types and even for the full Dirac type. It also sounds to me like the Majorana type is the one that is built not to distinguish neutrinos and antineutrinos, so that requires some special construction. The Dirac type is more general, and does allow a distinction between neutrinos and antineutrinos, expressly because it has a more general construction. So if experiments show that neutrinos are in fact of Majorana type, why doesn't that quite clearly indicate that they are built specially to provide no meaning to the phrase "beam of antineutrinos"?

Given this, I could see an argument for retaining the idea that neutrinos can have an antimatter character, because we allow the more general theory until the more specifically built one is demonstrated. But what I don't see is why it is controversial that if neutrinos are found to be purely of Majorana type, then there is no such thing as a "beam of antineutrinos."

 

[PeterDonis]

I believe the implication of the quote is that two neutrinos that come from the same process, say beta decays that also produced electrons, could never annihilate each other even if one of them managed to flip helicity, if they are Dirac fermions. Flipping helicity is all that is required for Majorana, impossible in all cases for Fermions.

I don't think this is correct. (Whether it's what the viewgraphs are saying is hard to say, since, as I note below, the viewgraphs don't give any math, and ordinary language is a bad tool for describing the physics involved.)

In two-component spinor language, a Dirac mass term couples two two-component spinors together, while a Majorana mass term couples the two components of one two-component spinor. But in either case the "flipping" that the coupling induces ends up producing the CPT conjugate of the original. The Dirac mass term just does it by "flipping" two two-component spinors instead of only one.

You appear to be thinking of a "flipping" that only flips one two-component spinor even if the fermion is a Dirac fermion with two two-component spinors, but I'm not aware of any such operation.

I'm certain the person who presented those viewgraphs knows that

The statements you quoted from the viewgraphs talk about helicity, not chirality. Helicity is frame dependent. Chirality is not. I have been talking about chirality, and the $L$ and $R$ subscripts in the post by @Vanadium 50 refer to chirality.

The viewgraphs talk about helicity vs. chirality, but appears to focus on helicity because "physical particles occur with a definite helicity in nature". But that statement appears to contradict the statement just above it on the same slide: "helicity of massive particle depends on reference frame".

The viewgraphs don't give any math, so I don't think they are a good reference for this discussion, since many of the communication issues we are having are due to ordinary language being a bad tool for describing the physics involved.

 

[Ken G]

In two-component spinor language, a Dirac mass term couples two two-component spinors together, while a Majorana mass term couples the two components of one two-component spinor. But in either case the "flipping" that the coupling induces ends up producing the CPT conjugate of the original. The Dirac mass term just does it by "flipping" two two-component spinors instead of only one.

Yes, but as I understand what those quotes mean, the flipping is only happening to one of the two neutrinos in the double beta decay. For Majorana, that would be enough for annihilation, for Dirac, not enough.

The statements you quoted from the viewgraphs talk about helicity, not chirality. Helicity is frame dependent.

Yes, this is why the effect only happens at order m/E, a measure of the accessibility of a frame that flips the helicity.

Chirality is not. I have been talking about chirality, and the $L$ and $R$ subscripts in the post by @Vanadium 50 refer to chirality.

Yes, I know, I am merely quoting from the viewgraphs, which are talking about flipping helicity not chirality.

The viewgraphs talk about helicity vs. chirality, but appears to focus on helicity because "physical particles occur with a definite helicity in nature". But that statement appears to contradict the statement just above it on the same slide: "helicity of massive particle depends on reference frame".

I mentioned that above parenthetically, I expected them to say that chirality was the particle-dependent thing and helicity was more malleable. They seemed to say the opposite, so that is indeed confusing. It's not clear the distinction matters in the rest of their argument, maybe it was even a typo.

The viewgraphs don't give any math, so I don't think they are a good reference for this discussion, since many of the communication issues we are having are due to ordinary language being a bad tool for describing the physics involved.

Still, the math must be interpreted. The issue of the thread is what is the meaning of the phrase "a beam of antineutrinos." That's language, not math. If it was true that all we need is math, we'd never even need the word "antineutrino." But math is not good enough, because physics does more than just predict quantitative outcomes, it creates a way to talk about nature. That gets sticky, I know, but that's why it requires a discourse like this one. The question is, if neutrinos are pure Majorana particles, is there any such thing as a "beam of antineutrinos", and if not, what is the better way to say a beam of neutrinos that is going to produce a whole lot of positrons and not many electrons when you bash it into neutrons and protons?

 

[Vanadium 50]

Why would you put words in my mouth?

I did no such thing,.

Four times, I have asked you to be civil.

 

[PeterDonis]

as I understand what those quotes mean, the flipping is only happening to one of the two neutrinos in the double beta decay

There is only one neutrino line in the lowest order diagram for double beta decay. That diagram is made with two ordinary beta decay vertices (I described this vertex in an earlier post), and one neutrino line linking them (so the neutrino line is internal and there is no outgoing neutrino external leg). That means the neutrino line must have opposite chirality at the two vertices, which means that, somewhere on that internal neutrino line, there must be a "flipping" operation that flips the chirality. But of course, since the neutrino line has the same weak interaction vertex at both ends, the "flipping" must also preserve the weak interaction coupling.

A Majorana mass term couples the two components of the $\nu_L$ two-component spinor that has a weak interaction coupling, so it could serve as the required "flipping" operation above. It would "flip" $\nu_L$ to its CPT conjugate $\bar{\nu}_R$.

A Dirac mass term, however, would couple $\nu_L$ with the separate "sterile" neutrino $\nu_R$, which has no weak interaction coupling, so it can't serve as the required "flipping" operation above.

The above seems to me to be what the viewgraphs with the contrasting "Dirac" and "Majorana" statements were trying to get at. But I'm not sure they did a very good job.

 

[PeterDonis]

The question is whether the term "beam of antineutrinos" actually means anything at all for a beam of Majorana neutrinos.

@Vanadium 50 already gave an operational definition of "beam of antineutrinos"--a beam that produces negative leptons when it hits a target containing baryons. By his definition, of course the term has meaning, since such beams have been produced many, many times in experiments.

We had a question under discussion for a while in this thread about how a model of neutrinos as pure Majorana fermions could produce such a beam, but that has been resolved (the chirality of the neutrinos emitted at the source is sufficient for that given the smallness of neutrino masses).

There might be physicists who would want to adopt a different term than "beam of antineutrinos" to describe the kind of beam that the above operational definition refers to, if neutrinos turn out to be Majorana fermions. But it does not appear that @Vanadium 50 is one of them, and if that is the case, it is pointless to continue to ask him the question you are asking him. He's already given all the answer he's going to give.

 

[Ken G]

There is only one neutrino line in the lowest order diagram for double beta decay. That diagram is made with two ordinary beta decay vertices (I described this vertex in an earlier post), and one neutrino line linking them (so the neutrino line is internal and there is no outgoing neutrino external leg). That means the neutrino line must have opposite chirality at the two vertices, which means that, somewhere on that internal neutrino line, there must be a "flipping" operation that flips the chirality. But of course, since the neutrino line has the same weak interaction vertex at both ends, the "flipping" must also preserve the weak interaction coupling.

A Majorana mass term couples the two components of the $\nu_L$ two-component spinor that has a weak interaction coupling, so it could serve as the required "flipping" operation above. It would "flip" $\nu_L$ to its CPT conjugate $\bar{\nu}_R$.

A Dirac mass term, however, would couple $\nu_L$ with the separate "sterile" neutrino $\nu_R$, which has no weak interaction coupling, so it can't serve as the required "flipping" operation above.

The above seems to me to be what the viewgraphs with the contrasting "Dirac" and "Majorana" statements were trying to get at. But I'm not sure they did a very good job.

OK thanks, that makes sense-- the "flip" is not going to produce annihilation for the Dirac neutrino because there are those sterile states to flip into, not available for the Majorana neutrinos. So that's what the quote means.

Now for the question this is all leading to: if neutrinos are Majorana, their mass eigenstates do, or do not, distinguish matter from antimatter in any way?

 

[PeterDonis]

this is why the effect only happens at order m/E, a measure of the accessibility of a frame that flips the helicity

This doesn't make sense as it is stated (and not just by you, the viewgraphs appear to be stating it the same way). I can't make a piece of actual physics happen or not happen just by changing which frame I use to describe it.

This is one of the items that I think really suffers from the lack of math in the viewgraphs.

 

[Ken G]

@Vanadium 50 already gave an operational definition of "beam of antineutrinos"--a beam that produces negative leptons when it hits a target containing baryons. By his definition, of course the term has meaning, since such beams have been produced many, many times in experiments.

Yes I know, that is ducking the question completely. One could give the same operational definition for Bobneutrinos, that isn't the issue. The issue is, is there any justification for calling that beam a beam of antineutrinos, or is there not? The term "antineutrino" is supposed to mean more than some operational definition that could also apply to "Bobneutrinos". In particular, it is supposed to mean that if you take the C conjugate, you are supposed to get a beam of neutrinos that makes leptons instead of antileptons. Would that indeed happen? It all gets to the core issue-- what is the difference between a beam of neutrinos that makes leptons, and one that makes antileptons? Is it purely the chirality? If so, that's not matter/antimatter.

We had a question under discussion for a while in this thread about how a model of neutrinos as pure Majorana fermions could produce such a beam, but that has been resolved (the chirality of the neutrinos emitted at the source is sufficient for that given the smallness of neutrino masses).

Yes, this is what I thought the resolution was. So imagine my confusion when chirality is getting given "operational definitions" that don't mean chirality, but rather matter/antimatter. If Majorana neutrinos do not distinguish matter from antimatter, but do distinguish chirality, then clearly those are not the same things if neutrinos turn out to be of Majorana type, even if they are shoehorned in with unjustified operational definitions that seem to stem from nowhere except an accident of history that Dirac fermions were favored over Majorana. That's precisely the way we got rid of the geocentric model of the solar system, even though it is a perfectly acceptable "operational definition" of how the solar system works (in, for example, Tycho's model, a model which stressed the idea that the Earth was not allowed to move, rather than that it was the arbitrary origin of the coordinates.) It's not about tautologies, it is about using words that connect with their implied meanings to avoid promoting misconceptions, like that neutrinos are different from antineutrinos if they are Majorana.

There might be physicists who would want to adopt a different term than "beam of antineutrinos" to describe the kind of beam that the above operational definition refers to, if neutrinos turn out to be Majorana fermions. But it does not appear that @Vanadium 50 is one of them, and if that is the case, it is pointless to continue to ask him the question you are asking him. He's already given all the answer he's going to give.

The issue is what is the justification. It is always pointless to ask someone who feels allowed to define any term how they wish without justification, but the term "antimatter" is supposed to mean something, so does require justification to use, even if "Bobneutrino" does not.

 

[PeterDonis]

if neutrinos are Majorana, their mass eigenstates do, or do not, distinguish matter from antimatter in any way?

It depends on what you mean by "distinguish matter from antimatter".

Very roughly speaking, if neutrinos are Majorana, a neutrino mass eigenstate would look something like $\nu_L + \nu_L^c = \nu_L + \bar{\nu}_R$, which obviously goes into itself under CPT conjugation. But if neutrinos are Dirac, we would have one mass eigenstate that looks like $\nu_L + nu_R$, and its CPT conjugate would be $\nu_L^c + \nu_R^c = \bar{\nu}_R + \bar{\nu}_L$, which is a mass eigenstate, but not the same state as before. (Of course we already have an example of this in the Standard Model since this is how electrons and positrons work.)

So in the above sense, yes, a Majorana mass eigenstate would be "its own antiparticle", whereas a Dirac mass eigenstate would not.

However, as I believe has already been noted in this thread, the actual interactions that neutrinos undergo do not involve mass eigenstates. They involve two-component spinors where the "thing" component is of left-handed chirality, and the "antithing" component, the CPT conjugate of the "thing" component, is of right-handed chirality. The difference in chirality can be used to distinguish "things" from "antithings" regardless of what kind of mass eigenstates are present in the theory. This is the basis for the distinction @Vanadium 50 made between "beams of neutrinos" and "beams of antineutrinos".

Of course if you let such a beam propagate long enough, it will lose its definite nature as a "beam of neutrinos" or a "beam of antineutrinos", because of the mixing induced by the mass terms in the propagator. But how long "long enough" is depends on the masses--the smaller the masses, the longer you have to wait for a detectable amount of mixing to occur. In practical terms, it seems like "long enough" is way longer than any length of time we have so far probed in experiments.

 

[PeterDonis]

that is ducking the question completely.

I understand that this is your opinion. You have stated it repeatedly. Continuing to state it adds nothing to the discussion. Either people will give responses, or they won't.

 

[PeterDonis]

imagine my confusion when chirality is getting given "operational definitions" that don't mean chirality, but rather matter/antimatter

The reason for this is simple: the nature of weak interactions links the two. Weak interactions only involve "things" with left-handed chirality and "antithings" with right-handed chirality. This is not limited to neutrinos: it also applies to electrons and quarks.

 

[Ken G]

It depends on what you mean by "distinguish matter from antimatter".

Very roughly speaking, if neutrinos are Majorana, a neutrino mass eigenstate would look something like $\nu_L + \nu_L^c$, which obviously goes into itself under CPT conjugation.

OK, but that is the predicate here: if neutrinos are Majorana.

But if neutrinos are Dirac, we would have one mass eigenstate that looks like $\nu_L + nu_R$, and its CPT conjugate would be $\nu_L^c + \nu_R^c = \bar{nu}_R + \bar{nu}_L$, which is a mass eigenstate, but not the same state as before. (Of course we already have an example of this in the Standard Model since this is how electrons and positrons work.)

That is the alternative predicate, the one we can consider for purposes of contrast.

So in the above sense, yes, a Majorana mass eigenstate would be "its own antiparticle", whereas a Dirac mass eigenstate would not.

There has always been the discrepancy between whether particles that have a wavefunction with indeterminate energy count as particles, or if they have to be eigenstates of energy, and a superposition of eigenstates is then a superposition of particles, one of which gets picked out in the experimental resolution. In ordinary quantum mechanics, we use the former approach-- the particle is the free photon, say, and it can have an indeterminate energy, that is "collapsed" on measurement but it's still the same particle it always was. But we have the definition from @vanhees71 that in field theory, the opposite choice is made by definition, and a particle is always its mass eigenstate. So a beam of particles is a beam of mass eigenstates, by the same logic. We seem to be having our cake and eating it too here, to deny that the state of a "beam of antineutrinos" has something to do with mass eigenstates in field theory.

However, as I believe has already been noted in this thread, the actual interactions that neutrinos undergo do not involve mass eigenstates. They involve two-component spinors where the "thing" component is of left-handed chirality, and the "antithing" component, the CPT conjugate of the "thing" component, is of right-handed chirality. The difference in chirality can be used to distinguish "things" from "antithings" regardless of what kind of mass eigenstates are present in the theory. This is the basis for the distinction @Vanadium 50 made between "beams of neutrinos" and "beams of antineutrinos".

Again it sounds like you are saying the difference in chirality can be used to distinguish outcomes of experiment, but it is then just complete tautological choice to call that "things" and "antithings." That's not what chirality normally means, correct? I mean, what is the "things" and "antithings" doing here if we already have chirality and the chirality already tells us what will happen in the experiment? Do you see my analogy with aether, that doesn't do anything either but we are free to include it as an "operational definition" since it won't violate any experiments if we still use Lorentz transformation from the aether to all other inertial frames. It's a distinction that does not nothing. It's not even wrong.

Of course if you let such a beam propagate long enough, it will lose its definite nature as a "beam of neutrinos" or a "beam of antineutrinos", because of the mixing induced by the mass terms in the propagator. But how long "long enough" is depends on the masses--the smaller the masses, the longer you have to wait for a detectable amount of mixing to occur. In practical terms, it seems like "long enough" is way longer than any length of time we have so far probed in experiments.

Yes, that's the order m/E "flipping" that they were talking about, but the viewgraphs seemed to associate that with helicity rather than chirality. But we're still not super clear on the distinction they were making there, it doesn't seem to matter because that's more about how we test if they are Majorana or not, we are simply predicating that they are Majorana for the purposes of the discussion.

 

[PeterDonis]

what is the "things" and "antithings" doing here if we already have chirality and the chirality already tells us what will happen in the experiment?

Because, historically, the distinction between "things" and "antithings" was discovered first, before chirality was even considered at all. That distinction came along in the late 1920s and 1930s, when quantum field theory was first developed and it was realized that antiparticles were necessary to make the theory work. It wasn't until the CP violations in the weak interactions were discovered in the 1950s that chirality entered the picture and the limiting of weak couplings to left-handed "things" and right-handed "antithings" was proposed to explain that CP violation.

As I have already noted, that violation is not limited to neutrinos; it involves electrons and quarks as well (in fact it was first observed in electrons). So it was natural for experimentalists to describe the CP violations they were seeing as an asymmetry between "things" and "antithings", a distinction that was already there in existing theory, and to use that same description for all of the particles involved in the interactions--quarks, electrons, and neutrinos. At the time (the 1950s, 1960s, and 1970s, when electroweak theory was being worked out and tested in experiments), neutrinos were believed to be massless, so the question of Majorana vs. Dirac masses didn't even arise.

 

[Ken G]

The reason for this is simple: the nature of weak interactions links the two. Weak interactions only involve "things" with left-handed chirality and "antithings" with right-handed chirality. This is not limited to neutrinos: it also applies to electrons and quarks.

But that's just it, that statement is built from the interactions of particles that have additional degrees of freedom, like charge and lepton number, but what about when the "things" you are talking about have zero charge and zero lepton number (like Majorana neutrinos)? Then there is not two things in that sentence, there is only one. That's my point, for this type of particle, isn't a distinction being made about how the weak force operates, based on how it operates on other particles with additional degrees of freedom, where no such distinction exists or is needed for that particle?

I note what you are saying about the history of things, and I agree with all of that, but we must distinguish historical accident from theoretical justification. The history of light was to expect an aether, and no experiment denies the existence of an aether. But we got rid of it anyway, not because it was wrong, but because it really didn't have any essential meaning.

Here's a situation that might be a decent analogy for making this point. Let's imagine we have a type of bird, the leptonhawk, that likes to eat mice, but it only eats mice that have male attributes and are left-handed. Then we have the antileptonhawk, that only eats mice that have female attributes and are right-handed. There are tons and tons of mice that are male or female, and right- or left-handed, so our history of studying these birds is that we get very used to thinking that anything a leptonhawk eats is definitively a lefthanded male mouse. But then it turns out that there is a class of hermaphrodite gerbils, and the leptonhawk eats the left-handed ones because it sees that it has male attributes, and the antileptonbird eats the right-handed ones because it sees it has female parts. Now we prepare a "beam" of lefthanded hermaphrodite gerbils, and we notice the leptonbirds feast and the antileptonbirds go hungry. Shall we create the operational definition that this must have been a beam of male gerbils, on grounds that male animals are all that leptonhawks eat? Or should we notice that we don't have male gerbils in our beam, we have a different class of animal that leptonhawks also eat, which we didn't think to allow in the first place because we didn't know animals could be hermaphrodites? I think we would say that leptonhawks eat lefthanded male mice, and lefthanded gerbils, and leave it at that, so our beam would be a beam of lefthanded gerbils and that's all.

 

[PeterDonis]

for this type of particle, isn't a distinction being made about how the weak force operates, based on how it operates on other particles with additional degrees of freedom, where no such distinction exists or is needed for that particle?

But interactions never involve just that particle. The weak interacting $\nu_L$ two-component spinor is in a weak isospin doublet with the weak interacting $e_L$ two-component spinor. They always occur together in interactions. So the distinction is always there in every interaction. It doesn't go away for that interaction just because one of the particles involved happens to be a Majorana fermion. If both fermions involved were Majorana fermions, that would be different; but they aren't.

Whether considerations like that would end up keeping the term "antineutrino" in use if it were discovered that neutrinos are Majorana fermions is a matter of trying to predict the future. If past history is any guide, ordinary language terminology in physics is often not very logical from a strictly "current theory" point of view, so I would not be surprised if the term "antineutrino" did not go away. But terminology changes do sometimes happen, so I would not be particularly surpirsed if it did go away, either. I don't think a very strong prediction can be made one way or the other.

 

[Dr.AbeNikIanEdL]

but what about when the "things" you are talking about have zero charge and zero lepton number

The “things” and “antithings” taking part in the electroweak interaction dont have zero charges (if they had they would not be interacting with anything) or zero lepton number.

 

[Dr.AbeNikIanEdL]

Now people keep using the phrase "Majorana mass term", but I'm saying, the particle is a Majorana fermion, which we have seen in quite a few places means the particle is of a very different nature than a Dirac neutrino.

This expectation of a drastic change in the behavior of neutrinos depending on their type is just wrong. It is only in effects suppressed by the smallness of the masses, which are only important in very specific cases.
Of course, experiments designed to distinguish Majorana from Dirac fermions focus on these specific cases. So if you look at a presentation of such an experiment it’s clear that the behavior in the two cases is drastically different. But that doesn’t mean everything else changes.

 

[Ken G]

The “things” and “antithings” taking part in the electroweak interaction dont have zero charges (if they had they would not be interacting with anything) or zero lepton number.

I'm talking about how many quantum numbers can be different in a beam of Majorana neutrinos. We heard earlier that beams are free particles so the particles in a beam must always be mass eigenstates, by definition. Hence this is the question: in a beam of Majorana neutrinos, how many quantum numbers can be different among the mass eigenstates in such a beam?

 

[Ken G]

This expectation of a drastic change in the behavior of neutrinos depending on their type is just wrong.

I said nothing about a "drastic change in behavior," I said a drastic difference in nature, meaning the identity of the particle. If the behaviors were drastically different, we'd know by now! Two very different objects can have very similar behaviors, that's why I keep returning to the analogies of the aether, or heliocentric vs. geocentric models of the solar system. Revolutions in science happen around small differences in behavior connected to large differences in nature, which sometimes "are to be looked for in the sixth place of decimals" (to quote Michelson).

It is only in effects suppressed by the smallness of the masses, which are only important in very specific cases.

Yes, I know, the issue is whether we are forcing quantum numbers onto the Majorana neutrino that it does not recognize, just to describe it in language we are accustomed to. Like the aether, like the geocentric model.

Of course, experiments designed to distinguish Majorana from Dirac fermions focus on these specific cases. So if you look at a presentation of such an experiment it’s clear that the behavior in the two cases is drastically different. But that doesn’t mean everything else changes.

I agree.

 

[Ken G]

But interactions never involve just that particle. The weak interacting $\nu_L$ two-component spinor is in a weak isospin doublet with the weak interacting $e_L$ two-component spinor. They always occur together in interactions. So the distinction is always there in every interaction. It doesn't go away for that interaction just because one of the particles involved happens to be a Majorana fermion. If both fermions involved were Majorana fermions, that would be different; but they aren't.

So the same question: if the only "free particles" in a beam are mass eigenstates, then how many quantum numbers can be different in a beam of Majorana neutrinos? You speak of the interactions, I speak of the demonstrable differences in the identities of the particles.

Whether considerations like that would end up keeping the term "antineutrino" in use if it were discovered that neutrinos are Majorana fermions is a matter of trying to predict the future. If past history is any guide, ordinary language terminology in physics is often not very logical from a strictly "current theory" point of view, so I would not be surprised if the term "antineutrino" did not go away. But terminology changes do sometimes happen, so I would not be particularly surpirsed if it did go away, either. I don't think a very strong prediction can be made one way or the other.

All right, we won't frame it is an exercise in prognostication. We can just focus on the identities of the particles in the beam, and how many quantum numbers are needed to completely specify a beam of Majorana neutrinos.

 

[jedishrfu]

Following @PeterDonis excellent post, I think we can safely close this very long thread.

Thank you all for contributing here.

Jedi