# Majorana Neutrinos: Different Physics than Oscillation

• I
In summary: What does Majorano mean by 'its own antiparticle'?In summary, Majorana postulated that particles like neutrinos could have a property called "its own antiparticle" which would make their wavefunction transform into itself after the CPT transformation. However, this idea is not currently included in the Standard Model, and is only possible for particles that are electrically neutral.
Ken G said:
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.

Ken G said:
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.

ohwilleke and malawi_glenn
PeterDonis said:
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.

PeterDonis said:
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.
PeterDonis said:
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.
PeterDonis said:
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.
PeterDonis said:
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.

Ken G said:
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.

malawi_glenn and vanhees71
PeterDonis said:
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.

Ken G said:
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.

vanhees71
Ken G said:
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.

Ken G said:
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.

vanhees71
Dr.AbeNikIanEdL said:
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?

Last edited:
Dr.AbeNikIanEdL said:
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).
Dr.AbeNikIanEdL said:
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.
Dr.AbeNikIanEdL said:
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.

PeterDonis said:
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.
PeterDonis said:
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.

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

Thank you all for contributing here.

Jedi

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