The three flavors of neutrinos apparently oscillate. At least I believe that is the current thinking. Do the three types of electrons oscillate as well? What about the +2/3 and -1/3 quark types? Do they perhaps oscillate in theory, but there much higher masses mean that there is essentially no effect?
Since no one has provided a good answer yet, here is an article on the topic (at least on charged lepton oscillations). Short answer, no. The decays that produce charged leptons either produce them in mass eigenstates, which do not oscillate, or superpositions that could oscillate, but decohere before any reasonable chance of detection. The electrons we have hanging around all over the place are also in mass eigenstates, so they don’t oscillate.
Thank you. The paper was beyond my background, but it is nice to know that the question I asked is of interest to physicists.
To add a bit…
Yep. The evidence for neutrino oscillation is rock solid.
The short answer given above by lechcim is correct: no. Mathematically, there is no reason they can’t oscillate. The neutral leptons are not special as viewed by the weak interaction. All that is specified is that the charged leptons of known mass do not correspond to the neutral leptons of known mass. That is, if you create a charged lepton and neutral lepton together via the weak interaction, and you somehow know the mass of one of them, you cannot know the mass of the other. Notice that the word “flavor” hasn’t appeared yet.
The charged leptons are much heavier than the neutrinos and have wildly different masses from one another. When you create a charged/neutral lepton pair, you are essentially guaranteed to know the charged lepton’s mass (either because only one of their masses is kinematically allowed, or because the coherence time is ridiculously short, or because of electromagnetic interaction in the environment, or …). Knowing the mass of the charged lepton sets which superposition of neutral leptons you are dealing with. Quantitatively, it is so overwhelmingly the case that the charged lepton is in a fixed mass state that it’s useful to give a name to the particular superposition of neutral leptons you get alongside each of the electron, muon, or tau. These are, of course, the neutrino flavors. In this language, the charged leptons are states of known mass and known flavors, while the neutral leptons are mixed, with the mass states and flavor states being superpositions of one another.
One can conceive of experimental scenarios in which things play out the other way, but they are all far-fetched. Among the multiple impractical requirements would be definitively measuring the mass of the neutrino that was produced alongside the charged lepton.
Quarks are mixed in the same fashion as leptons, but they have the additional burden of being confined inside hadrons. Since you cannot have a freely propagating quark, you can’t get quark oscillation. Quark mixing manifests itself the weak decays of hadrons and in another form of oscillation: neutral meson oscillation. Here, the entire meson is oscillating between itself and its antiparticle rather than individual quarks, but quark mixing is an essential part of the process.
What’s the difference between the electron, muon, and tau neutrinos? Presumably, they all have different masses. However, before neutrino oscillation was discovered, it was believed that they all had no mass, yet they were still considered separate particles. What quantum numbers are different between them?
If you take a process that produces a muon and a neutrino, and you let that neutrino interact in a nearby detector, it can produce a muon but not an electron or a tau. If you take a process that produces a tau and a neutrino, that neutrino can interact to produce a tau but not an electron or a muon.
Neutrinos, thus, carry a quantum number (flavor) that says what type of charged lepton they are associated with, and this quantum number can be measured by letting the neutrino interact and produce its charged lepton partner. The 1962 discovery that muon neutrinos were distinct from electron neutrinos was awarded the 1988 Nobel Prize in physics. Distinct observation of the tau neutrino came only in 2000 via the DONUT experiment.
Aside: since the thread is in part about neutrino masses and flavors, I would be remiss not to make a note here even though it isn’t germane to your sub-question. The electron, muon, and tau neutrinos don’t have well-defined masses. The neutrinos with definite mass are usually labeled 1, 2, and 3 rather than e, mu, and tau. The latter three are linear superpositions of the former three. So, neutrinos 1, 2, and 3 all have different masses. The electron, muon, and tau neutrinos are all different superpositions of the mass states, so one could loosely say that they have “different masses”, but this shouldn’t be taken to mean that the flavor states have any particular masses at all.
I read the paper, but I’m still not clear on why the charged leptons don’t oscillate. The author talked about oscillation or not in terms of decay from a massive particle. But for the neutrinos, it’s described in terms of mixing angles, which seem to be fixed angles, not something dependent on how the neutrinos were formed. The mass eigenstates of the neutrinos don’t align with the flavor eigenstates. On preview, what Pasta just said.
In the paper, the author states right off the bat
But why are they aligned for the charged leptons and not for neutrinos? Is this based on measurements, based on an assumption, or based on a definition?
As I understand it the charged lepton flavour eigenstates are defined to be the mass eigenstates. The flavour eigenstates for neutrinos are defined to be those states which couple to the equivalent charged lepton flavour eigenstates through the weak interaction, which, by lack of coincidence, aren’t also mass eigenstates.
One could in principle define the flavours by the neutrino mass eigenstates and then the charged leptons would be superpositions, but it’s just so much more convenient to call those things bound to atoms “electrons” instead of “some superposition of electron, muon, and tau”.
There is an equivalent convention with quarks where the +2/3-charged quarks’ mass eigenstates are equal to the flavour eigenstates by definition, while the -1/3-charged quarks’ flavour eigenstates are superpositions.
The charged lepton mass eigenstates are defined to have definite flavor, but that’s not why they don’t oscillate. Rather: because they don’t oscillate, it’s convenient to define them as having definite flavor.
Mass eigenstates are stationary states of the free Hamiltonian. They do not change with time, or in the language of oscillation, they do not change as they propagate. If you can create a neutrino in one of the three mass eigenstates, that neutrino will not oscillate. If you can create a charged lepton in one of the three mass eigenstates, that charged lepton will not oscillate.
In practice, it is nigh impossible not to produce a charged lepton in a mass eigenstate given the wildly different masses of the charged leptons (wildly different as compared to the typical quantum uncertainties, energies, and momenta at play). The simplest example for this is beta decay, where a neutron turns into a proton plus the lightest charged lepton plus an antineutrino. There isn’t enough energy released in the decay to produce the second-lightest charged lepton, so the outgoing charged lepton has no admixture of the heavier charged lepton. With the charged lepton state set (and given the name “electron”), the neutrino state is also set and happens not to be a pure mass eigenstate but rather a superposition of all three of them, thanks to mixing. If, unlike beta decay, the process can kinematically produce electrons or muons (or taus), the outgoing charged lepton state decoheres so quickly that the state remains stationary (if mixed) at any observable distance scale and so still does not oscillate.
In a sufficiently contrived gedanken experiment, the roles of the neutrinos and the charged leptons can be flipped. In practical scenarios, though, the charged leptons are always observed in mass eigenstates, so talking about non-stationary superpositions of these isn’t ever relevant. Thus, flavor gets defined by the charged lepton mass eigenstates.
Because the experimental view has been historically unambiguous, the theoretical side of this issue has only gotten rigorous attention in the past couple of decades, and new pedagogical approaches are still emerging (and sometimes wrong ones!) A recent novelty is to avoid talking about the propagating neutrino as a real particle at all since you never measure it directly. You just measure the charged lepton produced alongside the neutrino at its source and the charged lepton produced when the neutrino interacts in the detector. So far these theoretical machinations haven’t impacted experimental effort, but as experiments push toward very low energy and high precision measurements, they could start to have bearing.
Note that, while the three flavor eigenstates of neutrino don’t have definite mass, you can define the expectation value of the mass for each of them. Last I heard, the best experimental data was that the electron and mu neutrinos were both approximately equal mixtures of nu1 and nu2 (the lightest and second-lightest neutrino mass eigenstates) with almost no contribution from nu3, while the tau neutrino is almost pure nu3 with almost no contribution from nu1 or nu2. This means that the expected value for the mass of an electron or mu neutrino is approximately equal, but that the expected value for the mass of a tau neutrino is significantly more than either of them.
Chronos, your concept is, of course, sound, but the data is a bit jumbled. Of the three mass eigenstates, it is not known which is heaviest. It is known that nu[sub]1[/sub] and nu[sub]2[/sub] are close in mass (with nu[sub]2[/sub] heavier than nu[sub]1[/sub]) and that nu[sub]3[/sub] is somewhat different in mass from those two, but it might be heavier or lighter than them. For the flavor mixing: mu and tau neutrinos are the similar ones, with each being about half nu[sub]3[/sub] with the rest from nu[sub]1[/sub] and nu[sub]2[/sub]; and electron neutrinos are about two-thirds nu[sub]1[/sub], one-third nu[sub]2[/sub], and a smidge nu[sub]3[/sub]. (For anyone interested is numbers instead of words, this is all encapsulated in this matrix.)
Reference on the topic of mass vs flavour eigenstates and neutrino oscillation that for some reason I couldn’t find earlier.
OK, obviously the data have move on from when I was last actively involved in this field. I had thought, though, that nu1, nu2, and nu3 were defined to be the least-massive, median-mass, and most-massive mass eigenstates: What’s the actual definition? Is it just that 2 is the more-massive of the small-split pair, 1 is the less-massive, and 3 is the one that’s the outlier?
That’s how it works out empirically, but that’s not how it was defined. Pontecorvo (the “P” in “PMNS matrix”) originally put forth the neutrino oscillation idea as a transition between neutrino and antineutrino, as there was only one neutrino known at the time. When the second distinct neutrino flavor was discovered, the oscillation idea evolved to nu[sub]e[/sub]<–>nu[sub]mu[/sub], and the mass eigenstates were assigned such that if the mixing were small, nu[sub]e[/sub] would be mostly nu[sub]1[/sub] and nu[sub]mu[/sub] would be mostly nu[sub]2[/sub]. This assignment was preserved when three-flavor mixing was introduced, so that’s pretty much the long and short of the definition. (Since solar oscillations necessarily involve nu[sub]e[/sub], the mass eigenstate with the least nu[sub]e[/sub] would end up being the new nu[sub]3[/sub]). The actual ordering of the masses is empirical from there. The relative 1-2 mass ordering is known only because the neutrinos exiting the sun have to pass through the sun’s high- and varying-density matter. This influences the oscillation in a mass-ordering-dependent way, and one can back out from that that the more electron-y state has to be the lighter of the two most electron-y states. Determining the relative mass of nu[sub]3[/sub] through a similar matter-influenced oscillation is a hot topic at the moment.
Ooh, neat, I hadn’t heard about that. Of course, neutrino physics is currently one of the fastest-advancing fields in particle physics.
EDIT: That is, I think I knew that that would be possible in principle, but I didn’t know anyone had done it.