humanino said:
This is a mix of hand waving and physical intuition I gathered to satisfy myself with an answer. I certainly do not claim it has been published, and it may very well be wrong.
Having slept overnight on it, I don't think it's wrong, I agree with it, but I prefer to specify whether one is talking about mass eigenstates or flavor eigenstates. Then I think it is no longer hand waving.
The best introduction to neutrino oscillation I've found is by Smirnov when he taught a seminar in Iran. Smirnov is the "S" in the MSW effect, which has to do with what happens to neutrino oscillation when they pass through matter. The paper is huge, 2.4 MB, and it takes a long time to download. So don't try to read it from the source, download it and then open it with acrobat. See the section labeled "Oscillations" which begins around slide 18:
http://physics.ipm.ac.ir/conferences/lhp06/notes/smirnov1.pdf
If you read from there through to where he begins talking about matter effects, it will be clear that neutrino oscillations should be thought of as interference effects between the mass eigenstates. This is what I wrote up in my blog post, but in a more natural way, without the confusion of talking about flavor neutrinos. I think it would be more natural to a student if you simply didn't talk about neutrino flavors any more than we talk about charged lepton flavors.
The Smirnov paper is a pretty obscure source. The only reason I found it is because I googled my name; Smirnov referenced me in one of his later lectures at the same meeting.
When I discuss with neutrino physicists, I get all sorts of hand waving arguments, such as the fact that a full blown QFT calculation including the Higgs should be taken into account to resolve those questions. I however feel that this is merely another example of elementary quantum mechanics which goes against our intuition.
Yes, exactly. For me, the intuition is that (1) particles that fly at ~c for 8 minutes must be on their mass shells, and (2) particles on their mass shells cannot interact (or interfere) with each other.
The end point of the electron energy spectrum in beta decay has a shape signing in principle unambiguously the mass of the neutrino. Unfortunately, this is very undoable in practive, because of the low statistics at this end point, and because of the resolution requirements.
The mass you would get from double beta decay would be a mixture of masses appropriate for the electron flavor neutrino. The only possible way of getting a sharp mass out of a decay that produces a neutrino is to find one where the available energy is enough for only the lightest neutrino; so the other mass eigenstates are excluded by energy conservation. Since the heaviest neutrino weighs about 0.05 eV, this seems to be impossible.
This is similar to how one excludes muon production in a beta decay. That is, if there were beta decays that emitted electrons with energies greater than the mass of the muon, we'd see muons as well as electrons coming out of them. And in detecting these, we would have interference between the electrons and muons and could look for charged lepton oscillation, other than the fact that the difference in mass is so large that the oscillations would have very short wave lengths. But this would happen only in another universe with different atomic masses / energies, etc., so maybe in that universe we could detect the oscillations,
.
I suppose I should admit that I haven't searched the literature to find the highest energy beta decay, but these are the facts as I believe them. If someon knows of a beta decay where the electron has even 0.1 atomic mass units of energy available, please inform.
By some weird piece of fate, one of my first tasks in grad school was designing and building the trigger module for Steve Elliott's PhD project at U. Cal., Irvine. I think it was the first time projection chamber search for double beta decay. We had gone to the same high school in Albuquerque (3000 km away) and both played on the school chess team. Steve is still in experimental neutrino physics.
To put the numbers into perspective, Steve's double beta experiment used Selenium 82. The decay energy for this is 3MeV, over a billion times too large to pick out a single mass eigenstate:
http://en.wikipedia.org/wiki/Selenium
Getting back to the idea of charged lepton oscillations, that's less than 1/30th the mass of a muon so no oscillation.
Actual fits, although compatible with zero mass, tend to have a mysterious systematic shift towards negative mass values...
I've often wondered about this. My claim to fame in neutrinos was extending Koide's formula for the charged leptons to the neutrinos. Before I did this, it had been written several times in the literature that his formula was incompatible with the neutrinos. Smirnov put a review paper on neutrinos up on the arXiv (that he co-wrote with Mohapatra) and I corrected error by email.
Koide's formula for the charged leptons is:
2(\sqrt{m_e} + \sqrt{m_\mu} + \sqrt{m_\tau})^2<br />
= 3(m_e + m_\mu + m_\tau)
In order to get this to work for the neutrinos, I effectively changed the smallest square root to a minus sign. (Actually, what happened is that I rewrote the equation as a eigenvector equation. The details are in
http://www.brannenworks.com/MASSES2.pdf , but the overall effect was to make the smallest neutrino's square root of mass be negative.)
I think I've been told that negative masses would, in QFT, act the same as positive masses. And certainly the amount is so small that the difference would be very hard to detect. But if that were the case, I suspect it blows relativity out of the water, and so the assumption is that the negative masses are experimental error (or theoretical error because the calculations behind double beta decay are horrendously complicated if I recall). But I haven't thought about this much.
