# Neutrino Oscillations

1. Oct 24, 2007

### ylem

I have a few questions about Neutrino Oscillations...

Firstly, why are they called oscillations? Is it because they can go back and forth to different flavours/masses?

Next, if, for example, a tau neutrino is produced in the sun, will it oscillate to the other flavours on its way to earth, or just stay as a tau??

Thanks for your help! Sam x

2. Oct 24, 2007

### Staff: Mentor

These are "flavor oscillations." If a neutrino is produced as a tau-neutrino (e.g. via the decay of a tau lepton), it can interact (be detected) later as either a tau-neutrino, an electron-neutrino, or a muon-neutrino. The probabilities of getting each flavor vary with distance (and time) in an oscillatory fashion.

(Likewise if the neutrino is produced as an electron-neutrino or a muon-neutrino.)

I don't think it's really appropriate to say that the neutrino goes "back and forth" between the different flavors. When you detect a neutrino, or it interacts, it is destroyed, and doesn't have a chance to "oscillate back" to its original flavor. While the neutrino is "in flight," before detection, all we can say about it is that we can describe it as a quantum-mechanical superposition of the three flavors. What it is "really really doing" during that time is beyond our knowledge at present, and falls in the category of "interpretations" of QM.

Last edited: Oct 24, 2007
3. Oct 29, 2007

### ylem

Thanks! That's really helpful! :-) x

4. Jun 18, 2008

### ghery

Another question

Hi:

Ihave another question about neutrino oscillations, If the masses of the diferent kinds of neutrinos are different, how is it possible that they change families ? how is it possible that for example a muon neutrino that is lighter than a tau neutrino transforms into it if they have different masses?

5. Jun 18, 2008

### Staff: Mentor

The way I understand it, the mass of a neutrino does not change between its creation and its destruction, but its flavor can change. A neutrino that is created as (say) an electron-neutrino can have any of the three neutrino masses, with some probability for each. When it interacts with something and is destroyed, it may do so as a different flavor, but with the same mass that it started with.

6. Jun 18, 2008

### BDOA

Neutrino Oscillation

Its because the states with the different masses are not the states matching the muon, tau
or electron. So mass state 1, is a superposition of an electron and muon neutrino. And so on.
Neutrinos are born (and die) as a definite lepton type state. But the velocity they travel at
depends on the mass, so they change type, as they travel.

7. Jun 19, 2008

### CarlB

The mass of a flavor neutrino is indeterminate. If you knew its mass precisely enough, then you could tell what mass eigenstate it was, but that still wouldn't tell you what flavor it was.

The whole thing is easier to understand if you look at neutrino oscillation (of flavors) as an effect caused by neutrino interference (between the mass eigenstates).

Pretty much any interaction where a neutrino is involved has such high energies that any of the mass eigenstate neutrinos could be produced. That means that in calculating the probabilities of a neutrino interaction you have to include the possibility for all three neutrino types.

This is best explained by thinking of a particular example. Suppose it is an "electron neutrino" that is emitted and an "electron neutrino" that is recieved. The electron neutrino is defined as a particular set of amplitudes (complex number) for the three mass eigenstates. Immediately after creation, those amplitudes will be unchanged so it will still look like an electron neutrino. But as time goes on, the three neutrinos will end up with different phases in their amplitudes because they have different masses. Note that all three are assumed to have the same energy, if this is unknown in the process, then you have to integrate over available energies.

As the relative phases change, the total amplitude for the three neutrinos being perceived as an electron neutrino changes. And so we say they oscillate. But you could also see it as the mass eigenstates interfering.
This will be 3 separate complex numbers that you will add together before taking the magnitude and squaring. And therefore they can beat against each other.

8. Jun 19, 2008

### humanino

Neutrinos are created in a proper (eigen) state of flavor, but they propagate in the mass basis, which is slightly different from the flavor basis. I think at this point nobody worries. Actually, if the energy of the neutrino is much greater than any of the neutrino masses, then there is not much conceptual difficulty.

The trouble ghery might have, could rather be the following. Consider just a two neutrino case, suppose the mass of the lightest one is small compared to the difference with the heavier one. Since neutrinos have mass, I can hold the light one in my hand (don't ask me, this is a thought experiment... ok, I accelerate myself in the rest frame of the neutrino ). I would definitely have a certain of mass in my hand, I can feel (in principle), or measure with a scale. Now if I wait, I could get the heavier one and have more mass in my hand !? But this contradicts energy conservation ! In fact, oscillation from the light state to the higher mass state can occur only if the neutrino propagates, so there is no such problem.

9. Jun 23, 2008

### CarlB

I can't figure out if I agree or disagree with this. If the two neutrinos you began with were the mass eigenstates, $$\nu_1, \nu_2$$, then they would not oscillate and energy (and mass too, in this case) would be conserved. On the other hand, if the neutrino was in a flavor eigenstate, then you can't hold it in your hand because a flavor eigenstate is intrinsically a virtual state (only the mass eigenstates can be on their mass shell).

The subject keeps coming up, so I wrote up a blog post that explains neutrino oscillation the way I think it should be explained:
http://carlbrannen.wordpress.com/2008/06/21/neutrino-oscillation

10. Jun 24, 2008

### humanino

I would be glad to follow up this discussion I took a very specific case where the mass of the lightest is negligible against the difference with the mass of the heaviest. Now take the momentum to be slow enough, typically you need a big hand (to compensate for Heisenberg). The energy of the high mass component will thus be imaginary, resulting in a damping instead of an oscillation, leaving only the lightest component.

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.

One paper addressing directly those issues is Phys Rev D, vol 44 number 11 (Dec 1991) "When do neutrino oscillate ? Quantum mechanics of neutrino oscillations" by C. Guinti, C.W. Kim & U.W. Lee

Another is Phys Rev D, vol 49 number 9 (Nov 1993) "Quantum mechanics of neutrino oscillations" by J. Rich

I also have "Fondamentals of neutrino physics and astrophysics" by C. Guinti & C.W. Kim (Oxford) where they give plenty of historical references. I'm sure that if I went through them I could figure out the answers to those considerations, but I simply do not have time right now.

Usually, when dropping the ultra-relativistic approximation and dealing with those academic questions, people assume momentum conservation, and energy uncertainty arises from the assumption that the detector is located in space better than the oscillation length, which saves energy conservation.

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.

"Neutrino mass and oscillation" in Annu. Rev. Nucl. Part. Sci. 1999.49:481-527 by P. Fisher, B. Kaiser & K.S. McFarland describe interesting and elegant "Kinematic searches for neutrino mass". 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. Actual fits, although compatible with zero mass, tend to have a mysterious systematic shift towards negative mass values...

Anyway, I have been hesitating about reposting here during the last days, because I myself am not satisfied by my previous post. So I am glad if anybody is interested, and thank you Carl for bringing it back

11. Jun 24, 2008

### CarlB

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.

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 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.

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:
$$2(\sqrt{m_e} + \sqrt{m_\mu} + \sqrt{m_\tau})^2 = 3(m_e + m_\mu + m_\tau)$$

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.

Last edited by a moderator: Apr 23, 2017
12. Jun 26, 2008