Nuetrinos change flavor, energy transfer

[Albertgauss]

Ok, so want to clarify something:

A nuetrino can change between flavors as it moves through space. A nuetrino that starts out as an electron nuetrino can turn into a tau nuetrino or a lepton nuetrino, or mixtures of the two. It can then turn back into its original electron nuetrino.

Suppose I start out with a Tau neutrino, the most massive of the three nuetrinos. This nuetrino has some total energy E, and some very big mass M. Much of the energy of the tau nuetrino will be in its rest mass.

When the tau nuetrino turns into an electron nuetrino, the energy E remains constant, but the rest mass of the electron nuetrino is much less than the tau nuetrino. What happens to rest of the energy that was originally part of the tau nuetrino's rest mass? Does it go into kinetic energy?

 

[AdamLin]

The rest of the energy is converted into kinetic energy. The velocity increases to compensate for the lower mass.

 

[francesco85]

This is a not very easy topic and it is related to what is called neutrino oscillations. (Since I don't know your background, I suppose that you know the Quantum mechanics, otherwise the whole wuestion would take a very very long time).
Very roughly speaking, this is what is going on: there are three kinds of neutrinos, namely electron neutrino, muonic neutrino and tauonic neutrino; these are usually called "flavor eigenstates" (particles with definite flavor, where the flavor can be the following: electron, nuon, tau); moreover each of these flavor eigenstates can be seen as a superposition (quantumly) of three mass eigenstates (particles with a definite mass: m1, m2 and m3); so, suppose that an electron neutrino is produced; since this is the superposition of three mass eigenstates, the evolution of the initial state does not preserve the flavor, because the masses m1, m2 and m3 are different. If you want, there is no violation of the energy,simply the fact that the initial state is not an eigenstate of the hamiltonian.
This is the standard version.



More precisely (interpretation) : let us consider the standard model and let's add neutrino masses; then what we can say for the quarks, can be also said for the leptons; in particular there is an analogous of the CKM matrix (called PMNS matrix, if I remember correctly); let us analyze a process like the beta decay: what is happening is the following: there are various possible process (what is produced in a real physical process are always mass eigenstates): n->pe nu1, n->pe nu2, n->pe nu3, where nu1, nu2 and nu3 are the three neutrino mass eigenstates.
The Feynman diagram for every such process is weighted with factors of the PMNS matrix; so why are we speaking about electron neutrinos? The point is that we are not able to measure and observe the mass eigenstates of the neutrinos, our experimental apparatus are not so powerful. What we can say, in my opinion, is that we can treat the system as a statistical mixture of three kind of neutrinos. If we were able to see the mass eigenstates, then we would not observe oscillations.


Francesco

 

[kurros]

Suppose I start out with a Tau neutrino, the most massive of the three nuetrinos. This nuetrino has some total energy E, and some very big mass M. Much of the energy of the tau nuetrino will be in its rest mass.

"Very big mass M"? The tau neutrino may be the heaviest of the neutrinos, but it is still a neutrino and still has a ridiculously tiny mass. Certainly "Much of the energy of the tau nuetrino will be in its rest mass" is totally false. Practically none of its energy will be in its rest mass.

Of course as francesco85 says, really there is no tau neutrino mass, just the 3rd generation neutrino mass which is some superposition of the flavour states. But assume we are talking about these. If there was a big mass difference between the neutrinos then the different mass eigenstates would propagate at different speeds (as you say, the different in rest mass energy would be accounted for by different velocities), and the superposition would quickly decohere. If I remember correctly.

 

[Albertgauss]

Yes, I was a physics major and know all about eigenstates and such. The level you are presenting is fine; I know what is going on.

Let me see if I can try again:

All particles below are nuetrinos.

The flavor eigenstates are electron, muon, and Tau.

Each of these flavor states is a superposition of three mass eigenstates m1, m2, m3.
The electron flavor state would correspond to some combination of m1, m2, and m3. The Muon flavor state would be a different combination of states m1, m2, and m3. The Tau flavor state would be a combination of m1, m2, and m3.

Now, the masses that are quoted as upper limits on the nuetrinos: 2.2 eV, 170 keV, and 15.5 MeV, are these the masses associated with the individual mass states m1, m2, and m3, or are they the masses associated with the flavor states? When I use such language as “tau neutrino having a mass of 15.5 MeV”, does this mean:

the Tau flavor state has mass 15.5 MeV,

Or

the Tau flavor state corresponds to the m3 state of 15.5 MeV being the dominant superposition mass state over the two other mass states.

Also, I am not looking for energy violation. What I am curious about is that if an tau starts out with some energy E and rest mass 15.5 MeV, and then the electron flavor state dominates a little later so that the mass drops to 2.2 eV, where does the energy go? It appears unanimous on this post that the energy will be kinetic. Or perhaps, as the neutrino evolves, it could be a combination of states of 2.2 eV (electron) and muon (170 keV) with all the rest of the energy as kinetic for a time. If I started with a Tau, then stop it and see that it has evolved into an electron, where would the difference in rest mass energy go?

Are the three flavor states the only possible combinations of the mass states m1, m2, and m3? It seems there could be many combinations of the mass states to other flavor states, but nature restricts only to three. Is this logic correct?

"Very big mass M"? The tau neutrino may be the heaviest of the neutrinos, but it is still a neutrino and still has a ridiculously tiny mass. Certainly "Much of the energy of the tau nuetrino will be in its rest mass" is totally false. Practically none of its energy will be in its rest mass.

Yes, I see what you’re saying. But a Tau neutrino at 15.5 MeV will have much more energy in its rest mass than an electron neutrino of 2.2 eV, even if they are both very energetic.

 

[kurros]

The flavor eigenstates are electron, muon, and Tau.

Each of these flavor states is a superposition of three mass eigenstates m1, m2, m3.
The electron flavor state would correspond to some combination of m1, m2, and m3. The Muon flavor state would be a different combination of states m1, m2, and m3. The Tau flavor state would be a combination of m1, m2, and m3.

Now, the masses that are quoted as upper limits on the nuetrinos: 2.2 eV, 170 keV, and 15.5 MeV, are these the masses associated with the individual mass states m1, m2, and m3


, or are they the masses associated with the flavor states? When I use such language as “tau neutrino having a mass of 15.5 MeV”, does this mean:

the Tau flavor state has mass 15.5 MeV,

Or

the Tau flavor state corresponds to the m3 state of 15.5 MeV being the dominant superposition mass state over the two other mass states.

Where are you getting these upper limits? They are vastly larger than my understanding of the expected masses of neutrinos. To explain neutrino oscillations the difference between their masses has to be many orders of magnitude smaller than your numbers suggest; consider this quote from the wikipedia page on neutrinos, which matches what I remember:
"The best estimate of the difference in the squares of the masses of mass eigenstates 1 and 2 was published by KamLAND in 2005: |Δm^2(21)| = 0.000079 eV^2.[38] In 2006, the MINOS experiment measured oscillations from an intense muon neutrino beam, determining the difference in the squares of the masses between neutrino mass eigenstates 2 and 3. The initial results indicate |Δm^2(32)| = 0.0027 eV^2, consistent with previous results from Super-Kamiokande."

But to answer your question, the masses are limits on the mass eigenstates, which should be called simply 1,2,3, although people may sometimes be slack and call them by the name of the dominant flavour eigenstate. I'll come back to the rest of your post later if no-one else answers your questions in the meantime, but I think a lot of your confusion comes from thinking that the mass differences between neutrinos are much bigger than they really are.

 

[francesco85]

Also, I am not looking for energy violation. What I am curious about is that if an tau starts out with some energy E and rest mass 15.5 MeV, and then the electron flavor state dominates a little later so that the mass drops to 2.2 eV, where does the energy go? It appears unanimous on this post that the energy will be kinetic. Or perhaps, as the neutrino evolves, it could be a combination of states of 2.2 eV (electron) and muon (170 keV) with all the rest of the energy as kinetic for a time. If I started with a Tau, then stop it and see that it has evolved into an electron, where would the difference in rest mass energy go?

I think that this could be answered as in my previous post in the "more precisely" section: if we were able to observe mass eigenstates then we would not observe any oscillation; the particles that are produced in a process are always mass eigenstates; we speak about oscillations just because of our limited experimental apparatus; so what we call electron neutrino is just a statistical mixtures of different mass eigenstates. In other words, speaking in a rigorous way, we can never start with a Tau neutrino if it is produced through a scattering or decay process.

Are the three flavor states the only possible combinations of the mass states m1, m2, and m3? It seems there could be many combinations of the mass states to other flavor states, but nature restricts only to three. Is this logic correct?

If I have understood your question correctly, one can of course make infinite combinations with three mass eigenstates; but the flavor eigenstates actually correspond to those particular combinations for which the interactions between these combinations and the gauge fields are diagonal, in the sense that, roughly speaking, they belong to the "standard" representaton of the electroweak group.


Francesco

 

[Albertgauss]

Let me first answer this question: "Where are you getting these upper limits" of 2.2 eV, 170 keV, and 15.5 MeV.

Here on wikipedia, I confess.

http://en.wikipedia.org/wiki/Neutrino

If you scroll down to "Neutrinos in the Standard Model
of elementary particles", you will see the upper limits I am quoting.

 

[kurros]

Hmm, well that is some poor wikipedia writing, there is no citation I can see for those values. I expect though that they are from some kind of direct attempts to measure the mass. There is however quite a bit of indirect evidence that their masses are way below these upper bounds, which is discussed a bit in the 'masses' section of the same article: http://en.wikipedia.org/wiki/Neutrino#Mass

 

[Vanadium 50]

I think we need to sweep away some debris.

We know all three neutrinos weigh less than about an eV (perhaps as much as 2.2, but that's unlikely) and have mass differences of a tiny fraction of an eV.

Second, oscillation is fundamentally quantum mechanical, so you need to specify what variables you are in an eigenstate of and what variables you are not. If you are in an energy eigenstate and a momentum eigenstate you are in a mass eigenstate, not a flavor eigenstate.

 

[Albertgauss]

I took another look at the wikipedia section you mentioned, and saw what you wrote about the oscillations on the order of milli-eV. They don't talk about what the mass of the muon nuetrino or tau nuetrino are. They do have constraints on the oscillations, which would mean the muon and tau nuetrino would be on the order of eV as well. There are a lot of contradictory information on this wiki website. There is this: These indicate that the combined mass of the three neutrino varieties must be less than 0.3 eV. The estimate in the article puts the electron nuetrino at 1.5 eV.

When I look at Wiki's lepton page, it shows the numbers I quoted I before as upper limits. But, there is some analogy with the types of electrons: the electron, muon, and tau have vastly different masses. It would seem that neutrinos might also have such vast differences in masses as well. I have to admit that a tau neutrino with a mass of 15 MeV is really high. Why is the article quoting such high masses upper limits if the oscillation data fixes the muon and tau nuetrinos to be in the realm of eV? How solid is the oscillation data? It also seems that a lot of tau neutrinos have not been observed, which I don't know if this is true or not.

Also, maybe something that would help, is to help me re-write the following I wrote earlier so that it would be correct, using the correct language of flavor, mass, and energy states.

A tau starts out with some energy E and rest mass m3, and then, when I check my tau neutrino later, it is in an electron flavor state where the mass drops to m1. Where does the missing rest mass energy go (assuming tau is more massive than electron)? It appears unanimous on this post that the energy will be kinetic.

 

[jtbell]

A tau starts out with some energy E and rest mass m3

(I assume you mean tau-neutrino, not tau)

If it starts out as definitely a tau-neutrino (e.g. from the decay of a tau), then it does not have a definite mass. It can have either mass m1, or m2, or m3, with certain probabilities.

 

[AdrianTheRock]

You may find reading this thread helps.