With a given fixed flavor neutrino produced, after a long flight, will the measured flavor always be the same at the detector?

In theories explaining neutrino oscillations (with 3 neutrinos to make it simple), it is explained that a neutrino flavor eigenstate that is produced with an electroweak process is actually a superposition of various neutrinos mass eigenstates.

During their flight, each mass eigenstate evolves in a different way, thus, at an arbitrary non trivial distant, the flavor of the neutrino is a mixture of all flavors together. Do you agree with my sentence ? (Books typically don't state that the neutrino at a given distance is a flavor superposition... they typically only say that a given flavor neutrino is a superposition of mass eigenstates, which is not enough to fully understand.)

Thus my question is : let's consider a given flavor neutrino produced, that flight to a long distant that is known with an extremely good precision. Let's suppose that in the detector, it will interact (I know that cross-section is low) and transform to a charged lepton.

Will the flavor of the neutrino at the detector always be the same ? That is exactly reproducible result.

-> Or is it the same spirit of the quantum mechanism : when interacting with the detector, there will be projection of the system on one of the flavor, with a given probability : that is non reproducible result : the result is reproducible only on an average/statistics base.

Do the laws explain in average the mechanism, but don't explain why each measurement will be a specific given flavor instead of another one ?

• I a very real sense this is a question about quantum mechanics and not about neutrinos at all (there is nothing special about neutrinos as a system for this kind of question). And the answer is that experiments on Bell's theorem rule out some possible answers but leave a selection of other options that comes down to "Maybe". – dmckee --- ex-moderator kitten Jan 7 at 20:43
• @dmckee : I do know quantum mechanisms and principles of overlap of various states. My question is really on neutrino, to know if this obeys to the same principles. – Mathieu Krisztian Jan 7 at 20:58

Will the flavor of the neutrino at the detector always be the same?

Yes. It has the same flavour as the charged lepton the detector saw. For example, a detection of a muon implicates that the flavour of the neutrino was muon-neutrino. However immediately before the detector interaction the neutrino is a nontrivial superposition of three flavour states. The detector could have seen an electron with a nonzero probability, and that would indicate that the flavour of the neutrino was electron-neutrino at the moment of interaction. The neutrino wavefunction collapses at the moment of the interaction to one of the three possible flavour states.

Or is it the same spirit of the quantum mechanism : when interacting with the detector, there will be projection of the system on one of the flavor, with a given probability.

This is also what happens. Your two statements are not mutually exclusive. However some may disagree on your interpretation of reproducibility.

Do the laws explain in average the mechanism, but don't explain why each measurement will be a specific given flavor instead of another one?

Neutrino oscillation can be interpreted as a quantum-mechanical effect, and since QM is probabilistic by construction, this is correct. A detection of a neutrino flavour different from the source neutrinos implies this is a real effect. Historically this was hinted by observing a deficit of solar and atmospheric neutrinos, where the neutrinos oscillated to flavours invisible to the detector.

• Thank you, so, it is the same as quantum mechanic : if the neutrino wave function at the level of detector as for example 90 % of of nu_e, 9 % of nu_mu, and 1 % of nu_tau, the interction could in very rare cases collapses the wave function to a tau neutrino for example. And we do not have, in science, an explanation (apart from probability explanation) on why quantum mechanic chooses a given state instead of another one, among the possible states that composes the mixture of the flavor of the neutrinos at the distant detector. Right ? – Mathieu Krisztian Jan 7 at 21:07
• Correct. If we had an explanation why exactly QM chooses this state instead of that state, we would have a different theory. – Zeick Jan 7 at 21:12
• Perfect. Thank you so much Zeich for your explanations. – Mathieu Krisztian Jan 7 at 21:21

The neutrino starts in a particular flavor state, ideally purely one flavor.

As it propagates, the mass states evolve at different rates.

After some distance and hence time, the neutrino is in a different mix of flavor states, and the interaction samples that.

If that’s all there is, that final mix of states would always be exactly the same.

But in real experiments, it’s a bit more complicated. Neutrinos are created with a range of energies, so the time evolution to a given distance is not always the same. Matter effects can add to the mixing. And real beams are not always of a pure flavor to start with.

So the final superposition of flavor states is not always the same in a real experiment.

• ok thank you. I forgot to write in my question that I was assuming a exact fixed energy. So you seem to confirm that the measurement is doing a projection that chooses (according to the probability) one of the flavor state that compose, at that given distance, the neutrino. – Mathieu Krisztian Jan 7 at 21:01
• Right! But that measurement can’t actually be done with real beams. – Bob Jacobsen Jan 7 at 21:03