You are clear on the meaning of mass eigenstate and flavor eigenstate. That's a good place to start.

Now, recall that every state can be written in terms of any basis at any time.

So, treat the processes of emission, propagation and interaction (detection in an experimental setting) thus:

• A weak interaction produces a well defined flavor state with a particular momentum thanks to the creation operator.

• That same state (with it's existing momentum) is also described in the mass basis (but as an admixture, rather than a eigenstate), and as the particle is now in free motion it is this basis we use to describe the time evolution of the state. The different states have different frequencies, which gives rise to a oscillation in the mass-basis content of the state.

• The neutrino may interact with any matter it encounters along the way, but must do so in a flavor state and the cross-section for doing so depends on the amplitude for the appropriate flavor state(s), which in turn depends on the current admixture of mass states. In any case the neutrino is observed to have the original momentum.

This should give rise to some questions, the foremost of which is 'How can the momentum be the same for all the different mass states?', which is not a trivial thing. I'm now officially out of my depth, but I think that it helps that the neutrinos we experiment on are all ultra-relativistic.

You are clear on the meaning of mass eigenstate and flavor eigenstate. That's a good place to start.

Now, recall that every state can be written in terms of any basis at any time.

So, treat the processes of emission, propagation and interaction (detection in an experimental setting) thus:

• A weak interaction produces a well defined flavor state with a particular momentum thanks to the creation operator.

• That same state (with it's existing momentum) is also described in the mass basis (but as an admixture, rather than a eigenstate), and as the particle is now in free motion it is this basis we use to describe the time evolution of the state. The different states have different frequencies, which gives rise to a oscillation in the mass-basis content of the state.

• The neutrino may interact with any matter it encounters along the way, but must do so in a flavor state and the cross-section for doing so depends on the amplitude for the appropriate flavor state(s), which in turn depends on the current admixture of mass states. In any case the neutrino is observed to have the original momentum.

This should give rise to some questions, the foremost of which is 'How can the momentum be the same for all the different mass states?', which is not a trivial thing. I'm now officially out of my depth, but I think that it helps that the neutrinos we experiment on are all ultra-relativistic.