# Neutrino Oscillation Question

## Main Question or Discussion Point

Hi, this is probably pretty simple but it's puzzling me...

In neutrino oscillation, you produce and detect neutrinos with a specific flavour (e,μ,τ) but they travel as mass eigenstates (1,2,3).

The flavour eigenstates are just linear superpositions of mass eigenstates:
nu_e = U_e1 nu_1 + U_e2 nu_2 + U_e3 nu_3
nu_μ = U_μ1 nu_1 + U_μ2 nu_2 + U_μ3 nu_3
nu_τ = U_τ1 nu_1 + U_τ2 nu_2 + U_τ3 nu_3

where U_ij are the PMNS matrix elements. So for example, an electron neutrino will consist of ~68% nu_1, ~30% nu_2 and ~2% nu_3.

During propagation the mass eigenstates travel at different velocities so at any given time, the neutrino you started with will consist of a certain fraction of nu_1,2,3 but not necessarily the correct ratio which corresponds to nu_e, nu_μ or nu_τ.

Therefore, I don't understand why whenever you detect a neutrino, it is always one the three flavours.

If it were ~66% nu_1, 33% nu_2 and 1% nu_3, would it "become" an electron neutrino because it's closest to this state? Is the PMNS matrix just probabilistic so the average ratio is ~68% nu_1, ~30% nu_2 and ~2% nu_3 but this is not fixed? Does it have something to do with never detecting neutrinos directly but only through interactions and e.g. a W boson can only ever interact with one of the flavour states? Or some other reason altogether? =s

Ryan