# Neutrino Oscillation Question

by ryanwilk
Tags: neutrino, oscillation
 P: 57 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 Thanks in advance, Ryan
Mentor
P: 10,808
 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?
No. You can invert the matrix and express the mass eigenstates as linear combination of flavor eigenstates. This allows to add the present mass eigenstates (with their amplitudes and relative phases!) to calculate the flavor eigenstate contributions. It is random which state you measure, you can just calculate probabilities*.
Measurements are always done via the weak interaction, so you detect flavor eigenstates.

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