I have seen that the argument of why neutrino oscillations exist is that their mass matrix is nondiagonal and complex and so one needs to transform it into diagonal by unitary rotations:$$\nu_\alpha=\sum_i U_{\alpha i}\nu_i$$ $\alpha $ for flavor eigenstates and $i$ for mass eigenstates. At a later time the state of the neutrino $|\nu(t)>$ is given by a linear combination of the $\nu_i$ by their respective time evolution operator and so there is a probability to find then in different eigenstates at a later time by $|<\nu_\alpha|\nu(t)>|^2$.

Why not using the same argument to say that leptons or quarks change of flavor as they propagate? I don't know much of this, any wisdom on the subject would be appreciated.

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    $\begingroup$ have a look at the questions and answers in this blog about neutrion oscillations; profmattstrassler.com/articles-and-posts/… . I think it has to do with the smallness of the effect for charged leptons. $\endgroup$ – anna v Aug 31 '16 at 18:01
  • $\begingroup$ Plug in values in the neutrino oscillation formula except now use ultrarelativistic charged leptons, say e and μ. In natural units, do you see that L ≈ π E / Δm² ? For a μ with mass of 0.1 GeV and an e of relatively negligible mass, and an E of hundreds of GeVs, do you see that we are still talking about fermis for L? $\endgroup$ – Cosmas Zachos Sep 19 '16 at 22:13
  • $\begingroup$ Well, let's say nanometers, instead. $\endgroup$ – Cosmas Zachos Sep 19 '16 at 22:22

Flavor is defined by the eigenstates of the lepton mass matrix. Neutrino oscillations happen not just because their mass matrix is not diagonal, but because their mass matrix is not diagonal when the lepton mass matrix is.

The way you see neutrino oscillation is by generating neutrinos from leptons of a specific mass, and then seeing if they interact with leptons of a different mass after traveling some distance. If neutrinos generated from $511$ keV leptons always interact only with $511$ keV leptons then there is no mass oscillation.

We can imagine reversing the experiment. Use neutrinos of a specific mass to generate leptons, let the leptons travel, and then measure their interactions. If we could do this, we would see "lepton flavor oscillation." The only difference is that we can't isolate neutrinos of specific mass because they are so hard to interact with and manipulate.


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