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Consider scattering process: $\nu_x + e^- \to \nu_x + e^-$

Why does this only undergo weak neutral current interaction for $\mu$ and $\tau$ neutrinos but can involve exchange of either $W$ or $Z$ for $\nu_e$?

My guess is charged current for $\nu_\mu$ and $\nu_\tau$ would violate some rules for the Feynmann diagrams? certain conservation laws at the vertices? although I'm not exactly sure what would be violated.

I realise this might be a really elementary question but I'm new to particle physics.

Thanks

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  • $\begingroup$ You're on the right track. Try drawing the diagrams for which the exchange particle is a $W$ for both cases (electron and either of the others). Compare to the case where the exchange particle is a $Z$ (for any species). Is there something different about one of these? $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented Feb 5, 2015 at 23:29
  • $\begingroup$ I did try to draw the diagrams, but I don't actually know what the rules are for these...my lecture notes (if you can call it that) are horribly incomplete...my diagrams for W show the incoming neutrino and electron exchanging a W and then "swapped over" when they go out. what's the significance in that?? $\endgroup$
    – Tobyhas
    Commented Feb 5, 2015 at 23:58
  • $\begingroup$ Label the lepton lines for flavor, then stare at all the diagrams... $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented Feb 6, 2015 at 0:00
  • $\begingroup$ I'm not trying to be annoying but I literally have no clue. Doesn't flavour just mean the different kinds of leptons? In all the diagrams for W exchange, there's 1 electron and 1 neutrino ($\nu_\mu$, $\nu_\tau$ or $\nu_e$) coming in and same going out...why is it that only $\nu_e$ works?... $\endgroup$
    – Tobyhas
    Commented Feb 6, 2015 at 0:34
  • $\begingroup$ Mmmm ... no need to apologize. I was taking that Socratic approach because these thing never stuck when they were explained to me, and finally did stick when I puzzled them out for myself. In any case, flavor in the lepton sector means the $e$, $\mu$ or $\tau$ label and is conserved at weak vertexes. Note that flavor in the quark sector is not fully respected by weak interactions. $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented Feb 6, 2015 at 1:04

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In order for a W boson to be exchanged, there has to be a vertex where a neutrino has turns into the corresponding charged lepton or vice-versa. $\nu_e \to W^+ + e^-$, for example. Hopefully you can see why the equivalent for a muon neutrino ($\nu_\mu \to W^+ + e^-$) couldn't happen.

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