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I have been introduced to Feynman diagrams in a particle physics University module and I just created this diagram to practice checking conservation laws:

enter image description here

I have been told that charge, baryon and lepton numbers have to be conserved at vertices, and this is true for my diagram. I have also been told that "if the exchange particle is a neutral boson (photon, gluon, Z), quark and lepton flavours have to be conserved". Pions are also bosons, since their spin is zero (integer). So since the lepton flavour is changed in this diagram, that means that this interaction would not be allowed. However, assuming it was allowed, I then ask myself this question: which type of interaction would be going on here? It is not the strong force since leptons are not colour charged, and it is not electromagnetic since this pion is neutral. So I am left with weak nuclear force. Then would this diagram be part of a more complicated one involving W or Z boson exchanges? If someone could clarify my thoughts I would be so grateful.

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    $\begingroup$ Lepton numbers are not conserved at either vertex in your diagram. The number of electrons/electron neutrinos and the number of muons/muon neutrinos are separately conserved. $\endgroup$
    – probably_someone
    Commented Oct 11, 2018 at 11:43
  • $\begingroup$ Why would you think an electron can emit a pion? $\endgroup$
    – Mitchell Porter
    Commented Oct 11, 2018 at 13:19
  • $\begingroup$ I was just playing around with flavour and other conservation laws. No real reason behind it appart from curiosity. $\endgroup$
    – Luismi98
    Commented Oct 11, 2018 at 15:16

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This is not a possible interaction, because the three lepton numbers must be separately conserved: electron, muon and tau number. You can't turn one into the other with a pion, which has zero lepton number, and as far as I know there are no particles with lepton number $\pm 2$, so there are no electron-muon vertices at all.

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    $\begingroup$ There are flavor-changing neutral currents in the Standard Model beyond tree-level, but they are highly suppressed, and have never been observed. $\endgroup$
    – probably_someone
    Commented Oct 11, 2018 at 11:56
  • $\begingroup$ @probably_someone Loop-level FCNC has been observed for decades $\endgroup$
    – dukwon
    Commented Oct 19, 2018 at 7:02

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