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So for example, is the following reaction possible?:

$$ \mu^- \rightarrow e^- + \gamma $$

In the textbook it says this is possible, as it conserves the lepton number. However, the lepton flavour is not conserved, as no muon neutrino is produced, and no antielectron neutrino is produced as well. Shouldn’t this not be possible? Or is family lepton number conservation not required for reactions?

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Lepton family is not conserved in the SM due to neutrino oscillations. However, the rate of neutrino oscillation is so low that you would not expect to be able to detect it.

Other theories such as SUSY theories do predict that this decay mode is possible with a higher rate, and experiments such as MEG are looking for evidence of these theories through this decay route.

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  • $\begingroup$ Why do neutrino oscillations violate lepton flavor conservation? $\endgroup$ Jan 2 '20 at 17:58
  • $\begingroup$ @PeterShor you can have a diagram with a decay to a virtual muon neutrino which oscillates to an electron neutrino that then produces the final electron. I'm not a particle physicist, but I understand that real neutrino oscillation is a measured phenomenon and one that clearly violates lepton flavor conservation (its the only known process to do so though). $\endgroup$
    – jacob1729
    Jan 2 '20 at 18:15
  • $\begingroup$ Strictly, SM neutrinos are massless and neutrino oscillation is the only directly observed BSM physics. $\endgroup$
    – dukwon
    Jan 5 '20 at 1:30

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