I was reading a bit about nuclear/particle physics when I came up to Cours et problèmes corrigés de physique nucléaire et de physique des particules by Philippe Miné in 2016 ISBN 2340011566, which is a french book about Nuclear & Particle Physics.

The conservation of leptonic numbers is introduced in the chapter named 'Neutrinos'. And few examples are given.

  • The first example is a muon splitting into an electron, an electron antineutrino and a muon neutrino. The leptonic number of the muon is +1. The leptonic number of an electron is +1. The leptonic number of the electron antineutrino is -1. The leptonic number of the muon neutrino is +1. $+1 = +1 + (-1) + 1$ so the leptonic number is conserved.
  • The second example is a tauon giving an electron, an electron antineutrino and a tau neutrino. We get $+1 = +1 + (-1) + 1$.
  • The third example is a tauon giving a muon, a muon antineutrino and a tau neutrino. We get $+1 = +1 + (-1) + 1$

So far I understood the conservation of leptons except when an example was given by the following sentence:

Par contre il lui est interdit de se désintégrer par un processus où la saveur n'est pas conservée: $\mu^- \not\to e^- + \gamma$

which roughly translates to:

However, it is forbidden to disintegrate by a process in which flavour is not conserved: $\mu^- \not\to e^- + \gamma$

So I was curious about the leptonic number of the $\gamma$, which is a photon, so a boson. Therefore it's leptonic number is 0. So $+1 = +1 + 0$. However, the reaction is crossed, so there must be something I missed. What is wrong in my reasoning?

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    $\begingroup$ Each lepton number is separately conserved: electron lepton number, muon lepton number, and tau lepton number. $\endgroup$ – pfnuesel May 21 '19 at 22:00
  • $\begingroup$ Thank you very much @pfnuesel $\endgroup$ – PackSciences May 21 '19 at 22:08
  • $\begingroup$ Note though that in certain processes flavor is not conserved, e.g. neutrino oscillation: en.wikipedia.org/wiki/Neutrino_oscillation $\endgroup$ – safesphere May 21 '19 at 23:31
  • $\begingroup$ @safesphere The book covers the part about neutrino oscillation and the break of leptonic numbers conservation. But thanks for adding this element :) $\endgroup$ – PackSciences May 21 '19 at 23:32
  • $\begingroup$ The physical meaning of flavor, but more precisely, why there generations of particles exist in nature instead of just one, is an unresolved mystery. While there are certain arguments and formulas on this topic, there still is no clear and meaningful answer. $\endgroup$ – safesphere May 21 '19 at 23:39

The answer was given by the user pfnuesel in the comment.

Basically you have to consider each kind of leptonic number, one for electron, one for muon and one for tau. These are known as "lepton family numbers." The equation was incorrect because they were both +1, but in different kinds. LHS was muon leptonic number and RHS was electron leptonic number.

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  • $\begingroup$ Well electron, muon, tau lepton number is violated by neutrinos. Only total lepton number is conserved by all leptons. $\endgroup$ – Roghan Arun May 19 at 20:18

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