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?