I got given a homework problem to check various particle decays, whether they're allowed under the different conversation laws (Baryon, Lepton, charge etc.)
Currently im stuck at the following one:
$$ \pi^0 \rightarrow \mu^+ + e^- $$
The literature seems to say that the neutral Pion only decays into a pair of Photons or a Electron-Positron pair. So im puzzled why this seems to be impossible.
- The lepton number is fine since its 0 before and $1-1 \rightarrow 0 $ after.
- Baryon as well $1-1 \rightarrow 0 $.
- And electrical charge also $0 \rightarrow 1-1$
The resting energy of the Pion is $134$ MeV and thus enough to create the Muon and Electron mass $105.66 + 0.511$ MeV.
Any help is appreciated!