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!

  • 2
    $\begingroup$ Note that the electron and the muon have different lepton numbers. $\endgroup$ – Davide Morgante Feb 1 at 11:38
  • $\begingroup$ @DavideMorgante Ah thanks $\endgroup$ – Jakob Sachs Feb 1 at 11:47

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