# Why is this decay of the neutral pion suppressed?

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!

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