Charged pion decay in to Tau

[Oreith]

Main Question or Discussion Point

This may be a silly question, but what prevents the decay of a Pion in to a (anti) Tau and (anti)Tau neutrino. I can see the process for the electron but not for the tau.

 

[Orodruin]

Conservation of energy. The tau lepton is heavier than the pion.

 

[ChrisVer]

In the CM of the pion, it will have $E = m_\pi \approx 135 ~MeV$
Then decaying to something that needs at least (for its mass purposes) energy of $E \sim M_\tau \approx 1777 ~MeV$ is impossible.
That's something one has to check everytime he has a decay of the form : $X \rightarrow A_1 + A_2 + ... +A_n$
That's not though the case of $X+Y \rightarrow N- \text{particles}$