Decay into an electron and an electron-anti-neutrino?

[Soff]

$$\pi ^- \rightarrow \mu^- +\bar{\nu_\mu}$$

Why doesn't it decay into an electron and an electron-anti-neutrino? I guess it has something to do with the conservation of the helicity. But how does it work?

 

[Meir Achuz]

The pi-->e nu decay occurs but at about 10^-4 compared to the mu decay channel. Helicity is involved. Because the pi has spin zero, the two decay particles have to have the same helicity (giving total S_z=0). But the V-A theory of weak interactions tries to give them opposite helicities. This mismatch leads to a factor (m_e/m_mu)^2 in the ratio of e to mu decay.