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.

 

[sir-pinski]

The decay of a pion into a muon and a muon-anti-neutrino is a well-established process in particle physics. This decay is mediated by the weak force, which is responsible for the decay of many subatomic particles. The weak force is governed by certain conservation laws, including the conservation of lepton number and the conservation of helicity.

In the decay of a pion, the lepton number is conserved since the initial particle (the pion) has a lepton number of 0, and the final particles (the muon and muon-anti-neutrino) also have a combined lepton number of 0.

The conservation of helicity is a more subtle concept. Helicity is a property of a particle that describes its spin relative to its direction of motion. In the decay of a pion, the helicity of the initial particle is 0, and the helicity of the final particles is also 0. This conservation of helicity is necessary in order to conserve angular momentum in the decay process.

If the pion were to decay into an electron and an electron-anti-neutrino instead of a muon and muon-anti-neutrino, the conservation of helicity would be violated. This is because the helicity of the electron is opposite to the helicity of the electron-anti-neutrino. Therefore, this decay process is not allowed.

In summary, the decay of a pion into a muon and a muon-anti-neutrino is allowed due to the conservation of lepton number and helicity. Decaying into an electron and an electron-anti-neutrino would violate the conservation of helicity and is therefore not possible.