# Negative Pion Decay

1. Oct 22, 2008

### ylem

Hello! I was just wondering something...

Why is it that a negative pion always decays into a muon and antimuon neutrino? Why not an electron and antielectron neutrino? (and the same for a positive pion)

Any answers would be grately appreciated :-)

Samantha

2. Oct 22, 2008

### malawi_glenn

Yes they do decay into an electron and antielectron neutrino.
But that decay mode is suppressed due to helicity considerations:

The pion is a spin 0 particle, and thus the spins of the lepton and neutrino must be in oppsite direction. Also their momentum vectors must be in opposite directions aswell (in the rest frame of the pion).

Since in the weak interaction, only left handed leptons (http://en.wikipedia.org/wiki/Helicity_(particle_physics [Broken]) ) are coupled to the W boson, and only right handed antileptons. For massive particles, the left handed component are proprtional to 1 - v/c. A muon from pion decay have 1 - v/c = 0.72, whereas the electron have 1 - v/c = 2.5E-5, the muons have larger left handed part then the electron.

This gives branching ratio: Gamma(pi+ -> e+ eletron_neutrino) / Gamma(pi+ -> mu+ muon_neutrino) = 1.23 E-4

Last edited by a moderator: May 3, 2017