Pion Decay to Muons and not Electrons

[ylem]

Hello! I'm afraid I've asked this before, a while ago, but I still don't completely understand. It's not a homework question as such, but I thought this might be an appropriate place to put it.

Homework Statement

Why is it that pions decay via pi^+ --> mu^+ + antimuon neutrino 98% of the time and only to a positron and anti electron neutrino 2% of the time.

The Attempt at a Solution

I understand it is something to do with helicity (as neutrinos are not chiral, as they have mass) and something to do with a spin flip which is dependent on the mass, and since a muon has a larger mass, this is why it's favoured. But everyone I asked (even professors) seem to give a description that is a bit fuzzy.

Any help would be appreciated a lot. :-)

Samantha

 

[NateD]

The reason pions decay via pi^+ --> mu^+ + antimuon neutrino 98% of the time and only to a positron and anti electron neutrino 2% of the time is because of the conservation of lepton number. Since the muon has two units of lepton number, while the electron has only one, it is energetically favorable for the pion to decay into a muon plus an antimuon neutrino rather than an electron plus an antielectron neutrino. This is also related to the mass of the particles: since the muon is heavier than the electron, it is easier for the pion to decay into a heavier particle, which conserves momentum.