Negative Pion Decay: Muon & Antimuon Neutrino

[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

 

[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 as well (in the rest frame of the pion).

Since in the weak interaction, only left handed leptons (http://en.wikipedia.org/wiki/Helicity_(particle_physics ) ) 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

 

[sir-pinski]

, thank you for your question. The reason why a negative pion always decays into a muon and antimuon neutrino is because of the conservation of certain quantum numbers, specifically lepton number and strangeness. Lepton number is a quantum number that is conserved in all particle interactions, meaning that the total number of leptons (such as electrons, muons, and neutrinos) before and after the interaction must remain the same. In the decay of a negative pion, the initial particle only contains one lepton (the pion itself), so the final state must also contain one lepton. This is why an electron and antielectron neutrino cannot be produced, as they would add up to two leptons in the final state.

Additionally, the negative pion also has a strangeness quantum number of -1, while the muon has a strangeness of 0. In particle interactions, strangeness is also conserved, meaning that the total strangeness before and after the interaction must be the same. Therefore, in order to conserve both lepton number and strangeness, the negative pion must decay into a particle with a strangeness of 0 (the muon) and a particle with a strangeness of +1 (the antimuon neutrino).

The same reasoning applies to the decay of a positive pion, which decays into a positron (antielectron) and electron neutrino. In this case, the initial particle has a strangeness of +1, so the final state must also have a strangeness of +1 to conserve this quantum number.

I hope this helps to answer your question. If you have any further questions, please feel free to ask.