helicityparticle-physicspions
I'm reading through M. Thomson's Modern Particle Physics to better understand why the positron electron neutrino decay channel is suppressed relative to the muon and muon neutrino decay route.
I know it has to do with helicity supression, but I can't quite formulate a description of what helicity supression is concisely by reading Thomson's explanation. If anyone could concisely explain this to me it would be greatly appreciated!
In the pion reference frame the two outgoing leptons are very boosted, hence helicity and chirality almost coincide. The angular momentum conservation forces them to have opposite spins, since the pion spin is zero. Therefore, they will have the same helicity, which is highly suppressed in this kinematic regime, because of the vector nature of the QED interactions (see for example Thomson, Modern Particle Physics, chapter 6). Just my two cents.
Pions and neutrons are hadrons, composite particles built from quarks:
From this information, and knowing that only one type of vertex is allowed in EM (photon, fermion in, fermion out), you can see how the neutral pion decays:
On the other hand, for charged pions you have a quark without the corresponding antiquark, you cannot get rid of them just by EM vertices, as the vertices have the same fermion on both legs.
Also think about the electric charge - photons carry no charge, but the initial charged pion does.
Best Answer
In an imaginary world where the leptons and the neutrinos are all massless, they would exist only in the left-handed helicity version.
In this imaginary world the decay of the pion in lepton plus neutrino would be prohibited: you could not conserve both the total spin (zero) and the total momentum, in that this would imply emitting two particles both with the spin in the direction of motion (i.e. right handed).
In our real world the leptons are not massless, so that they can be emitted with a component along the direction of motion. Heuristically, the probability of this kind of emission grows bigger with the mass of the lepton (being zero for zero mass), so that the decay in heavier particles (ie muons) is favorable wrt lighter particles (electrons) one.