Spin Polarization and Momentum in Particle Decay

[FortranMan]

In an elementary particle decay, such as the decay of a positive pion into a positive muon and a muon neutrino, are the spin polarizations of either product always parallel (or anti-parallel) to their momentum? If so why?

 

[pam]

The muon neutrino is so close to massless that its spin must be aligned with its momentum (helicity=+1/2). Since the pi is spinless, the muon must also have +1/2 helicity. For other decays, the polarization may not be 100%.
The momentum direction makes a good z axis to describe polarization because then L_z=0.

 

[Barmecides]

The muon neutrino is so close to massless that its spin must be aligned with its momentum (helicity=+1/2). Since the pi is spinless, the muon must also have +1/2 helicity. For other decays, the polarization may not be 100%.
The momentum direction makes a good z axis to describe polarization because then L_z=0.

Hi,

I think neutrinos are Left-handed so helicity = -1/2 ?

 

[pam]

You are right about neutrinos, but a positive muon is an anti-lepton, so the "neutrino" in this case is really a right-handed anti-neutrino.

 

[kdv]

You are right about neutrinos, but a positive muon is an anti-lepton, so the "neutrino" in this case is really a right-handed anti-neutrino.

I thought that if the muon emitted is an antilepton, the muon neutrino had to be a neutrino, not an antineutrino. no?

 

[pam]

I am greatly embarrassed by making the same silly mistake twice, and apologize to all.
I must have been sleepthinking. Thank you Barmecides and kdv for your corrections.