Spin Polarization and Momentum in Particle Decay

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Discussion Overview

The discussion revolves around the relationship between spin polarization and momentum in the context of particle decay, specifically examining the decay of a positive pion into a positive muon and a muon neutrino. Participants explore theoretical implications and the nature of helicity in this decay process.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether the spin polarizations of the decay products are always parallel or anti-parallel to their momentum.
  • Another participant asserts that the muon neutrino, being nearly massless, must have its spin aligned with its momentum, suggesting that the muon also has +1/2 helicity due to the spinless nature of the pion.
  • A participant challenges the helicity of neutrinos, suggesting that they are left-handed with helicity = -1/2.
  • In response, another participant clarifies that the positive muon is an anti-lepton, indicating that the muon neutrino in this case is actually a right-handed anti-neutrino.
  • A further participant expresses confusion about the relationship between the muon and the neutrino, questioning the classification of the muon neutrino as an anti-neutrino.
  • One participant acknowledges their mistake in the discussion and thanks others for their corrections.

Areas of Agreement / Disagreement

Participants exhibit disagreement regarding the helicity of neutrinos and the classification of the muon neutrino, with no consensus reached on these points.

Contextual Notes

The discussion includes assumptions about the nature of helicity and the classification of particles, which may not be universally accepted or fully resolved within the conversation.

FortranMan
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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?
 
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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.
 
pam said:
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 ?
 
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.
 
pam said:
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?
 
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.
 

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