# Spin Polarization and Momentum in Particle Decay

• FortranMan
In summary, the spin polarizations of the products in an elementary particle decay, such as the decay of a positive pion into a positive muon and a muon neutrino, are always parallel (or anti-parallel) to their momentum. This is because the muon neutrino is nearly massless and must have a spin aligned with its momentum, while the positive muon, being an anti-lepton, also has a spin aligned with its momentum. However, for other decays, the polarization may not be 100%. The momentum direction is often used as a good z axis to describe polarization because it results in a L_z value of 0.
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?

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.

## What is spin polarization and momentum in particle decay?

Spin polarization and momentum in particle decay refers to the direction and strength of the spin and momentum vectors of a particle as it decays into smaller particles.

## Why is spin polarization and momentum important in particle decay?

Spin polarization and momentum play a crucial role in determining the properties and behavior of the particles that are produced in the decay process. It can also provide important insights into the underlying fundamental interactions between particles.

## How is spin polarization and momentum measured in particle decay?

Spin polarization and momentum can be measured by analyzing the angular distributions of the decay products. This involves studying the trajectory and energy of the decay products and comparing it to theoretical predictions.

## What factors can affect spin polarization and momentum in particle decay?

The spin polarization and momentum of particles can be affected by various factors, such as the initial spin and momentum of the decaying particle, the interactions between particles, and external forces such as magnetic fields.

## What are some potential applications of studying spin polarization and momentum in particle decay?

Studying spin polarization and momentum in particle decay can provide valuable information for understanding the fundamental laws governing the universe and developing new technologies, such as particle accelerators and medical imaging devices.

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