Relation between chirality and spin

In summary: When learning about chirality I was surprised to find that for QED and QCD the decay modes that would produce 2 particles with the same chirality had a Matrix Element of 0. This I took to mean that angular momentum was being conserved. Even the W only decay into RH antiparticles and LH particles, conserving momentum. And the Z, that weird bastard, decays into pairs of fermion and anti-fermion where one is RH and the other is LH. All of this seemed to me a consequence of conservation of angular momentum that not even the Weak Force could break. But then I learn that the Higgs **only** decays into pairs of fermion-anti-fermion *
  • #1
Frigorifico
32
0
When learning about chirality I was very surprised to find that for QED and QCD the decay modes that would produce 2 particles with the same chirality had a Matrix Element of 0, which I took to mean that angular momentum was being conserved.

Even the W only decay into RH antiparticles and LH particles, conserving momentum. And the Z, that weird bastard, decays into pairs of fermion and anti-fermion where one is RH and the other is LH.

All of this seemed to me a consequence of conservation of angular momentum that not even the Weak Force could break.

But then I learn that the Higgs **only** decays into pairs of fermion-anti-fermion *with the same chirality*... how does that make any sense?

If chirality is Lorentz-invariant helicity, and helicity is spin projected with momentum, then non-conservation of chirality surely breaks the conservation of either spin or momentum, right?
 
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  • #2
For massive particles chirality is NOT the same as helicity. Of course the fundamental conservation laws of the proper orthochronous Poincare group (energy, momentum, angular momentum) are strictly conserved within the Standard Model, which is based on this very symmetry to begin with!
 
  • #3
vanhees71 said:
For massive particles chirality is NOT the same as helicity. Of course the fundamental conservation laws of the proper orthochronous Poincare group (energy, momentum, angular momentum) are strictly conserved within the Standard Model, which is based on this very symmetry to begin with!

Then I just want to understand, if I have a spin 0 massive particle and it decays into 2 RH particles, how does that conserve momentum?, what calculation can I make?
 
  • #4
Again, you are confusing helicity with chirality. To ask a clear question, you need to state whether "RH" refers to helicity or chirality.
 
  • #5
In the standard Standard Model it's pretty easy to understand that the Higgs boson must decay in the way you describe since the corresponding Yukawa couplings can only take this form according to the local gauge symmetry ##\mathrm{SU}(2)_{\text{WISO}} \times \mathrm{U}(1)_{\text{Y}}##. For details, see the QFD section of the following lecture (presentation):

https://th.physik.uni-frankfurt.de/~hees/hqm-lectweek14/ebernburg14-1.pdf
 

1. What is chirality and how does it relate to spin?

Chirality is a property of molecules or particles that have a non-superimposable mirror image. In terms of spin, chirality refers to the direction of rotation of a particle's spin. This can be either clockwise or counterclockwise.

2. How does chirality affect the behavior of particles?

The chirality of a particle can affect its interactions with other particles and its overall behavior. For example, two particles with opposite chiralities can have different magnetic properties and may interact differently with electromagnetic fields.

3. Can chirality and spin be changed or manipulated?

Yes, both chirality and spin can be changed or manipulated through various methods such as applying magnetic fields or using certain chemical reactions. This can have significant effects on the properties and behavior of the particles.

4. Are there any practical applications for understanding the relationship between chirality and spin?

Yes, understanding the relationship between chirality and spin is important in various fields such as chemistry, physics, and materials science. It has applications in areas such as drug development, nanotechnology, and quantum computing.

5. How does chirality and spin relate to the concept of symmetry?

Chirality and spin are both related to symmetry, as they involve the concept of mirror images and directionality. The chirality of a particle can affect its overall symmetry, and the spin of a particle can also have symmetrical properties.

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