A Relation between chirality and spin

[Frigorifico]

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?

 

[vanhees71]

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!

 

[Frigorifico]

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?

 

[Vanadium 50]

Again, you are confusing helicity with chirality. To ask a clear question, you need to state whether "RH" refers to helicity or chirality.

 

[vanhees71]

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