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It is said that the Weak Interaction only couples to left-handed particles which a negative spin (left-handed). However some sources say that spin or helicity is dependent on the observer's position and velocity relative to the particle.

What I don't understand following this principles, is that an observer (1) might see a left-handed particle couple the W,Z bosons. However, if the spin of that particle is relative to the motion of an observer, an additional observer 2 seeing this particle but this time with a positive spin (right-handed) will not see the particle couple to the W,Z bosons because the weak interaction couples to left-handed particles only, I cannot understand this because the particle does couple or does not couple with the W,Z boson and this event should not depend on the observer's relative motion.

Chiral Anomaly
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qubitz
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1 Answers1

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The vocabulary "left-handed" and "right-handed" is used for two distinct concepts: one is chirality, and one is helicity.

  • Chirality distinguishes between two inequivalent matrix representations of the even part of the algebra of Dirac matrices. The concept of chirality applies to the field operators that are used to construct the model, rather than to particles. When people say that the $SU(2)$ weak interaction couples only to left-handed fermions, they're talking about chirality, not helicity.

  • Helicity distinguishes between the two different possible orientations of the angular momentum of a massless particle. Because of electroweak symmetry breaking (EWSB), most elementary particles have a significant mass. Neutrinos remain (nearly) massless. Helicity is Lorentz-invariant only for a massless particle.

The relationship between field operators and particles is not as straightforward as perturbative calculations sometimes portray. Field operators are used to construct the model's observables and states. Particles are phenomena that the model predicts.

Here are a few related posts, from newest to oldest:

So is it not $CP$ instead of $C$ that is responsible for changing a particle to its antiparticle?

What is polarisation, spin, helicity, chirality and parity?

How can we measure chirality in experiments?

What's the difference between helicity and chirality?

Chiral Anomaly
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  • Someone mentioned to me that fermions gain mass because before symmetry breaking all particles are massless and therefore travel at the speed of light and this causes the spin of the particle to be invariant to the observer and therefore it can only be left-handed or right-handed not both.When there is symmetry breaking particles can be both left and right handed which means that they now must have mass. He used the definition of helicity to explain this because it is a quantity relative to observers but when thing move at the speed of light the quantities are observer invariant. – qubitz Nov 04 '18 at 22:58
  • This is the consequencence of the Weak interaction interacting only with the left-handed particles. At the speed of light if a particle interacts with the weak force it wills always be left-handed(because observers must observe the same events and so it cannot be right-handed) but when they gain mass they can be both left and right handed. Does this explanation still works even if chirality is not the same as helicity ? – qubitz Nov 04 '18 at 23:01
  • @ValenciaG. For a massless particle, its chirality and helicity are both invariant, and we can relate them to each other. Maybe this a useful way to think about electroweak symmetry breaking, but I have not thought about that enough to be sure. If the symmetry-breaking interactions (with the Higgs field) are deleted from the model, then maybe the model would be in a phase with only massless fermions, but I am not even sure about that. QFTs can have surprisingly rich phase diagrams, like confinement in QCD. I think it's an interesting question, and I wish I had a better answer for you. – Chiral Anomaly Nov 05 '18 at 02:13