Wednesday, August 31, 2016

particle physics - Weak interaction, parity violation, and the observer-dependence of helicity


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.



Answer



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?


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