I am having some conceptual difficulties here. Lets start with the electron-photon vertex piece of the QED Lagrangian:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]-e\overline{\psi}\gamma^\mu\psi A_\mu[/itex]

Now we can write this in the chiral representation as

[itex]-e\overline{\psi}_L\sigma^\mu\psi_R A_\mu - e\overline{\psi}_R\overline{\sigma}^\mu\psi_L A_\mu[/itex]

So this implies that every time an electron (in a chirality eigenstate) interacts with a photon then its chirality gets flipped. Ok I'll roll with that for now...

Next, there is helicity. Imagine our electron propagating along, then it softly emits a photon and continues with almost unchanged momentum. It's helicity must be flipped because a unit of angular momentum gets carried off by the photon. If it was a really hard event then ok helicity might not flip, but at least spin projected along some constant direction must flip.

Alright.

Now what if I am at the SLC and I have made myself a polarised electron beam? This means we have a beam of electrons in a known helicity eigenstate right? But how can this beam stay polarised given my above comments? Shouldn't the spins be flipping all over the place each time an interaction with a photon occurs? Which should be all the time?

Since this does not happen I guess I am wrong that every interaction with a photon flips the spin of an electron. So what is wrong with my reasoning?

Also I am not very clear on the benefits of colliding a polarised electron beam with a positron beam, as opposed to an unpolarised beam. I initially thought it must be because different beam polarisations would behave differently under weak interactions, but that is related to chirality, not helicity.

I'm so confused.

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# Chirality, helicity, and electron-photon vertices, and polarised electron beams

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