General Gauge Invariance Problem

[llorgos]

Hi!

I have to prove that the amplitude of the process

$\gamma \gamma \to W^+ W^-$

does not depend on the gauge we will choose, $R_{\xi}$.

So I use the most general expressions for the propagators and vertices. I find 5 diagrams. One that involves only the 4 fields and a vertex, 1 t and one u channel with a W boson as propagator and 1 t and 1 u where the propagator is a non-physical field $\phi$.

I just sum up the last 4, since the first one does not depend on the $\xi$ parameter but then I am stuck since nothing seems to make the horrible expressions in such a way that there will be no gauge dependence in the end..

Any help?

 

[jeppetrost]

non-physical field $\phi$.

What is this unphysical field? - A ghost? If it is, I don't see how you make the diagram. If it's some field I don't know, please elaborate.

 

[llorgos]

It is a goldstone boson coming around in the $R_{\xi}$ gauge. Actually it is the charged one.