I'm trying to calculate the spin and color averaged gg->gg cross section, and I am stumbling upon gauge invariance:
Must the amplitude not be invariant under replacements $\epsilon_i \to \epsilon_i + \kappa_i p_i$ where $p_i\cdot\epsilon_i=0$ and $\kappa_i$ is arbitrary? For me it is not :/
I have summed the 4-gluon diagram and s,t,u-channel diagrams with two 3-gluon vertices each.
When I square the amplitude and carry out the spin averaged polarization sum in axial gauge, the extra "n"-vector does not vanish.
Am I missing something trivial? Can someone point me to some resource? I do not want to calculate the amplitude with spinor helicity formalism. I am thankful for any hints because I've been sitting on this problem with a collegue for quite a while.