# External ghost in QCD (specifically gluon-gluon scattering)

As a kind of followup question to my question of gauge invariance of gluon-gluon scattering (Gauge invariance of gg->gg scattering amplitude?), where I calculated gg->gg scattering with a unitary gauge, I now want to calculate it using nonabelian ghosts as external particles.

I have problems finding any resources on doing calculations with external ghosts. For the gluon-gluon scattering I have to add to the (gggg->0) squared amplitude itself all possible ghost contributions, 18 in total: ["CCcc","CcCc","CccC","Ccgg","Cgcg","Cggc","cCCc","cCcC","cCgg","ccCC","cgCg","cggC","gCcg","gCgc","gcCg","gcgC","ggCc","ggcC"] where c specifies the ghost field and C the antighost. I only get the correct result when I subtract the squared amplitude of these that contain two ghost(antighost) fields, and add the squared amplitudes with four ghost(antighost) fields.

Can someone explain where these signs come from, why (-) for 2 ghosts, and (+) for four external ghosts. Where does the rule to add/subtract all possible ghost squared amplitudes come from at a fundamental level from the path-integral formulation?

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