I have a short question about the possible gluon polarization in loop diagrams. For external gluons, we only want the 2 transverse polarizations.
In Peskin-Schroeder it is explained that in Feynman-gauge we need the ghost-loops to cancel the longitudinal polarization states in gluon loops because otherwise unitarity would be violated, which is shown by using the optical theorem on p.512.
But since ghosts do not couple to quarks, how does the argument work when there are loops involving a gluon with a quark, for example the quark self energy? How are the longitudinal polarizations cancelled there? Thanks a lot :).