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When you perform the calculus of $S$ matrix in, for instance, QCD maybe you need to add ghosts in external legs or internal loops. E.g.: $q\bar{q} \rightarrow gg$ needs 2 ghosts diagrams with ghosts instead of gluons for the final state, if you work taking into account non-transverse gluons. Recall that due to gauge fixing term you have actually broke the gauge invariance so it's no longer true that $p_\mu\epsilon^\mu(p) = 0$ for the gluon since that would imply $\partial_\mu A^\mu = 0$. Then you have to count physical and non-physical polarization states.

Therefore my question is: do these ghosts diagrams give interference terms in the calculus of the probability or they are added directly to the probability of the diagrams without ghosts?


EDIT

I have made the example $q\bar{q} \rightarrow gg$ and to obtain the same as the Particle Data Group says is the correct cross section, you have to add ghosts to the probability with a global minus sign and without interference terms with s, t, u channels or among the ghost diagrams. Recall there are 2 ghost diagrams with these fields in the final state switching which is the ghost and which the anti-ghost.

But I don't know why you have to do it in that way yet.

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  • $\begingroup$ Are you following a reference other than the PDG? $\endgroup$
    – Qmechanic
    Feb 19, 2020 at 9:07
  • $\begingroup$ The PDG only gives the final result for the cross-section and taking into account that the PDG is the most trustworthy reference for these matters, no I'm not. But I insist, my calculus are not from PDG, they are mine. PDG is only to check my result $\endgroup$
    – Vicky
    Feb 19, 2020 at 20:13
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    $\begingroup$ Consider to include some calculations/results for clarity. $\endgroup$
    – Qmechanic
    Feb 21, 2020 at 20:52

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