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By the way, you can also demand that the auxiliary vector n^mu that enters the polarization sum satisfies n^2=0. Then the term that bothers you will not appear at all.

This is for example done in Ellis, Stirling and Weber, QCD and Collider Physics Eq. 4.61 or in this lecture note

<https://cds.cern.ch/record/454171/files/p41.pdf>

by Magnano (Eq. 28). For this reason, in real computations (see e.g. Field's Applications of QCD, Eq. 7.2.59) it is often convenient to take the four momentum of another gluon to be the auxiliary vector, as it automatically satisfies n^2=0. Such tricks simplify the computations but do not change the final result for physical, gauge independent quantities.

Cheers,

Vladyslav

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