M. Kachelriess, M.N. Malmquist
Covariant gauges lead to spurious, non-physical polarisation states of gauge bosons. In QED, the use of the Feynman gauge, ∑λϵ(λ)μϵ(λ)∗ν=−ημν, is justified by the Ward identity which ensures that the contributions of non-physical polarisation states cancel in physical observables. In contrast, the same replacement can be applied only to a single external gauge boson in squared amplitudes of non-abelian gauge theories like QCD. In general, the use of this replacement requires to include external Faddeev-Popov ghosts. We present a pedagogical derivation of these ghost contributions applying the optical theorem and the Cutkosky cutting rules. We find that the resulting cross terms A(c1,c¯1;…)A(c¯1,c1;…)∗ between ghost amplitudes cannot be transformed into (−1)n/2|A(c1,c¯1;…)|2 in the case of more than two ghosts. Thus the Feynman rule stated in the literature holds only for two external ghosts, while it is in general incorrect.
Comments: 9 pages, 3 pdf figures