Ghost-gluon vertex (${\mathcal{L}}_{\bar{c}Ac}=-g{f}^{abc}({\partial }^{\mu }{\bar{c}}^a)A_{\mu }^b{c}^c$)

Expanding the ghost covariant derivative in Yang-Mills theory produces an interaction between the Faddeev-Popov ghost field, Faddeev-Popov antighost field, and gauge boson. For the displayed kinetic convention, Fourier factors $e^{-ipx}$ and all momenta incoming give vertex $-g{f}^{abc}{k}_{\mu }$, where $k$ is the antighost momentum. The structure constants encode the Adjoint representation. Propagator, vertex, Fourier, and ghost-order conventions must be chosen consistently.

For canonically normalized fields with action $-\int [\frac{1}{4}{F}^2+\frac{1}{2}(\partial \cdot A{)}^2+\partial \bar{c}\cdot Dc]$, use signature $(-,+,+,+)$ and incoming Fourier modes $e^{ipx}$. The ghost-gluon vertex is $g{p}_{\mu }{f}_{abc}$ and the ghost propagator is $-i/(p^2-i0)$. The open ghost-line one-particle-irreducible two-point vertex at one loop is $i{g}^{2}C{I}_d(p)$, whereA counterterm ${\mathcal{L}}_{\mathrm{ct}}=-\delta Z_c\partial \bar{c}\cdot \partial c$ inserts $-i\delta Z_c{p}^2$ and cancels this pole. Equivalently, writing $d=4-2ϵ$ gives $\delta Z_c=g^{2}C/(32{\pi }^2ϵ)$. There is no closed ghost-loop sign for this open-line graph. The Feynman i-epsilon prescription, Fourier convention and antighost sign must be kept consistent throughout.