= Solution
For $L[A^a]=\partial^\mu A_\mu^a$, eliminating the <Nakanishi-Lautrup field> gives the <covariant gauge> Lagrangian
$$
\mathcal L=\frac14F_{\mu\nu}^aF^{\mu\nu,a}
+\frac1{2\xi}(\partial^\mu A_\mu^a)^2
-\bar c^a\partial^\mu(D_\mu c)^a.
$$
The first term supplies the gluon kinetic term, three-gluon vertex, and four-gluon vertex. The second makes the quadratic gauge-field operator invertible. The last supplies the ghost propagator and ghost-antighost-gluon vertex.
The nonzero one-loop contributions to the <gluon propagator> are a gluon bubble with two three-gluon vertices and a closed ghost bubble with two ghost-antighost-gluon vertices. A four-gluon tadpole is also present with a cutoff regulator; for massless fields it is a scaleless integral and vanishes in <dimensional regularization>.
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