We construct a general Ansatz for the three-particle vertex describing the
interaction of one background and two quantum gluons, by simultaneously solving
the Ward and Slavnov-Taylor identities it satisfies. This vertex is known to be
essential for the gauge-invariant truncation of the Schwinger-Dyson equations
of QCD, based on the pinch technique and the background field method. A key
step in this construction is the formal derivation of a set of crucial
constraints (shown to be valid to all orders), relating the various form
factors of the ghost Green's functions appearing in the aforementioned
Slavnov-Taylor identity. When inserted into the Schwinger-Dyson equation for
the gluon propagator, this vertex gives rise to a number of highly non-trivial
cancellations, which are absolutely indispensable for the self-consistency of
the entire approach.Comment: 26 pages, 4 figures; v3: more typos correcte
