
In this paper we study the nonperturbative structure of the SU(3) fourgluon vertex in the Landau gauge, concentrating on contributions quadratic in the metric. We employ an approximation scheme where 'oneloop' diagrams are computed using fully dressed gluon and ghost propagators, and treelevel vertices. When a suitable kinematical configuration depending on a single momentum scale p is chosen, only two structures emerge: the treelevel fourgluon vertex, and a tensor orthogonal to it. A detailed numerical analysis reveals that the form factor associated with this latter tensor displays a change of sign (zerocrossing) in the deep infrared, and finally diverges logarithmically. The origin of this characteristic behavior is proven to be entirely due to the masslessness of the ghost propagators forming the corresponding ghostloop diagram, in close analogy to a similar effect established for the threegluon vertex. However, in the case at hand, and under the approximations employed, this particular divergence does not affect the form factor proportional to the treelevel tensor, which remains finite in the entire range of momenta, and deviates moderately from its naive treelevel value. It turns out that the kinematic configuration chosen is ideal for carrying out lattice simulations, because it eliminates from the connected Green's function all oneparticle reducible contributions, projecting out the genuine oneparticle irreducible vertex. Motivated by this possibility, we discuss in detail how a hypothetical lattice measurement of this quantity would compare to the results presented here, and the potential interference from an additional tensorial structure, allowed by Bose symmetry, but not encountered within our scheme.
