Nonperturbative study of the four gluon vertex

Understand

In this paper we study the nonperturbative structure of the SU(3) four-gluon vertex in the Landau gauge, concentrating on contributions quadratic in the metric.

• We employ an approximation scheme where "one-loop" diagrams are computed using fully dressed gluon and ghost propagators, and tree-level vertices.
• When a suitable kinematical configuration depending on a single momentum scale $p$ is chosen, only two structures emerge: the tree-level four-gluon 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 (zero-crossing) in the deep infrared, and finally diverges logarithmically.