Gluonic vertices of Landau gauge Yang-Mills theory in the Dyson-Schwinger approach

We report on a self-consistent solution of the Landau gauge four-gluon vertex DSE. Our calculation includes all perturbatively leading one-loop diagrams, which constitutes the state-of-the-art truncation. As only input we use results for lower Green functions from previous Dyson-Schwinger studies that are in good agreement with lattice results. Within the truncation, no higher Green functions enter. Hence, the results depend only indirectly on models of Green functions. Our self-consistent solution resolves the full momentum dependence of the four-gluon vertex but is limited to the tree-level tensor structure. We calculate a few exemplary dressings of other tensor structures and find that they are suppressed compared to the tree-level structure except for the deep infrared where they diverge logarithmically. We employ the results to derive a running coupling. Furthermore, we study the coupled system of the three- and the four-gluon vertices to reduce the model dependence and to explore the convergence of the system of DSEs within the truncation scheme employed. For the scaling solution we establish a solution of the coupled system of vertices which provides promising evidence for the convergence.