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We present a self-consistent calculation of the four-gluon vertex of Landaugauge Yang--Mills theory from a truncated Dyson--Schwinger equation. Theequation contains the leading diagrams in the ultraviolet and is solved usingas the only input results for lower Green functions from previousDyson--Schwinger calculations that are in good agreement with lattice data. Allquantities are therefore fixed and no higher Green functions enter within thistruncation. Our self-consistent solution resolves the full momentum dependenceof the vertex but is limited to the tree-level tensor structure at the moment.Calculations of selected dressing functions for other tensor structures fromthis solution are used to exemplify that they are suppressed compared to thetree-level structure except for possible logarithmic enhancements in the deepinfrared. Our results furthermore allow one to extract a qualitative fit forthe vertex and a running coupling.

A Dyson-Schwinger study of the four-gluon vertex