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We report on the first self-consistent solution of the Dyson--Schwinger equation (DSE) for the three-gluon vertex. Based on earlier results for the propagators which match data from lattice Monte Carlo simulations, we obtain results for the three-gluon vertex that are in very good agreement with available lattice data likewise. Feeding these results back into the propagator DSEs leads to some changes especially in the gluon propagator. These changes allow us to assess previously used models for the three-gluon vertex and to systematically estimate the influence of neglected two-loop diagrams with four-gluon interactions. In the final step, a full iterative solution to the coupled DSEs of pure Landau gauge QCD without quarks is then obtained for the first time in an extended truncation which now dynamically includes the complete set of three-point vertex functions.
Blum et al. (Tue,) studied this question.