Eur. Phys. J. C (2015) 75: 102
https://doi.org/10.1140/epjc/s10052-015-3312-1

Regular Article - Theoretical Physics

A Dyson–Schwinger study of the four-gluon vertex

¹ Technische Universität Darmstadt, Institut für Kernphysik, Theoriezentrum, 64289, Darmstadt, Germany
² Ruprecht-Karls-Universität Heidelberg, Institut für Theoretische Physik, 69120, Heidelberg, Germany
³ University of Graz, Institute of Physics, NAWI Graz, 8010, Graz, Austria
⁴ Justus-Liebig-Universität Gießen, Institut für Theoretische Physik, 35392, Gießen, Germany

^* e-mail: markus.huber@uni-graz.at

Received: 14 October 2014
Accepted: 12 February 2015
Published online: 4 March 2015

Abstract

We present a self-consistent calculation of the four-gluon vertex of Landau gauge Yang–Mills theory from a truncated Dyson–Schwinger equation. The equation contains the leading diagrams in the ultraviolet and is solved using as the only input results for lower Green functions from previous Dyson–Schwinger calculations that are in good agreement with lattice data. All quantities are therefore fixed and no higher Green functions enter within this truncation. Our self-consistent solution resolves the full momentum dependence of the vertex but is limited to the tree-level tensor structure at the moment. Calculations of selected dressing functions for other tensor structures from this solution are used to exemplify that they are suppressed compared to the tree-level structure except for possible logarithmic enhancements in the deep infrared. Our results furthermore allow one to extract a qualitative fit for the vertex and a running coupling.