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.
Highlights
The non-perturbative analysis of quantum field theories is one of the great challenges in physics
Since it is expected that the ghost box yields the IR leading contribution to the four-gluon vertex both for scaling and decoupling solutions [33,56,74] we start by a dedicated analysis of this diagram
We confirm the finiteness of the tree-level dressing function beyond configuration A, for which this was already found in Ref. [66]
Summary
The non-perturbative analysis of quantum field theories is one of the great challenges in physics. The Landau gauge propagators have been well studied with various methods, e.g., lattice simulations [15,16,17,18,19,20], Dyson– Schwinger equations (DSEs) [21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37], the functional renormalization group (FRG) [32,38], a variational approach [39], a one-loop model calculation with gluon mass term [40], or the (refined) Gribov–Zwanziger framework [41,42,43,44,45,46]. Some technical details as regards color contractions, tensor bases, and the numerical calculations to solve the four-gluon vertex DSE can be found in the appendices
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