Abstract
The infrared behaviour of vertex functions in an SU(N) Yang-Mills theory in Landau gauge is investigated employing a skeleton expansion of the Dyson-Schwinger equations. The three- and four-gluon vertices become singular if and only if all external momenta vanish while the dressing of the ghost-gluon vertex remains finite in this limit. The running coupling as extracted from either of these vertex functions possesses an infrared fixed point. In general, diagrams including ghost-loops dominate in the infrared over purely gluonic ones.
Highlights
Fifty years after the formulation of Yang-Mills theory its infrared (IR) structure is still largely unknown despite the fact that this knowledge is central to any effort in understanding the strong interactions from first principles
Lattice calculations include in principle all non-perturbative features of YangMills theories but are in practice limited by the finite lattice volume in the study of possible IR singularities [1,2,3,4]
In Landau gauge the Dyson-Schwinger equations (DSEs) for the ghost and gluon propagators have been analytically solved in the IR assuming ghost dominance [5,6,7,8,9,10,11]
Summary
Fifty years after the formulation of Yang-Mills theory its infrared (IR) structure is still largely unknown despite the fact that this knowledge is central to any effort in understanding the strong interactions from first principles. The running of the gauge coupling is intimately related to the momentum dependence of the primitively divergent vertex functions in an SU(Nc) YangMills theory. In the latter the IR behavior of the ghost-gluon interaction in Landau gauge has been determined either from DSEs or the Exact Renormalization Group Equations (ERGEs) [8,9,18,19] and yield an IR fixed point with α(0) ≈ 8.9/Nc. The corresponding couplings from the three- and four-gluon vertex functions have not yet been studied with these techniques.
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