On non-primitively divergent vertices of Yang–Mills theory

Abstract

Two correlation functions of Yang-Mills beyond the primitively divergent ones, the two-ghost-two-gluon and the four-ghost vertices, are calculated and their influence on lower vertices is examined. Their full (transverse) tensor structure is taken into account. As input, a solution of the full two-point equations -including two-loop terms -is used that respects the resummed perturbative ultraviolet behavior. A clear hierarchy is found with regard to the color structure that reduces the number of relevant dressing functions. The impact of the two-ghost-two-gluon vertex on the three-gluon vertex is negligible, which is explained by the fact that all non-small dressing functions drop out due to their color factors. Only in the ghost-gluon vertex a small net effect below 2% is seen. The four-ghost vertex is found to be extremely small in general. Since these two four-point functions do not enter into the propagator equations, these findings establish their small overall effect on lower correlation functions.

Gluonic Vertices and the Gluon Propagator in Landau Gauge Yang--Mills Theory

“…3. Left: The UV behavior of the ghost and gluon dressing functions compared to the one-loop resummed perturbative behavior [15]. Right: The four-gluon vertex dressing function with the kinematic dependence restricted to the singlet and doublet.…”

Contribution of neutral pseudoscalar mesons to aμHLbL within a Schwinger-Dyson equations approach to QCD

“…where k = p − q, D 0 µν (k) is the tree-level gluon propagator in the Landau gauge and G(k 2 ) is an effective dressing function. We employ the well-known Qin-Chang interaction [77], compatible with our modern understanding of the gluon propagator [78][79][80]: it saturates in the infrared and monotonically decreases as the momentum increases. With the interaction strength (ωD = m 3 G ) fixed, all physical observables are practically insensitive to variations of ω ∈ (0.4, 0.6).…”

Dense two-color QCD from Dyson-Schwinger equations

“…Very often, a generalization of the Brown-Pennington projector is employed. Here, in order to compare with lattice results, for setup I we use a mass counter term C sub /p 2 which is fixed by a second renormalization condition [25,48,86,87]. The resulting longitudinal gluon propagators are shown in Fig.…”