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.Comment: 7 pages, 11 figs.; agrees with published versio
We solve the Dyson-Schwinger equations of the ghost and gluon propagators of Landau gauge Yang-Mills theory together with that of the ghost-gluon vertex. The latter plays a central role in many truncation schemes for functional equations. By including it dynamically we can determine its influence on the propagators. We also suggest a new model for the three-gluon vertex motivated by lattice data which plays a crucial role to obtain stable solutions when the ghost-gluon vertex is included. We find that both vertices have a sizable quantitative impact on the mid-momentum regime and contribute to the reduction of the gap between lattice and Dyson-Schwinger equation results. Furthermore, we establish that the three-gluon vertex dressing turns negative at low momenta as suggested by lattice results in three dimensions.
We present a more detailed picture of the infrared regime of Landau gauge
Yang-Mills theory. This is done within a novel framework that allows one to
take into account the influence of finite scales within an infrared power
counting analysis. We find that there are two qualitatively different infrared
fixed points of the full system of Dyson-Schwinger equations. The first extends
the known scaling solution, where the ghost dynamics is dominant and gluon
propagation is strongly suppressed. It features in addition to the strong
divergences of gluonic vertex functions in the previously considered uniform
scaling limit, when all external momenta tend to zero, also weaker kinematic
divergences, when only some of the external momenta vanish. The second solution
represents the recently proposed decoupling scenario where the gluons become
massive and the ghosts remain bare. In this case we find that none of the
vertex functions is enhanced, so that the infrared dynamics is entirely
suppressed. Our analysis also provides a strict argument why the Landau gauge
gluon dressing function cannot be infrared divergent.Comment: 29 pages, 25 figures; published versio
Restricting the functional integral to the Gribov region Ω leads to a deep modification of the behavior of Euclidean Yang-Mills theories in the infrared region. For example, a gluon propagator of the Gribov type, k 2 k 4 +γ 4 , can be viewed as a propagating pair of unphysical modes, called here i-particles, with complex masses ±iγ 2 . From this viewpoint, gluons are unphysical and one can see them as being confined. We introduce a simple toy model describing how a suitable set of composite operators can be constructed out of i-particles whose correlation functions exhibit only real branch cuts, with associated positive spectral density. These composite operators can thus be called physical and are the toy analogy of glueballs in the Gribov-Zwanziger theory.
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