Nontrivial ghost-gluon vertex and the match of the Refined-Gribov-Zwanziger, Dyson-Schwinger equations, and lattice Yang-Mills propagators

Either by solving the ghost propagator Dyson-Schwinger equations or through a one-loop computation in the refined Gribov-Zwanziger (RGZ) formalism, we show that a nontrivial ghost-gluon vertex is required to obtain a ghost propagator prediction compatible with the available corresponding lattice data in the SU(3) case. For the necessary gluon propagator input, we present RGZ tree-level fits which account well for the gluon lattice data. Interestingly, this propagator can be rewritten in terms of a running gluon mass. A comparison of both Dyson-Schwinger equations and RGZ results for the ghost propagator is furthermore provided. We also briefly discuss the connection between the RGZ and the operator product expansion $d=2$ gluon condensate.

Figure 1

Renormalized gluon propagator $D(p^2)$ (left) and gluon dressing function $p^{2}D(p^2)$ (right), the lattice data and the corresponding fits (solid lines) to Eq. (15) using the results reported in Table .

Figure 2

(Left) The value of fitting parameters obtained for $p<p_{\max }$, plotted in terms of $p_{\max }$. (Right) the RGZ mass function given by Eq. (7) for the parameters of Table . The dotted lines account for the statistical errors to define the 1-sigma allowed region. The “tachyonic” contribution, resulting from the gluon condensate, is clearly dominating the mass function above roughly 0.5 GeV.

Figure 3

(Left) ghost dressing data obtained by solving the ghost DSE, Eq. (33), with a ghost self-energy given by Eq. (34) and the gluon propagator predicted from Eq. (5) and fitted to lattice data as input for the kernel in Eq. (35). The results for the different set of parameters for the form factor $H_1$ collected (and labeled) in Table  are confronted to the ghost dressing lattice data taken from Ref. 41. (Right) the same, but applying the analytical perturbative approach described in Sec. 3a. The meaning of the labels for the different curves is explained in the main text.

Figure 4

The different vertex models used to obtain the numerical or the single iteration results for the ghost dressing function. They correspond to Eq. (37) where the different sets of parameters, labeled as in Fig. 3, should be read off from Table .