Gluon and ghost propagators in linear covariant gauges

We compute the gluon and ghost propagators of Yang-Mills theory in linear covariant gauges from the coupled system of Dyson-Schwinger equations. For small values of the gauge fixing parameter $\xi \sim 0.1$, the deviations to the Landau gauge already become clearly visible. For the ghost dressing function, this is reflected in a logarithmic infrared suppression. Also, the gluon dressing function changes—but only quantitatively—and the gluon propagator remains finite at zero momentum. From the results, a running coupling is extracted.

Figure 1

Truncated two-point Dyson-Schwinger equations. All internal propagators are dressed. Thick blobs denote dressed vertices. Wiggly lines are gluons, dashed ones ghosts. Plots were created with JaxoDraw [40].

Figure 2

Ghost (left panel) and gluon (right panel) dressing functions for various values of $\xi$.

Figure 3

Running couplings from the ghost-gluon (left panel) and three-gluon (right panel) vertices.