Abstract
We calculate gluon and ghost propagators in Yang-Mills theory in linear covariant gauges. To that end, we utilize Nielsen identities with Landau gauge propagators and vertices as the starting point. We present and discuss numerical results for the gluon and ghost propagators for values of the gauge parameter $0<\xi \le 5$. Extrapolating the propagators to $\xi \to \infty $ we find the expected qualitative behavior. We provide arguments that our results are quantitatively reliable at least for values $\xi\lesssim 1/2$ of the gauge fixing parameter. It is shown that the correlation functions, and in particular the ghost propagator, change significantly with increasing gauge parameter. In turn, the ghost-gluon running coupling as well as the position of the zero crossing of the Schwinger function of the gluon propagator remain within the uncertainties of our calculation unchanged.
Highlights
Functional approaches such as Dyson-Schwinger equations (DSEs) or functional renormalization group (FRG) equations have very successfully contributed to understanding many phenomena in quantum chromodynamics (QCD), ranging from the hadron resonance spectrum to the phase structure of QCD at nonvanishing temperatures and densities
We find at 0 and 1 GeV that the gluon propagator goes down by 8% and 7%, respectively, for ξ 1⁄4 0.5
The starting point has been results in the Landau gauge, ξ 1⁄4 0, which were obtained in a selfcontained DSE calculation
Summary
Functional approaches such as Dyson-Schwinger equations (DSEs) or functional renormalization group (FRG) equations have very successfully contributed to understanding many phenomena in quantum chromodynamics (QCD), ranging from the hadron resonance spectrum to the phase structure of QCD at nonvanishing temperatures and densities. The majority of the respective investigations have been carried out in the Landau gauge due to the technical as well as conceptual advantages this gauge provides Obtaining via such approaches results for physical observables requires truncations to the full hierarchy of coupled functional equations, typically chosen to be of a given order in a systematic approximation scheme such as the vertex expansion. Our investigation may serve for corroborating the current state of the art of functional studies in the Landau gauge; for the respective recent Landau gauge DSE results for propagators and vertex functions, see, e.g., Refs. Equations for the correlations functions can be integrated from the Landau gauge to any linear covariant gauge, and we are going to report on an investigation in which we used the quantitative DSE results for Landau gauge correlation functions from Ref. The results for the propagators can be downloaded from https://github .com/markusqh/YM_data_LinCov
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