Spurious divergences in Dyson-Schwinger equations

Abstract

We revisit the treatment of spurious ultraviolet divergences in the equation of motion of the gluon propagator caused by a momentum cutoff and the resulting violation of gauge invariance. With present continuum studies of the gluon propagator from its Dyson-Schwinger equation reaching the level of quantitatively accurate descriptions, it becomes increasingly important to understand how to subtract these spurious divergences in an unambiguous way. Here we propose such a method. It is based entirely on the asymptotic perturbative behavior of the QCD Green's functions without affecting non-perturbative aspects such as mass terms or the asymptotic infrared behavior. As a particular example, this allows us to assess the possible influence of the tadpole diagram beyond perturbation theory. Finally, we test this method numerically by solving the system of Dyson-Schwinger equations of the gluon and ghost propagators.

19 pages, 9 figs; agrees with published version

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Cited by in corpus (7)

• A Dyson-Schwinger study of the four-gluon vertex
• On gluon and ghost propagators in linear covariant gauges
• On non-primitively divergent vertices of Yang-Mills theory
• Yang-Mills propagators in linear covariant gauges from Nielsen identities
• Phase structure and propagators at nonvanishing temperature for QCD and QCD-like theories
• On bounds and boundary conditions in the continuum Landau gauge
• Running coupling in the conformal window of large-Nf QCD