Towards a self-consistent solution of the Landau gauge quark-gluon vertex Dyson-Schwinger equation

Abstract

The quark-gluon vertex in Landau gauge QCD is investigated in the Dyson-Schwinger approach. The aim is to obtain a fully self-consistent solution of the quark propagator and the quark-gluon vertex Dyson-Schwinger equation (DSE) in the vacuum using the gluon propagator as input from other calculations. The truncation scheme used in an earlier study is systematically improved and the first decisive step towards a full solution is presented. First results for the quark propagator with a fully dressed quarkgluon vertex in a truncation that incorporates all twelve vertex tensorstructures are shown.

Center Phase Transition from Fundamentally Charged Matter Propagators

“…Solving the Dyson-Schwinger equations for the corresponding matter propagators numerical results for these order parameters are presented. A parameter dependency of the employed matter-gluon vertices on the presented results is found and motivates a more detailed investigation of its temperature dependence (see also [20] for corresponding investigations at vanishing temperature).…”

The quark-gluon vertex in Landau gauge bound-state studies

“…In this paper, we present a solution strategy for a class of truncations of the quark-gluon vertex and quark propagator for both space-like [47,[59][60][61][62] Euclidean momenta and their analytic continuation to time-like momenta needed in bound-state equations [33,63]. We provide a specific model, constrained by the requirement that it be applicable for future bound-state studies, and investigate the flavour dependence of the quark propagators and quark-gluon vertex.…”

Equal-time quark propagator in Coulomb gauge

“…While we are very confident that the first assumption is reliable, the second one is less under control. It is well-known from Landau gauge studies [44][45][46][47][48][49][50][51][52][53][54][55][56][57] that a number of Dirac structures beyond the leading order γ µ contribute to the overall strength of the vertex. The quark-gluon vertex in Coulomb gauge is currently under investigation.…”

“…IR suppressed quarkgluon vertex) and η = 5. In view of the experience from FRG and DSE investigations in Landau gauge [44][45][46][47][48][49][50][51][52][53][54][55][56][57] such a strongly IR divergent spatial vertex appears quite unlikely. We are confident that the solution with δ = 0 and η = −1 represents the physically realized case.…”

“…(19)]. In the continuum QCD studies in Landau gauge both in the DSE and in the FRG approaches [44][45][46][47][48][49][50][51][52][53][54][55][56][57] a non-perturbative dressing of the quark-gluon vertex is crucial to obtain spontaneous breaking of chiral symmetry. In Coulomb gauge the situation is different: chiral symmetry breaking is already triggered by the instantaneous colour Coulomb potential (see Sec.…”