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The infrared behavior of the quark-gluon vertex of quenched Landau gauge QCDis studied by analyzing its Dyson-Schwinger equation. Building on previouslyobtained results for Green functions in the Yang-Mills sector we analyticallyderive the existence of power-law infrared singularities for this vertex. Weestablish that dynamical chiral symmetry breaking leads to the self-consistentgeneration of components of the quark-gluon vertex forbidden when chiralsymmetry is forced to stay in the Wigner-Weyl mode. In the latter case therunning strong coupling assumes an infrared fixed point. If chiral symmetry isbroken, either dynamically or explicitely, the running coupling is infrareddivergent. Based on a truncation for the quark-gluon vertex Dyson-Schwingerequation which respects the analytically determined infrared behavior numericalresults for the coupled system of the quark propagator and vertexDyson-Schwinger equation are presented. The resulting quark mass function aswell as the vertex function show only a very weak dependence on the currentquark mass in the deep infrared. From this we infer by an analysis of thequark-quark scattering kernel a linearly rising quark potential with an almostmass independent string tension in the case of broken chiral symmetry.Enforcing chiral symmetry does lead to a Coulomb type potential. Therefore weconclude that chiral symmetry breaking and confinement are closely related.Furthermore we discuss aspects of confinement as the absence of long-rangevan-der-Waals forces and Casimir scaling. An examination of experimental datafor quarkonia provides further evidence for the viability of the presentedmechanism for quark confinement in the Landau gauge.

The quark-gluon vertex in Landau gauge QCD: Its role in dynamical chiral symmetry breaking and quark confinement