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On the Landau gauge matter-gluon vertex in scalar QCD in a functional approach

Recently the quark-gluon vertex has been investigated in Landau gauge using a combined Dyson-Schwinger and nPI effective action approach. We present here a numerical analysis of a simpler system where the quarks have been replaced by charged scalar fields. We solve the coupled system of Dyson-Schwinger equations for the scalar propagator, the scalar-gluon vertex and the Yang-Mills propagators in a truncation related to earlier studies. The calculations have been performed for scalars both in the fundamental and the adjoint representation. A clear suppression of the Abelian diagram is found in both cases. Thus, within the used truncation the suppression of the Abelian diagram predominantly happens dynamically and is to a high degree independent of the colour structure. The numerical techniques developed here can directly be applied to the fermionic case.