On the quark-gluon vertex and quark-ghost kernel: combining lattice simulations with Dyson-Schwinger equations

We investigate the dressed quark-gluon vertex combining two established nonperturbative approaches to QCD: the Dyson-Schwinger equation (DSE) for the quark propagator and lattice-regularized simulations for the quark, gluon and ghost propagators. The vertex is modeled using a generalized Ball-Chiu ansatz parameterized by a single form actor (X) over tilde (0) which effectively represents the quark-ghost scattering kernel. The solution space of the DSE inversion for (X) over tilde (0) is highly degenerate, which can be dealt with by a numerical regularization scheme. We consider two possibilities: (i) linear regularization and (ii) the Maximum Entropy Method. These two numerical approaches yield compatible (X) over tilde (0) functions for the range of momenta where lattice data is available and feature a strong enhancement of the generalized Ball-Chiu vertex for momenta below 1GeV. Our ansatz for the quark-gluon vertex is then used to solve the quark Dyson-Schwinger equation which yields a mass function in good agreement with lattice simulations and thus provides adequate dynamical chiral symmetry breaking.