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##### On the Quark-Gluon Vertex and Quark-Ghost Kernel: combining Lattice Simulations with Dyson-Schwinger equations

**Authors**: E. Rojas, J.P.B.C. de Melo, B. El-Bennich, O. Oliveira, T. Frederico

**Ref.**: JHEP **10**, 193 (2013)

**Abstract**: We investigate the dressed quark-gluon vertex combining two established non-perturbative 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 factor $ ilde X_0$ which effectively represents the quark-ghost scattering kernel. The solution space of the DSE inversion for $ ilde X_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 $ ilde X_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 1 GeV. Our ansatz for the quark-gluon vertex is then used to solve the quark DSE which yields a mass function in good agreement with lattice simulations and thus provides adequate dynamical chiral symmetry breaking.

**URL**: link.springer.com