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arXiv · 1306.3022

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

E. Rojas·J. P. B. C. de Melo·B. El-Bennich·O. Oliveira·T. Frederico
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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 $\tilde X_0$ which effectively represents the quark-ghost scattering kernel. The solution space of the DSE inversion for $\tilde X_0$ 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 $\tilde X_0$ 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.

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E. Rojas, J. P. B. C. de Melo, B. El-Bennich, O. Oliveira, T. Frederico. 2013-06-14. On the Quark-Gluon Vertex and Quark-Ghost Kernel: combining Lattice Simulations with Dyson-Schwinger equations. https://doi.org/10.1007/jhep10(2013)193

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