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

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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 actor \( {{\widetilde{X}}_0} \) which effectively represents the quark-ghost scattering kernel. The solution space of the DSE inversion for \( {{\widetilde{X}}_0} \) 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 \( {{\widetilde{X}}_0} \) 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 Dyson-Schwinger equation which yields a mass function in good agreement with lattice simulations and thus provides adequate dynamical chiral symmetry breaking.

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Authors and Affiliations

  1. Laboratorio de Física Teórica e Computacional, Universidade Cruzeiro do Sul, São Paulo, 01506-000, SP, Brazil

    E. Rojas, J.P.B.C. de Melo & B. El-Bennich

  2. Departamento de Física, Universidade de Coimbra, 3004-516, Coimbra, Portugal

    O. Oliveira

  3. Departamento de Física, Instituto Tecnológico de Aeronáutica, DCTA 12.228-900, São José dos Campos, SP, Brazil

    O. Oliveira & T. Frederico

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  1. E. Rojas
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Rojas, E., de Melo, J., El-Bennich, B. et al. On the quark-gluon vertex and quark-ghost kernel: combining lattice simulations with Dyson-Schwinger equations. J. High Energ. Phys. 2013, 193 (2013). https://doi.org/10.1007/JHEP10(2013)193

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