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The Quark-Gluon Vertex and the QCD Infrared Dynamics

Authors: O. Oliveira, W. de Paula, T. Frederico, J.P.B.C. de Melo

Ref.: arXiv, 1807.10348 (2018)

Abstract: We solve the Dyson-Schwinger quark equation for the quark-gluon vertex taking for the quark, gluon and ghost propagators the most recent lattice data available in the Landau gauge. In our approach we go beyond the Ball-Chiu type of vertex by including other tensor structures that results on a vertex that is a function of the incoming quark momentum, incoming gluon momentum and the angle between these two momenta. Our calculation takes into account a recently derived normalization for a quark-ghost kernel form factors and also the gluon contribution for the quark-gluon vertex identified on the study of the lattice soft gluon limit of the tree level tensor structure. Our solution for the quark-gluon vertex returns longitudinal quark-gluon vertex form factors that are strongly enhanced at the infrared region and deviate significantly from their tree level results of quark and gluon momentum below 2 GeV. At high momentum the form factors approach their perturbative values. The computed quark-gluon vertex favours kinematical configurations where the quark momentum p and the gluon momentum q are small and parallel. Further, we find that the quark-gluon vertex is dominated by the form factors associated to the tree level vertex $\gamma_\mu$ and to the scalar $2 p_\mu+ q_\mu$. The higher rank tensor structures provide small contributions to the vertex.

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