The quark-gluon vertex and the QCD infrared dynamics

Abstract

The Dyson–Schwinger quark equation is solved for the quark-gluon vertex using the most recent lattice data available in the Landau gauge for the quark, gluon and ghost propagators, the full set of longitudinal tensor structures in the Ball-Chiu vertex, taking into account a recently derived normalisation for a quark-ghost kernel form factors and the gluon contribution for the tree level quark-gluon vertex identified on a recent study of the lattice soft gluon limit. A solution for the inverse problem is computed after the Tikhonov linear regularisation of the integral equation, that implies solving a modified Dyson–Schwinger equation. We get longitudinal form factors that are strongly enhanced at the infrared region, deviate significantly from the tree level results for quark and gluon momentum below 2 GeV and at higher momentum 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, the quark-gluon vertex is dominated by the form factors associated to the tree level vertex γμ and to the operator 2pμ+qμ. The higher rank tensor structures provide small contributions to the vertex.