Infrared properties of the quark-gluon vertex in general kinematics

Abstract

In the present work we determine the eight form factors of the transversely-projected quark-gluon vertex in general kinematics, in the context of Landau-gauge QCD with two degenerate light dynamical quarks. The study is based on the set of Schwinger-Dyson equations that govern the vertex form factors, derived within the formalism of the three-particle-irreducible (3PI) effective action. The analysis is performed by employing lattice data for the main ingredients, such as gluon and quark propagators, and three-gluon vertex. The numerical treatment is simplified by decoupling the system of integral equations: the classical form factor is determined from a single non-linear equation involving only itself, while the remaining ones are subsequently computed through simple integrations. The form factors are obtained for arbitrary values of space-like momenta, and their angular dependence is examined in detail. A clear hierarchy is established at the level of the corresponding dimensionless effective couplings, in agreement with results of earlier studies. Furthermore, the classical form factor is found to be in excellent agreement with recent unquenched lattice data in the soft-gluon configuration, while the two non-classical dressings depart substantially from the lattice results. Finally, the accurate implementation of multiplicative renormalizability is confirmed, and the transition from Minkoswski to Euclidean space is elucidated.