We show that the application of a novel gauge-invariant truncation scheme to the Schwinger-Dyson equations of QCD leads, in the Landau gauge, to an infrared finite gluon propagator and a divergent ghost propagator, in qualitative agreement with recent lattice data.

By resumming the Feynman graphs which contribute to any gauge-invariant process we explicitly construct, at one-loop order, a three-gluon vertex for QCD which is completely independent of the choice of gauge. This vertex satisfies a Ward identity of the type encountered in ghost-free gauges, relating the vertex to the proper self-energy of a previously constructed gluon propagator, also found by resumming graphs; like the vertex, this self-energy is completely gauge invariant. We also derive the gauge-invariant propagator and vertex via a second related technique which minimizes the dependence on embedding these objects in a gauge-invariant process; the same results are found as in the first technique. These results motivate a toy model of the nonlinear Schwinger-Dyson equation satisfied by the exact gauge-invariant three-gluon vertex. This model is nonperturbative and has infrared singularities, which we can remove via gluon mass generation; it shows many interesting features expected of QCD, such as a β function which is not Borel summable in perturbation theory.

Within contemporary hadron physics there are two common methods for determining the momentum-dependence of the interaction between quarks: the top-down approach, which works toward an ab initiocomputation of the interaction via direct analysis of the gauge-sector gap equations; and the bottom-up scheme, which aims to infer the interaction by fitting data within a well-defined truncation of those equations in the matter sector that are relevant to bound-state properties. We unite these two approaches by demonstrating that the renormalisation-group-invariant running-interaction predicted by contemporary analyses of QCD’s gauge sector coincides with that required in order to describe ground-state hadron observables using a nonperturbative truncation of QCD’s Dyson–Schwinger equations in the matter sector. This bridges a gap that had lain between nonperturbative continuum-QCD and the ab initioprediction of bound-state properties.Daniele Binosi, Lei Chang, Joannis Papavassiliou, Craig D.Robert

We study the nonperturbative behavior of two versions of the QCD effective charge, one obtained from the pinch technique gluon self-energy, and one from the ghost-gluon vertex. Despite their distinct theoretical origin, due to a fundamental identity relating various ingredients appearing in their respective definitions, the two effective charges are almost identical in the entire range of physical momenta, and coincide exactly in the deep infrared, where they freeze at a common finite value. Specifically, the dressing function of the ghost propagator is related to the two form factors in the Lorentz decomposition of a certain Green’s function, appearing in a variety of field-theoretic contexts. The central identity, which is valid only in the Landau gauge, is derived from the Schwinger-Dyson equations governing the dynamics of the aforementioned quantities. The renormalization procedure that preserves the validity of the identity is carried out, and various relevant kinematic limits and physically motivated approximations are studied in detail. A crucial ingredient in this analysis is the infrared finiteness of the gluon propagator, which is inextricably connected with the aforementioned freezing of the effective charges. Some important issues related to the consistent definition of the effective charge in the presence of such a gluon propagator are resolved. We finally present a detailed numerical study of a special set of Schwinger-Dyson equations, whose solutions determine the nonperturbative dynamics of the quantities composing the two effective charges.