The ghost-gluon scattering kernel is a special correlation function that is intimately connected with two fundamental vertices of the gauge sector of QCD: the ghost-gluon vertex, which may be obtained from it through suitable contraction, and the three-gluon vertex, whose Slavnov-Taylor identity contains that kernel as one of its main ingredients. In this work we present a detailed nonperturbative study of the five form factors comprising it, using as starting point the "one-loop dressed" approximation of the dynamical equations governing their evolution. The analysis is carried out for arbitrary Euclidean momenta, and makes extensive use of the gluon propagator and the ghost dressing function, whose infrared behavior has been firmly established from a multitude of continuum studies and large-volume lattice simulations. In addition, special Ansätze are employed for the vertices entering in the relevant equations, and their impact on the results is scrutinized in detail. Quite interestingly, the veracity of the approximations employed may be quantitatively tested by appealing to an exact relation, which fixes the value of a special combination of the form factors under construction. The results obtained furnish the two form factors of the ghost-gluon vertex for arbitrary momenta, and, more importantly, pave the way towards the nonperturbative generalization of the Ball-Chiu construction for the longitudinal part of the three-gluon vertex.

We present the detailed derivation of the longitudinal part of the three-gluon vertex from the Slavnov-Taylor identities that it satisfies, by means of a nonperturbative implementation of the Ball-Chiu construction; the latter, in its original form, involves the inverse gluon propagator, the ghost dressing function, and certain form factors of the ghost-gluon kernel. The main conceptual subtlety that renders this endeavor nontrivial is the infrared finiteness of the gluon propagator, and the resulting need to separate the vertex into two pieces, one that is intimately connected with the emergence of a gluonic mass scale, and one that satisfies the original set of Slavnov-Taylor identities, but with the inverse gluon propagator replaced by its "kinetic" term. The longitudinal form factors obtained by this construction are presented for arbitrary Euclidean momenta, as well as special kinematic configurations, parametrized by a single momentum. A particularly preeminent feature of the components comprising the tree-level vertex is their considerable suppression for momenta below 1 GeV, and the appearance of the characteristic "zero-crossing" in the vicinity of 100 − 200 MeV. Special combinations of the form factors derived with this method are compared with the results of recent large-volume lattice simulations, and are found to capture faithfully the rather complicated curves formed by the data. A similar comparison with results obtained from Schwinger-Dyson equations reveals a fair overall agreement, but with appreciable differences at intermediate energies. A variety of issues related to the distribution of the pole terms responsible for the gluon mass generation are discussed in detail, and their impact on the structure of the transverse parts is elucidated. In addition, a brief account of several theoretical and phenomenological possibilities involving these newly acquired results is presented.

We present a generalized theoretical framework for dealing with the important issue of dynamical mass generation in Yang-Mills theories, and, in particular, with the infrared finiteness of the gluon propagators, observed in a multitude of recent lattice simulations. Our analysis is manifestly gauge-invariant, in the sense that it preserves the transversality of the gluon self-energy, and gauge-independent, given that the conclusions do not depend on the choice of the gauge-fixing parameter within the linear covariant gauges. The central construction relies crucially on the subtle interplay between the Abelian Ward identities satisfied by the nonperturbative vertices and a special integral identity that enforces a vast number of 'seagull cancellations' among the oneand two-loop dressed diagrams of the gluon Schwinger-Dyson equation. The key result of these considerations is that the gluon propagator remains rigorously massless, provided that the vertices do not contain (dynamical) massless poles. When such poles are incorporated into the vertices, under the pivotal requirement of respecting the gauge symmetry of the theory, the terms comprising the Ward identities conspire in such a way as to still enforce the total annihilation of all quadratic divergences, inducing, at the same time, residual contributions that account for the saturation of gluon propagators in the deep infrared.