Three-gluon vertex in Landau gauge

Abstract

We present the first Dyson--Schwinger calculation of the three-gluon vertex in Landau-gauge QCD in which its full covariant structure is back-coupled self-consistently. We truncate a Bose-symmetrized version of the Dyson--Schwinger equation at the level of one-loop diagrams, model the four-gluon vertex, and neglect terms that contain nonprimitively divergent $n$-point functions; the ghost-gluon vertex is taken bare to good approximation. Fit functions for the ghost and gluon propagators that interpolate between scaling and decoupling are presented. In all aspects of our study, Bose symmetry is manifest, from the truncation to the basis decomposition and to the momentum invariants. We explore the uniform and soft-collinear infrared limits and obtain the expected infrared exponents. The presence of a zero crossing in the tree-level component of the vertex is confirmed for both scaling- and decoupling-type scenarios. The zero crossing appears at a scale $\ensuremath{\sim}1\text{ }\text{ }\mathrm{GeV}$; however, its location might be sensitive to the four-gluon vertex and missing components in the Dyson--Schwinger equation.