Quark-gluon vertex: A perturbation theory primer and beyond

Abstract

There has been growing evidence that the infrared enhancement of the form factors defining the full quark-gluon vertex plays an important role in realizing a dynamical breakdown of chiral symmetry in quantum chromodynamics, leading to the observed spectrum and properties of hadrons. Both the lattice and the Schwinger-Dyson communities have begun to calculate these form factors in various kinematical regimes of momenta involved. A natural consistency check for these studies is that they should match onto the perturbative predictions in the ultraviolet, where non-perturbative effects mellow down. In this article, we carry out a numerical analysis of the one-loop result for all the form factors of the quark-gluon vertex. Interestingly, even the one-loop results qualitatively encode most of the infrared enhancement features expected of their non-perturbative counter parts. We analyze various kinematical configurations of momenta: symmetric, on-shell and asymptotic. The on-shell limit enables us to compute anomalous chromomagnetic moment of quarks. The asymptotic results have implications for the multiplicative renormalizability of the quark propagator and its connection with the Landau-Khalatnikov-Fradkin transformations, allowing us to analyze and compare various Ansätze proposed so far.

The quark-gluon vertex and the QCD infrared dynamics

“…Our result differs significantly from the perturbative estimation of the form factors [5], where all the strength appears associated to λ 1 . For example, for the kinematical configuration defined by p 2 = (p − q) 2 at vanishing p they have The comparison of our results with those reported in [17,22,23] is difficult to perform but in these works λ 1 clearly dominates.…”

“…Despite its relevance for strong interactions, a e-mail: orlando@uc.pt b e-mail: wayne@ita.br c e-mail: tobias@ita.br d e-mail: joao.mello@cruzeirodosul.edu.br our knowledge of the quark-gluon vertex from first principles calculations is relatively poor. At the perturbative level, only recently a full calculation of the twelve form factors associated to this vertex was published [5] but only for some kinematical configurations, namely the symmetric configuration (equal incoming, outgoing quark and gluon squared momenta), the on-shell configuration (quarks on-shell with vanishing gluon momentum) and what the authors called its asymptotic limit. In particular, the vertex asymptotic limit was used to investigate ansätze that can be found in the literature [6][7][8][9][10][11] with the aim to test their description of the ultraviolet regime.…”

Non-Abelian Ball-Chiu vertex for arbitrary Euclidean momenta

“…The modification, proposed in Ref. [60] guarantees that the corresponding form factors are free of kinematic singularities in all covariant gauges [46,60]. In addition, this basis also permits one to establish a more transparent relation between the ST and the transverse parts of the vertex.…”

Quark Propagator in Minkowski Space

“…The motivation for this choice is that one expects singularities at timelike momentain in the quark-gluon kernel, coming either from the gluon propagator or from the quark-gluon vertex, or from both. Certainly, a much more complex singularity structure than of a single pole can be expected [40,4,41,42], but this singlepole Ansatz serves our needs here for an application to a concrete case. It is also rich enough to highlight interesting features of the propagator in Minkowski space.…”