%0 Journal Article
%T Non-Abelian Ball-Chiu vertex for arbitrary Euclidean momenta
%A Aguilar, A. C.
%A Cardona, J. C.
%A Ferreira, M. N.
%A Papavassiliou, J.
%J Physical Review D
%D 2017
%V 96
%N 1
%I Amer Physical Soc
%@ 2470-0010
%G English
%F Aguilar_etal2017
%O WOS:000406540300002
%O exported from refbase (https://references.ific.uv.es/refbase/show.php?record=3232), last updated on Mon, 21 Aug 2017 15:43:52 +0000
%X We determine the non-Abelian version of the four nontransverse form factors of the quark-gluon vertex, using exact expressions derived from the Slavnov-Taylor identity that this vertex satisfies. In addition to the quark and ghost propagators, a key ingredient of the present approach is the quark-ghost scattering kernel, which is computed within the one-loop dressed approximation. The vertex form factors obtained from this procedure are evaluated for arbitrary Euclidean momenta, and display features not captured by the well-known Ball-Chiu vertex, deduced from the Abelian (ghost-free) Ward identity. Particularly interesting in this analysis is the so-called soft-gluon limit, which, unlike other kinematic configurations considered, is especially sensitive to the approximations employed for the vertex entering in the quark-ghost scattering kernel, and may even be affected by a subtle numerical instability. As an elementary application of the results obtained, we evaluate and compare certain renormalization-point-independent combinations, which contribute to the interaction kernels appearing in the standard quark gap and Bethe-Salpeter equations. In doing so, even though all form factors of the quark-gluon vertex, and in particular the transverse ones which are unconstrained by our procedure, enter nontrivially in the aforementioned kernels, only the contribution of a single form factor, corresponding to the classical (tree-level) tensor, will be considered.
%R 10.1103/PhysRevD.96.014029
%U http://arxiv.org/abs/1610.06158
%U https://doi.org/10.1103/PhysRevD.96.014029
%P 014029-29pp