Non-Abelian Ball-Chiu vertex for arbitrary Euclidean momenta

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-gh...

Full description

Saved in:
Bibliographic Details
Published in:Physical review. D 2017-07, Vol.96 (1), Article 014029
Main Authors: Aguilar, A. C., Cardona, J. C., Ferreira, M. N., Papavassiliou, J.
Format: Article
Language:English
Subjects:
Form factors
Kernels
Mathematical analysis
Quarks
Scattering
Stability
Stability analysis
Tensors
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2470-0010
2470-0029
DOI:10.1103/PhysRevD.96.014029