New method for determining the quark-gluon vertex

A. C. Aguilar, D. Binosi, D. Ibañez, and J. Papavassiliou
Phys. Rev. D 90, 065027 – Published 23 September 2014

Abstract

We present a novel nonperturbative approach for calculating the form factors of the quark-gluon vertex in terms of an unknown three-point function, in the Landau gauge. The key ingredient of this method is the exact all-order relation connecting the conventional quark-gluon vertex with the corresponding vertex of the background field method, which is Abelian-like. When this latter relation is combined with the standard gauge technique, supplemented by a crucial set of transverse Ward identities, it allows the approximate determination of the nonperturbative behavior of all 12 form factors comprising the quark-gluon vertex, for arbitrary values of the momenta. The actual implementation of this procedure is carried out in the Landau gauge, in order to make contact with the results of lattice simulations performed in this particular gauge. The most demanding technical aspect involves the approximate calculation of the components of the aforementioned (fully dressed) three-point function, using lattice data as input for the gluon propagators appearing in its diagrammatic expansion. The numerical evaluation of the relevant form factors in three special kinematical configurations (soft-gluon and quark symmetric limit, zero quark momentum) is carried out in detail, finding qualitative agreement with the available lattice data. Most notably, a concrete mechanism is proposed for explaining the puzzling divergence of one of these form factors observed in lattice simulations.

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  • Received 19 May 2014

DOI:https://doi.org/10.1103/PhysRevD.90.065027

© 2014 American Physical Society

Authors & Affiliations

A. C. Aguilar1, D. Binosi2, D. Ibañez2, and J. Papavassiliou3

  • 1Institute of Physics “Gleb Wataghin”, University of Campinas-UNICAMP, 13083-859 Campinas, São Paulo, Brazil
  • 2European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT*) and Fondazione Bruno Kessler, Villa Tambosi, Strada delle Tabarelle 286, I-38123 Villazzano, Trento, Italy
  • 3Department of Theoretical Physics and IFIC, University of Valencia and CSIC, E-46100 Valencia, Spain

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Issue

Vol. 90, Iss. 6 — 15 September 2014

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