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Aguilar, A. C., Ferreira, M. N., Figueiredo, C. T., & Papavassiliou, J. (2019). Nonperturbative Ball-Chiu construction of the three-gluon vertex. Phys. Rev. D, 99(9), 094010–30pp.
Abstract: We present the detailed derivation of the longitudinal part of the three-gluon vertex from the Slavnov-Taylor identities that it satisfies, by means of a nonperturbative implementation of the Ball-Chiu construction; the latter, in its original form, involves the inverse gluon propagator, the ghost dressing function, and certain form factors of the ghost-gluon kernel. The main conceptual subtlety that renders this endeavor nontrivial is the infrared finiteness of the gluon propagator, and the resulting need to separate the vertex into two pieces, one that is intimately connected with the emergence of a gluonic mass scale, and one that satisfies the original set of Slavnov-Taylor identities, but with the inverse gluon propagator replaced by its “kinetic” term. The longitudinal form factors obtained by this construction are presented for arbitrary Euclidean momenta, as well as special kinematic configurations, parametrized by a single momentum. A particularly preeminent feature of the components comprising the tree-level vertex is their considerable suppression for momenta below 1 GeV, and the appearance of the characteristic “zero-crossing” in the vicinity of 100-200 MeV. Special combinations of the form factors derived with this method are compared with the results of recent large-volume lattice simulations, and are found to capture faithfully the rather complicated curves formed by the data. A similar comparison with results obtained from Schwinger-Dyson equations reveals a fair overall agreement, but with appreciable differences at intermediate energies. A variety of issues related to the distribution of the pole terms responsible for the gluon mass generation are discussed in detail, and their impact on the structure of the transverse parts is elucidated. In addition, a brief account of several theoretical and phenomenological possibilities involving these newly acquired results is presented.
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Aguilar, A. C., Ferreira, M. N., Figueiredo, C. T., & Papavassiliou, J. (2019). Nonperturbative structure of the ghost-gluon kernel. Phys. Rev. D, 99(3), 034026–26pp.
Abstract: The ghost-gluon scattering kernel is a special correlation function that is intimately connected with two fundamental vertices of the gauge sector of QCD: the ghost-gluon vertex, which may be obtained from it through suitable contraction, and the three-gluon vertex, whose Slavnov-Taylor identity contains that kernel as one of its main ingredients. In this work we present a detailed nonperturbative study of the five form factors comprising it, using as the starting point the “one-loop dressed” approximation of the dynamical equations governing their evolution. The analysis is carried out for arbitrary Euclidean momenta and makes extensive use of the gluon propagator and the ghost dressing function, whose infrared behavior has been firmly established from a multitude of continuum studies and large-volume lattice simulations. In addition, special Ansatze are employed for the vertices entering in the relevant equations, and their impact on the results is scrutinized in detail. Quite interestingly, the veracity of the approximations employed may be quantitatively tested by appealing to an exact relation, which fixes the value of a special combination of the form factors under construction. The results obtained furnish the two form factors of the ghostgluon vertex for arbitrary momenta and, more importantly, pave the way toward the nonperturbative generalization of the Ball-Chiu construction for the longitudinal part of the three-gluon vertex.
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Aguilar, A. C., Binosi, D., Ibañez, D., & Papavassiliou, J. (2014). New method for determining the quark-gluon vertex. Phys. Rev. D, 90(6), 065027–26pp.
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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Aguilar, A. C., Binosi, D., Ibañez, D., & Papavassiliou, J. (2014). Effects of divergent ghost loops on the Green's functions of QCD. Phys. Rev. D, 89(8), 085008–26pp.
Abstract: In the present work, we discuss certain characteristic features encoded in some of the fundamental QCD Green's functions, for which the origin can be traced back to the nonperturbative masslessness of the ghost field, in the Landau gauge. Specifically, the ghost loops that contribute to these Green's functions display infrared divergences, akin to those encountered in the perturbative treatment, in contradistinction to the gluonic loops, for which perturbative divergences are tamed by the dynamical generation of an effective gluon mass. In d = 4, the aforementioned divergences are logarithmic, thus causing a relatively mild impact, whereas in d = 3 they are linear, giving rise to enhanced effects. In the case of the gluon propagator, these effects do not interfere with its finiteness, but make its first derivative diverge at the origin, and introduce a maximum in the region of infrared momenta. The three-gluon vertex is also affected, and the induced divergent behavior is clearly exposed in certain special kinematic configurations, usually considered in lattice simulations; the sign of the corresponding divergence is unambiguously determined. The main underlying concepts are developed in the context of a simple toy model, which demonstrates clearly the interconnected nature of the various effects. The picture that emerges is subsequently corroborated by a detailed nonperturbative analysis, combining lattice results with the dynamical integral equations governing the relevant ingredients, such as the nonperturbative ghost loop and the momentumdependent gluon mass.
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Aguilar, A. C., Ibañez, D., Mathieu, V., & Papavassiliou, J. (2012). Massless bound-state excitations and the Schwinger mechanism in QCD. Phys. Rev. D, 85(1), 014018–21pp.
Abstract: The gauge-invariant generation of an effective gluon mass proceeds through the well-known Schwinger mechanism, whose key dynamical ingredient is the nonperturbative formation of longitudinally coupled massless bound-state excitations. These excitations introduce poles in the vertices of the theory, in such a way as to maintain the Slavnov-Taylor identities intact in the presence of massive gluon propagators. In the present work we first focus on the modifications induced to the nonperturbative three-gluon vertex by the inclusion of massless two-gluon bound states into the kernels appearing in its skeleton expansion. Certain general relations between the basic building blocks of these bound states and the gluon mass are then obtained from the Slavnov-Taylor identities and the Schwinger-Dyson equation governing the gluon propagator. The homogeneous Bethe-Salpeter equation determining the wave function of the aforementioned bound state is then derived, under certain simplifying assumptions. It is then shown, through a detailed analytical and numerical study, that this equation admits nontrivial solutions, indicating that the QCD dynamics support indeed the formation of such massless bound states. These solutions are subsequently used, in conjunction with the aforementioned relations, to determine the momentumdependence of the dynamical gluon mass. Finally, further possibilities and open questions are briefly discussed.
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