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Author |
Aguilar, A.C.; Ibañez, D.; Mathieu, V.; Papavassiliou, J. |
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Title |
Massless bound-state excitations and the Schwinger mechanism in QCD |
Type |
Journal Article |
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Year |
2012 |
Publication |
Physical Review D |
Abbreviated Journal |
Phys. Rev. D |
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Volume |
85 |
Issue |
1 |
Pages |
014018 - 21pp |
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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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[Aguilar, A. C.] Fed Univ ABC, CCNH, BR-09210170 Santo Andre, Brazil |
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Amer Physical Soc |
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English |
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1550-7998 |
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WOS:000299293600005 |
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no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
881 |
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Author |
Aguilar, A.C.; Ferreira, M.N.; Papavassiliou, J.; Santos, L.R. |
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Title |
Planar degeneracy of the three-gluon vertex |
Type |
Journal Article |
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Year |
2023 |
Publication |
European Physical Journal C |
Abbreviated Journal |
Eur. Phys. J. C |
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Volume |
83 |
Issue |
6 |
Pages |
549 - 20pp |
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Abstract |
We present a detailed exploration of certain outstanding features of the transversely-projected three-gluon vertex, using the corresponding Schwinger-Dyson equation in conjunction with key results obtained from quenched lattice simulations. The main goal of this study is the scrutiny of the approximate property denominated “planar degeneracy”, unveiled when the Bose symmetry of the vertex is properly exploited. The planar degeneracy leads to a particularly simple parametrization of the vertex, reducing its kinematic dependence to essentially a single variable. Our analysis, carried out in the absence of dynamical quarks, reveals that the planar degeneracy is particularly accurate for the description of the form factor associated with the classical tensor, for a wide array of arbitrary kinematic configurations. Instead, the remaining three form factors display considerable violations of this property. In addition, and in close connection with the previous point, we demonstrate the numerical dominance of the classical form factor over all others, except in the vicinity of the soft-gluon kinematics. The final upshot of these considerations is the emergence of a very compact description for the three-gluon vertex in general kinematics, which may simplify significantly nonperturbative applications involving this vertex. |
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Address |
[Aguilar, A. C.; Santos, L. R.] Univ Campinas UNICAMP, Inst Phys Gleb Wataghin, BR-13083859 Campinas, SP, Brazil, Email: aguilar@ifi.unicamp.br |
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Springer |
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1434-6044 |
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WOS:001117709800001 |
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no |
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yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
5847 |
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Author |
Aguilar, A.C.; Ferreira, M.N.; Papavassiliou, J. |
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Title |
Novel sum rules for the three-point sector of QCD |
Type |
Journal Article |
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Year |
2020 |
Publication |
European Physical Journal C |
Abbreviated Journal |
Eur. Phys. J. C |
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Volume |
80 |
Issue |
9 |
Pages |
887 - 18pp |
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Abstract |
For special kinematic configurations involving a single momentum scale, certain standard relations, originating from the Slavnov-Taylor identities of the theory, may be interpreted as ordinary differential equations for the “kinetic term” of the gluon propagator. The exact solutions of these equations exhibit poles at the origin, which are incompatible with the physical answer, known to diverge only logarithmically; their elimination hinges on the validity of two integral conditions that we denominate “asymmetric” and “symmetric” sum rules, depending on the kinematics employed in their derivation. The corresponding integrands contain components of the three-gluon vertex and the ghost-gluon kernel, whose dynamics are constrained when the sum rules are imposed. For the numerical treatment we single out the asymmetric sum rule, given that its support stems predominantly from low and intermediate energy regimes of the defining integral, which are physically more interesting. Adopting a combined approach based on Schwinger-Dyson equations and lattice simulations, we demonstrate how the sum rule clearly favors the suppression of an effective form factor entering in the definition of its kernel. The results of the present work offer an additional vantage point into the rich and complex structure of the three-point sector of QCD. |
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Address |
[Aguilar, A. C.; Ferreira, M. N.] Univ Estadual Campinas, Inst Phys Gleb Wataghin, UNICAMP, BR-13083859 Campinas, SP, Brazil, Email: aguilar@ifi.unicamp.br |
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Springer |
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1434-6044 |
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Notes |
WOS:000576141200005 |
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no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
4559 |
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Author |
Aguilar, A.C.; Ferreira, M.N.; Papavassiliou, J. |
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Title |
Gluon dynamics from an ordinary differential equation |
Type |
Journal Article |
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Year |
2021 |
Publication |
European Physical Journal C |
Abbreviated Journal |
Eur. Phys. J. C |
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Volume |
81 |
Issue |
1 |
Pages |
54 - 20pp |
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Abstract |
We present a novel method for computing the nonperturbative kinetic term of the gluon propagator from an ordinary differential equation, whose derivation hinges on the central hypothesis that the regular part of the three-gluon vertex and the aforementioned kinetic term are related by a partial Slavnov-Taylor identity. The main ingredients entering in the solution are projection of the three-gluon vertex and a particular derivative of the ghost-gluon kernel, whose approximate form is derived from a Schwinger-Dyson equation. Crucially, the requirement of a pole-free answer determines the initial condition, whose value is calculated from an integral containing the same ingredients as the solution itself. This feature fixes uniquely, at least in principle, the form of the kinetic term, once the ingredients have been accurately evaluated. In practice, however, due to substantial uncertainties in the computation of the necessary inputs, certain crucial components need be adjusted by hand, in order to obtain self-consistent results. Furthermore, if the gluon propagator has been independently accessed from the lattice, the solution for the kinetic term facilitates the extraction of the momentum-dependent effective gluon mass. The practical implementation of this method is carried out in detail, and the required approximations and theoretical assumptions are duly highlighted. |
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Address |
[Aguilar, A. C.; Ferreira, M. N.] Univ Campinas UNICAMP, Inst Phys Gleb Wataghin, BR-13083859 Campinas, SP, Brazil, Email: aguilar@ifi.unicamp.br |
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Springer |
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English |
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Series Volume |
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ISSN |
1434-6044 |
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Notes |
WOS:000611993400002 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
4730 |
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Permanent link to this record |
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Author |
Aguilar, A.C.; Ferreira, M.N.; Papavassiliou, J. |
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Title |
Exploring smoking-gun signals of the Schwinger mechanism in QCD |
Type |
Journal Article |
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Year |
2022 |
Publication |
Physical Review D |
Abbreviated Journal |
Phys. Rev. D |
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Volume |
105 |
Issue |
1 |
Pages |
014030 - 26pp |
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Keywords |
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Abstract |
In Quantum Chromodynamics, the Schwinger mechanism endows the gluons with an effective mass through the dynamical formation of massless bound-state poles that are longitudinally coupled. The presence of these poles affects profoundly the infrared properties of the interaction vertices, inducing crucial modifications to their fundamental Ward identities. Within this general framework, we present a detailed derivation of the non-Abelian Ward identity obeyed by the pole-free part of the three-gluon vertex in the softgluon limit, and determine the smoking-gun displacement that the onset of the Schwinger mechanism produces to the standard result. Quite importantly, the quantity that describes this distinctive feature coincides formally with the bound-state wave function that controls the massless pole formation. Consequently, this signal may be computed in two independent ways: by solving an approximate version of the pertinent BetheSalpeter integral equation, or by appropriately combining the elements that enter in the aforementioned Ward identity. For the implementation of both methods we employ two- and three-point correlation functions obtained from recent lattice simulations, and a partial derivative of the ghost-gluon kernel, which is computed from the corresponding Schwinger-Dyson equation. Our analysis reveals an excellent coincidence between the results obtained through either method, providing a highly nontrivial self-consistency check for the entire approach. When compared to the null hypothesis, where the Schwinger mechanism is assumed to be inactive, the statistical significance of the resulting signal is estimated to be 3 standard deviations. |
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Address |
[Aguilar, A. C.; Ferreira, M. N.] Univ Campinas UNICAMP, Inst Phys Gleb Wataghin, BR-13083859 Campinas, SP, Brazil |
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Publisher |
Amer Physical Soc |
Place of Publication |
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English |
Summary Language |
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Original Title |
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Series Editor |
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Abbreviated Series Title |
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Series Volume |
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Edition |
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ISSN |
2470-0010 |
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Notes |
WOS:000748623100001 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
5091 |
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Permanent link to this record |
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Author |
Aguilar, A.C.; Ferreira, M.N.; Oliveira, B.M.; Papavassiliou, J.; Santos, L.R. |
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Title |
Schwinger poles of the three-gluon vertex: symmetry and dynamics |
Type |
Journal Article |
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Year |
2023 |
Publication |
European Physical Journal C |
Abbreviated Journal |
Eur. Phys. J. C |
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Volume |
83 |
Issue |
10 |
Pages |
889 - 20pp |
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Keywords |
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Abstract |
The implementation of the Schwinger mechanism endows gluons with a nonperturbative mass through the formation of special massless poles in the fundamental QCD vertices; due to their longitudinal character, these poles do not cause divergences in on-shell amplitudes, but induce detectable effects in the Green's functions of the theory. Particularly important in this theoretical setup is the three-gluon vertex, whose pole content extends beyond the minimal structure required for the generation of a gluon mass. In the present work we analyze these additional pole patterns by means of two distinct, but ultimately equivalent, methods: the Slavnov-Taylor identity satisfied by the three-gluon vertex, and the nonlinear Schwinger-Dyson equation that governs the dynamical evolution of this vertex. Our analysis reveals that the Slavnov-Taylor identity imposes strict model-independent constraints on the associated residues, preventing them from vanishing. Approximate versions of these constraints are subsequently recovered from the Schwinger-Dyson equation, once the elements responsible for the activation of the Schwinger mechanism have been duly incorporated. The excellent coincidence between the two approaches exposes a profound connection between symmetry and dynamics, and serves as a nontrivial self-consistency test of this particular mass generating scenario. |
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Address |
[Aguilar, A. C.; Oliveira, B. M.; Santos, L. R.] Univ Campinas UNICAMP, Inst Phys Gleb Wataghin, BR-13083859 Campinas, SP, Brazil, Email: aguilar@ifi.unicamp.br |
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Corporate Author |
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Publisher |
Springer |
Place of Publication |
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Language |
English |
Summary Language |
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Abbreviated Series Title |
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Series Volume |
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ISSN |
1434-6044 |
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Notes |
WOS:001118963200001 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
5861 |
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Permanent link to this record |
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Author |
Aguilar, A.C.; Ferreira, M.N.; Oliveira, B.M.; Papavassiliou, J. |
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Title |
Schwinger-Dyson truncations in the all-soft limit: a case study |
Type |
Journal Article |
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Year |
2022 |
Publication |
European Physical Journal C |
Abbreviated Journal |
Eur. Phys. J. C |
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Volume |
82 |
Issue |
11 |
Pages |
1068 - 15pp |
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Keywords |
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Abstract |
We study a special Schwinger-Dyson equation in the context of a pure SU(3) Yang-Mills theory, formulated in the background field method. Specifically, we consider the corresponding equation for the vertex that governs the interaction of two background gluons with a ghost-antighost pair. By virtue of the background gauge invariance, this vertex satisfies a naive Slavnov-Taylor identity, which is not deformed by the ghost sector of the theory. In the all-soft limit, where all momenta vanish, the form of this vertex may be obtained exactly from the corresponding Ward identity. This special result is subsequently reproduced at the level of the Schwinger-Dyson equation, by making extensive use of Taylor's theorem and exploiting a plethora of key relations, particular to the background field method. This information permits the determination of the error associated with two distinct truncation schemes, where the potential advantage from employing lattice data for the ghost dressing function is quantitatively assessed. |
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Address |
[Aguilar, A. C.; Oliveira, B. M.] Univ Campinas UNICAMP, Inst Phys Gleb Wataghin, BR-13083859 Campinas, SP, Brazil, Email: aguilar@ifi.unicamp.br |
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Corporate Author |
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Publisher |
Springer |
Place of Publication |
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Editor |
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Language |
English |
Summary Language |
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Original Title |
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Abbreviated Series Title |
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Series Volume |
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ISSN |
1434-6044 |
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Conference |
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Notes |
WOS:000889065200003 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
5426 |
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Permanent link to this record |
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Author |
Aguilar, A.C.; Ferreira, M.N.; Ibañez, D.; Papavassiliou, J. |
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Title |
Schwinger displacement of the quark-gluon vertex |
Type |
Journal Article |
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Year |
2023 |
Publication |
European Physical Journal C |
Abbreviated Journal |
Eur. Phys. J. C |
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Volume |
83 |
Issue |
10 |
Pages |
967 - 22pp |
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Keywords |
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Abstract |
The action of the Schwinger mechanism in pure Yang-Mills theories endows gluons with an effective mass, and, at the same time, induces a measurable displacement to the Ward identity satisfied by the three-gluon vertex. In the present work we turn to Quantum Chromodynamics with two light quark flavors, and explore the appearance of this characteristic displacement at the level of the quark-gluon vertex. When the Schwinger mechanism is activated, this vertex acquires massless poles, whose momentum-dependent residues are determined by a set of coupled integral equations. The main effect of these residues is to displace the Ward identity obeyed by the pole-free part of the vertex, causing modifications to its form factors, and especially the one associated with the tree-level tensor. The comparison between the available lattice data for this form factor and the Ward identity prediction reveals a marked deviation, which is completely compatible with the theoretical expectation for the attendant residue. This analysis corroborates further the self-consistency of this mass-generating scenario in the general context of real-world strong interactions. |
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Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
6080 |
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Permanent link to this record |
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Author |
Aguilar, A.C.; Ferreira, M.N.; Ibañez, D.; Oliveira, B.M.; Papavassiliou, J. |
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Title |
Patterns of gauge symmetry in the background field method |
Type |
Journal Article |
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Year |
2023 |
Publication |
European Physical Journal C |
Abbreviated Journal |
Eur. Phys. J. C |
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Volume |
83 |
Issue |
1 |
Pages |
86 - 20pp |
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Keywords |
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Abstract |
The correlation functions of Yang-Mills theories formulated in the background field method satisfy linear Slavnov-Taylor identities, which are naive generalizations of simple tree level relations, with no deformations originating from the ghost-sector of the theory. In recent years, a stronger version of these identities has been found to hold at the level of the background gluon self-energy, whose transversality is enforced separately for each special block of diagrams contributing to the gluon Schwinger-Dyson equation. In the present work we demonstrate by means of explicit calculations that the same distinct realization of the Slavnov-Taylor identity persists in the case of the background three-gluon vertex. The analysis is carried out at the level of the exact Schwinger-Dyson equation for this vertex, with no truncations or simplifying assumptions. The demonstration entails the contraction of individual vertex diagrams by the relevant momentum, which activates Slavnov-Taylor identities of vertices and multi-particle kernels nested inside these graphs; the final result emerges by virtue of a multitude of extensive cancellations, without the need of performing explicit integrations. In addition, we point out that background Ward identities amount to replacing derivatives of propagators by zero-momentum background-gluon insertions, in exact analogy to standard properties of Abelian gauge theories. Finally, certain potential applications of these results are briefly discussed. |
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Address |
[Aguilar, A. C.; Oliveira, B. M.] Univ Campinas UNICAMP, Inst Phys Gleb Wataghin, BR-13083859 Campinas, SP, Brazil, Email: aguilar@ifi.unicamp.br |
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Publisher |
Springer |
Place of Publication |
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Editor |
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Language |
English |
Summary Language |
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Original Title |
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Series Editor |
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Series Title |
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Abbreviated Series Title |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
1434-6044 |
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Conference |
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Notes |
WOS:000923274000003 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
5481 |
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Permanent link to this record |
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Author |
Aguilar, A.C.; Ferreira, M.N.; Figueiredo, C.T.; Papavassiliou, J. |
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Title |
Nonperturbative structure of the ghost-gluon kernel |
Type |
Journal Article |
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Year |
2019 |
Publication |
Physical Review D |
Abbreviated Journal |
Phys. Rev. D |
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Volume |
99 |
Issue |
3 |
Pages |
034026 - 26pp |
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Keywords |
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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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Address |
[Aguilar, A. C.; Ferreira, M. N.; Figueiredo, C. T.] Univ Estadual Campinas, UNICAMP, Inst Phys Gleb Wataghin, BR-13083859 Campinas, SP, Brazil |
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Corporate Author |
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Thesis |
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Publisher |
Amer Physical Soc |
Place of Publication |
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Editor |
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Language |
English |
Summary Language |
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Original Title |
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Series Editor |
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Series Title |
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Abbreviated Series Title |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
2470-0010 |
ISBN |
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Area |
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Expedition |
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Conference |
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Notes |
WOS:000459909200003 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
3928 |
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Permanent link to this record |