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Author |
Aguilar, A.C.; Ferreira, M.N.; Papavassiliou, J. |
![goto web page (via DOI) doi](img/doi.gif)
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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 ![sorted by Address field, ascending order (up)](img/sort_asc.gif) |
[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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Expedition |
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Conference |
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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. |
![goto web page (via DOI) doi](img/doi.gif)
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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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Keywords |
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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 ![sorted by Address field, ascending order (up)](img/sort_asc.gif) |
[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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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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Abbreviated Series Title |
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Series Volume |
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ISSN |
1434-6044 |
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Expedition |
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Conference |
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Notes |
WOS:000576141200005 |
Approved |
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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Permanent link to this record |
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Author |
Aguilar, A.C.; Binosi, D.; Figueiredo, C.T.; Papavassiliou, J. |
![goto web page (via DOI) doi](img/doi.gif)
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Title |
Evidence of ghost suppression in gluon mass scale dynamics |
Type |
Journal Article |
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Year |
2018 |
Publication |
European Physical Journal C |
Abbreviated Journal |
Eur. Phys. J. C |
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Volume |
78 |
Issue |
3 |
Pages |
181 - 15pp |
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Keywords |
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Abstract |
In this work we study the impact that the ghost sector of pure Yang-Mills theories may have on the generation of a dynamical gauge boson mass scale, which hinges on the appearance of massless poles in the fundamental vertices of the theory, and the subsequent realization of the well-known Schwinger mechanism. The process responsible for the formation of such structures is itself dynamical in nature, and is governed by a set of Bethe-Salpeter type of integral equations. While in previous studies the presence of massless poles was assumed to be exclusively associated with the background-gauge three-gluon vertex, in the present analysis we allow them to appear also in the corresponding ghost-gluon vertex. The full analysis of the resulting Bethe-Salpeter system reveals that the contribution of the poles associated with the ghost-gluon vertex are particularly suppressed, their sole discernible effect being a slight modification in the running of the gluon mass scale, for momenta larger than a few GeV. In addition, we examine the behavior of the (background-gauge) ghost-gluon vertex in the limit of vanishing ghost momentum, and derive the corresponding version of Taylor's theorem. These considerations, together with a suitable Ansatz, permit us the full reconstruction of the pole sector of the two vertices involved. |
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Address ![sorted by Address field, ascending order (up)](img/sort_asc.gif) |
[Aguilar, A. C.; Figueiredo, C. T.] Univ Estadual Campinas, UNICAMP, Inst Phys Gleb Wataghin, BR-13083859 Campinas, SP, Brazil, Email: binosi@ectstar.eu |
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Publisher |
Springer |
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English |
Summary Language |
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Series Editor |
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Abbreviated Series Title |
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Series Volume |
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ISSN |
1434-6044 |
ISBN |
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Conference |
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Notes |
WOS:000426838900005 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
3515 |
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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. |
![goto web page (via DOI) doi](img/doi.gif)
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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 ![sorted by Address field, ascending order (up)](img/sort_asc.gif) |
[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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Thesis |
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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 |
ISBN |
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Area |
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Expedition |
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Conference |
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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. |
![goto web page (via DOI) doi](img/doi.gif)
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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 ![sorted by Address field, ascending order (up)](img/sort_asc.gif) |
[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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Thesis |
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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 |
ISBN |
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Medium |
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Area |
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Expedition |
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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 |