| Records |
| Author |
Aguilar, A.C.; Cardona, J.C.; Ferreira, M.N.; Papavassiliou, J. |
| Title |
Quark gap equation with non-Abelian Ball-Chiu vertex |
Type |
Journal Article |
| Year |
2018 |
Publication |
Physical Review D |
Abbreviated Journal |
Phys. Rev. D |
Volume  |
98 |
Issue |
1 |
Pages |
014002 - 15pp |
| Keywords |
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| Abstract |
The full quark-gluon vertex is a crucial ingredient for the dynamical generation of a constituent quark mass from the standard quark gap equation, and its nontransverse part may be determined exactly from the nonlinear Slav nov-Taylor identity that it satisfies. The resulting expression involves not only the quark propagator, but also the ghost dressing function and the quark-ghost kernel, and constitutes the non-abelian extension of the so-called “Ball-Chiu vertex,” known from QED. In the present work we carry out a detailed study of the impact of this vertex on the gap equation and the quark masses generated from it, putting particular emphasis on the contributions directly related with the ghost sector of the theory, and especially the quark-ghost kernel. In particular, we set up and solve the coupled system of six equations that determine the four form factors of the latter kernel and the two typical Dirac structures composing the quark propagator. Due to the incomplete implementation of the multiplicative renormalizability at the level of the gap equation, the correct anomalous dimension of the quark mass is recovered through the inclusion of a certain function, whose ultraviolet behavior is fixed, but its infrared completion is unknown; three particular Ansatze for this function are considered, and their effect on the quark mass and the pion decay constant is explored. The main results of this study indicate that the numerical impact of the quark-ghost kernel is considerable; the transition from a tree-level kernel to the one computed hem leads to a 20% increase in the value of the quark mass at the origin. Particularly interesting is the contribution of the fourth Ball-Chiu form factor, which, contrary to the Abelian case, is nonvanishing, and accounts for 10% of the total constituent quark mass. |
| Address |
[Aguilar, A. C.; Cardona, J. C.; Ferreira, M. N.] Univ Campinas UNICAMP, Inst Phys Gleb Wataghin, BR-13083859 Campinas, SP, Brazil |
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Thesis |
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| Publisher |
Amer Physical Soc |
Place of Publication |
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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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Medium |
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| Area |
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Expedition |
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Conference |
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| Notes |
WOS:000436941600003 |
Approved |
no |
| Is ISI |
yes |
International Collaboration |
yes |
| Call Number |
IFIC @ pastor @ |
Serial |
3642 |
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| Author |
Aguilar, A.C.; Cardona, J.C.; Ferreira, M.N.; Papavassiliou, J. |
| Title |
Non-Abelian Ball-Chiu vertex for arbitrary Euclidean momenta |
Type |
Journal Article |
| Year |
2017 |
Publication |
Physical Review D |
Abbreviated Journal |
Phys. Rev. D |
| Volume |
96 |
Issue |
1 |
Pages |
014029 - 29pp |
| Keywords |
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| Abstract |
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. |
| Address |
[Aguilar, A. C.; Cardona, J. C.; Ferreira, M. N.] Univ Campinas UNICAMP, Inst Phys Gleb Wataghin, BR-13083859 Campinas, SP, Brazil |
| 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 Title |
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Abbreviated Series Title |
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Series Issue |
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Edition |
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| ISSN |
2470-0010 |
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:000406540300002 |
Approved |
no |
| Is ISI |
yes |
International Collaboration |
yes |
| Call Number |
IFIC @ pastor @ |
Serial |
3232 |
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| Author |
Aguilar, A.C.; Ferreira, M.N.; Papavassiliou, J.; Santos, L.R. |
| Title |
Four-gluon vertex in collinear kinematics |
Type |
Journal Article |
| Year |
2024 |
Publication |
European Physical Journal C |
Abbreviated Journal |
Eur. Phys. J. C |
| Volume |
84 |
Issue |
7 |
Pages |
676 - 27pp |
| Keywords |
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| Abstract |
To date, the four-gluon vertex is the least explored component of the QCD Lagrangian, mainly due to the vast proliferation of Lorentz and color structures required for its description. In this work we present a nonperturbative study of this vertex, based on the one-loop dressed Schwinger-Dyson equation obtained from the 4PI effective action. A vast simplification is brought about by resorting to “collinear” kinematics, where all momenta are parallel to each other, and by appealing to the charge conjugation symmetry in order to eliminate certain color structures. Out of the fifteen form factors that comprise the transversely-projected version of this vertex, two are singled out and studied in detail; the one associated with the classical tensorial structure is moderately suppressed in the infrared regime, while the other diverges logarithmically at the origin. Quite interestingly, both form factors display the property known as “planar degeneracy” at a rather high level of accuracy. With these results we construct an effective charge that quantifies the strength of the four-gluon interaction, and compare it with other vertex-derived charges from the gauge sector of QCD. |
| 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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Thesis |
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| Publisher |
Springer |
Place of Publication |
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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 |
|
| Notes |
WOS:001264786100001 |
Approved |
no |
| Is ISI |
yes |
International Collaboration |
yes |
| Call Number |
IFIC @ pastor @ |
Serial |
6199 |
| Permanent link to this record |
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| Author |
Ferreira, M.N.; Papavassiliou, J. |
| Title |
Nonlinear Schwinger mechanism in QCD, and Fredholm alternatives theorem |
Type |
Journal Article |
| Year |
2024 |
Publication |
European Physical Journal C |
Abbreviated Journal |
Eur. Phys. J. C |
| Volume |
84 |
Issue |
8 |
Pages |
835 - 25pp |
| Keywords |
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| Abstract |
We present a novel implementation of the Schwinger mechanism in QCD, which fixes uniquely the scale of the effective gluon mass scale and streamlines considerably the procedure of multiplicative renormalization. The key advantage of this method stems from the nonlinear nature of the dynamical equation that generates massless poles in the longitudinal sector of the three-gluon vertex. An exceptional feature of this approach is an extensive cancellation involving the components of the integral expression that determines the gluon mass scale; it is triggered once the Schwinger-Dyson equation of the pole-free part of the three-gluon vertex has been appropriately exploited. It turns out that this cancellation is driven by the so-called Fredholm alternatives theorem, which operates among the set of integral equations describing this system. Quite remarkably, in the linearized approximation this theorem enforces the exact masslessness of the gluon. Instead, the nonlinearity induced by the full treatment of the relevant kernel evades this theorem, allowing for the emergence of a nonvanishing mass scale. The numerical results obtained from the resulting equations are compatible with the lattice findings, and may be further refined through the inclusion of the remaining fundamental vertices of the theory. |
| Address |
[Ferreira, M. N.] Nanjing Univ, Sch Phys, Nanjing 210093, Jiangsu, Peoples R China, Email: a.mauricio.ferreira@hotmail.com |
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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 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:001295063000001 |
Approved |
no |
| Is ISI |
yes |
International Collaboration |
yes |
| Call Number |
IFIC @ pastor @ |
Serial |
6236 |
| Permanent link to this record |
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| Author |
Aguilar, A.C.; Ferreira, M.N.; Ibañez, D.; Oliveira, B.M.; Papavassiliou, J. |
| Title |
Patterns of gauge symmetry in the background field method |
Type |
Journal Article |
| Year |
2023 |
Publication |
European Physical Journal C |
Abbreviated Journal |
Eur. Phys. J. C |
| Volume |
83 |
Issue |
1 |
Pages |
86 - 20pp |
| 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. |
| Address |
[Aguilar, A. C.; Oliveira, B. M.] Univ Campinas UNICAMP, Inst Phys Gleb Wataghin, BR-13083859 Campinas, SP, Brazil, Email: aguilar@ifi.unicamp.br |
| 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:000923274000003 |
Approved |
no |
| Is ISI |
yes |
International Collaboration |
yes |
| Call Number |
IFIC @ pastor @ |
Serial |
5481 |
| Permanent link to this record |
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| Author |
Aguilar, A.C.; Ferreira, M.N.; Papavassiliou, J.; Santos, L.R. |
| Title |
Planar degeneracy of the three-gluon vertex |
Type |
Journal Article |
| Year |
2023 |
Publication |
European Physical Journal C |
Abbreviated Journal |
Eur. Phys. J. C |
| Volume |
83 |
Issue |
6 |
Pages |
549 - 20pp |
| Keywords |
|
| 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. |
| 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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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 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:001117709800001 |
Approved |
no |
| Is ISI |
yes |
International Collaboration |
yes |
| Call Number |
IFIC @ pastor @ |
Serial |
5847 |
| Permanent link to this record |
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| Author |
Aguilar, A.C.; Ferreira, M.N.; Oliveira, B.M.; Papavassiliou, J.; Santos, L.R. |
| Title |
Schwinger poles of the three-gluon vertex: symmetry and dynamics |
Type |
Journal Article |
| Year |
2023 |
Publication |
European Physical Journal C |
Abbreviated Journal |
Eur. Phys. J. C |
| Volume |
83 |
Issue |
10 |
Pages |
889 - 20pp |
| Keywords |
|
| 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. |
| 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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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:001118963200001 |
Approved |
no |
| Is ISI |
yes |
International Collaboration |
yes |
| Call Number |
IFIC @ pastor @ |
Serial |
5861 |
| Permanent link to this record |
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| Author |
Aguilar, A.C.; Ferreira, M.N.; Ibañez, D.; Papavassiliou, J. |
| Title |
Schwinger displacement of the quark-gluon vertex |
Type |
Journal Article |
| Year |
2023 |
Publication |
European Physical Journal C |
Abbreviated Journal |
Eur. Phys. J. C |
| Volume |
83 |
Issue |
10 |
Pages |
967 - 22pp |
| 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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ISBN |
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Expedition |
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Conference |
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| Notes |
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Approved |
no |
| Is ISI |
yes |
International Collaboration |
yes |
| Call Number |
IFIC @ pastor @ |
Serial |
6080 |
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| Author |
Aguilar, A.C.; Ferreira, M.N.; Oliveira, B.M.; Papavassiliou, J. |
| Title |
Schwinger-Dyson truncations in the all-soft limit: a case study |
Type |
Journal Article |
| Year |
2022 |
Publication |
European Physical Journal C |
Abbreviated Journal |
Eur. Phys. J. C |
| Volume |
82 |
Issue |
11 |
Pages |
1068 - 15pp |
| 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. |
| Address |
[Aguilar, A. C.; Oliveira, B. M.] Univ Campinas UNICAMP, Inst Phys Gleb Wataghin, BR-13083859 Campinas, SP, Brazil, Email: aguilar@ifi.unicamp.br |
| 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 |
| Is ISI |
yes |
International Collaboration |
yes |
| Call Number |
IFIC @ pastor @ |
Serial |
5426 |
| Permanent link to this record |
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| Author |
Aguilar, A.C.; Ferreira, M.N.; Papavassiliou, J. |
| Title |
Gluon dynamics from an ordinary differential equation |
Type |
Journal Article |
| Year |
2021 |
Publication |
European Physical Journal C |
Abbreviated Journal |
Eur. Phys. J. C |
| Volume |
81 |
Issue |
1 |
Pages |
54 - 20pp |
| Keywords |
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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. |
| Address |
[Aguilar, A. C.; Ferreira, M. N.] Univ Campinas UNICAMP, Inst Phys Gleb Wataghin, BR-13083859 Campinas, SP, Brazil, Email: aguilar@ifi.unicamp.br |
| 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:000611993400002 |
Approved |
no |
| Is ISI |
yes |
International Collaboration |
yes |
| Call Number |
IFIC @ pastor @ |
Serial |
4730 |
| Permanent link to this record |
