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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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Springer |
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English |
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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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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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Keywords |
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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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Notes |
WOS:001117709800001 |
Approved |
no |
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Is ISI |
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.; 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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Springer |
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English |
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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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Author |
Nunes da Silva, T.; Chinellato, D.D.; Giannini, A.V.; Takahashi, J.; Ferreira, M.N.; Denicol, G.S.; Hippert, M.; Noronha, J.; Luzum, M. |
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Title |
Prehydrodynamic evolution in large and small systems |
Type |
Journal Article |
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Year |
2023 |
Publication |
Physical Review C |
Abbreviated Journal |
Phys. Rev. C |
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Volume |
107 |
Issue |
4 |
Pages |
044901 - 12pp |
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Keywords |
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Abstract |
We extend our previous investigation of the effects of prehydrodynamic evolution on final-state observables in heavy-ion collisions [38] to smaller systems. We use a state-of-the-art hybrid model for the numerical simulations with optimal parameters obtained from a previous Bayesian study. By studying p-Pb collisions, we find that the effects due to the assumption of a conformal evolution in the prehydrodynamical stage are even more important in small systems. We also show that this effect depends on the time duration of the pre-equilibrium stage, which is further enhanced in small systems. Finally, we show that the recent proposal of a free-streaming with subluminal velocity for the pre-equilibrium stage, thus effectively breaking conformal invariance, can alleviate the contamination of final-state observables. Our study further reinforces the need for moving beyond conformal approaches in pre-equilibrium dynamics modeling, especially when extracting transport coefficients from hybrid models in the high-precision era of heavy-ion collisions. |
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Address |
[da Silva, T. Nunes] Univ Fed Santa Catarina, Ctr Ciencias Fis & Matemat, Dept Fis, Campus Univ Reitor Joao David Ferreira Lima, BR-88040900 Florianopolis, Brazil, Email: t.j.nunes@ufsc.br; |
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Publisher |
Amer Physical Soc |
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English |
Summary Language |
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Abbreviated Series Title |
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Series Volume |
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ISSN |
2469-9985 |
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Expedition |
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Conference |
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Notes |
WOS:000974911400001 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
5524 |
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Author |
Krupczak, R.; da Silva, T.N.; Domingues, T.S.; Luzum, M.; Denicol, G.S.; Gardim, F.G.; Giannini, A.V.; Ferreira, M.N.; Hippert, M.; Noronha, J.; Chinellato, D.D.; Takahashi, J. |
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Title |
Causality violations in simulations of large and small heavy-ion collisions |
Type |
Journal Article |
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Year |
2024 |
Publication |
Physical Review C |
Abbreviated Journal |
Phys. Rev. C |
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Volume |
109 |
Issue |
3 |
Pages |
034908 - 12pp |
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Keywords |
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Abstract |
Heavy-ion collisions, such as Pb-Pb or p-Pb, produce extreme conditions in temperature and density that make the hadronic matter transition to a new state, called quark-gluon plasma (QGP). Simulations of heavy-ion collisions provide a way to improve our understanding of the QGP's properties. These simulations are composed of a hybrid description that results in final observables in agreement with accelerators like LHC and RHIC. However, recent works pointed out that these hydrodynamic simulations can display acausal behavior during the evolution in certain regions, indicating a deviation from a faithful representation of the underlying QCD dynamics. To pursue a better understanding of this problem and its consequences, this work simulated two different collision systems, Pb-Pb and p-Pb at root sNN = 5.02 TeV. In this context, our results show that causality violation, even though always present, typically occurs on a small part of the system, quantified by the total energy fraction residing in the acausal region. In addition, the acausal behavior can be reduced with changes in the prehydrodynamic factors and the definition of the bulk-viscous relaxation time. Since these aspects are fairly arbitrary in current simulation models, without solid guidance from the underlying theory, it is reasonable to use the disturbing presence of acausal behavior in current simulations to guide improvements towards more realistic modeling. While this work does not solve the acausality problem, it sheds more light on this issue and also proposes a way to solve this problem in simulations of heavy-ion collisions. |
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Address |
[Krupczak, Renata; da Silva, Tiago Nunes] Univ Fed Santa Catarina, Ctr Ciencias Fis & Matemat, Dept Fis, Campus Univ Reitor Joao David Ferreira Lima, BR-88040900 Florianopolis, Brazil, Email: rkrupczak@physik.uni-bielefeld.de; |
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Publisher |
Amer Physical Soc |
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English |
Summary Language |
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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 |
2469-9985 |
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Expedition |
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Conference |
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Notes |
WOS:001198699800003 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
6113 |
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Author |
Aguilar, A.C.; Cardona, J.C.; Ferreira, M.N.; Papavassiliou, J. |
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Title |
Non-Abelian Ball-Chiu vertex for arbitrary Euclidean momenta |
Type |
Journal Article |
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Year |
2017 |
Publication |
Physical Review D |
Abbreviated Journal |
Phys. Rev. D |
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Volume |
96 |
Issue |
1 |
Pages |
014029 - 29pp |
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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. |
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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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Publisher |
Amer Physical Soc |
Place of Publication |
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English |
Summary Language |
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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 |
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Conference |
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Notes |
WOS:000406540300002 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
3232 |
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Author |
Aguilar, A.C.; Cardona, J.C.; Ferreira, M.N.; Papavassiliou, J. |
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Title |
Quark gap equation with non-Abelian Ball-Chiu vertex |
Type |
Journal Article |
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Year |
2018 |
Publication |
Physical Review D |
Abbreviated Journal |
Phys. Rev. D |
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Volume |
98 |
Issue |
1 |
Pages |
014002 - 15pp |
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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. |
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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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Publisher |
Amer Physical Soc |
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English |
Summary Language |
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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 |
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Area |
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Expedition |
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Conference |
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Notes |
WOS:000436941600003 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
3642 |
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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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Amer Physical Soc |
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English |
Summary Language |
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Abbreviated Series Title |
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Edition |
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ISSN |
2470-0010 |
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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 |
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Author |
Aguilar, A.C.; Ferreira, M.N.; Figueiredo, C.T.; Papavassiliou, J. |
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Title |
Nonperturbative Ball-Chiu construction of the three-gluon vertex |
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 |
9 |
Pages |
094010 - 30pp |
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Keywords |
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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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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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Publisher |
Amer Physical Soc |
Place of Publication |
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English |
Summary Language |
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Abbreviated Series Title |
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Series Issue |
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ISSN |
2470-0010 |
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Expedition |
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Conference |
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Notes |
WOS:000467734600003 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
4010 |
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Author |
Aguilar, A.C.; Ferreira, M.N.; Figueiredo, C.T.; Papavassiliou, J. |
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Title |
Gluon mass scale through nonlinearities and vertex interplay |
Type |
Journal Article |
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Year |
2019 |
Publication |
Physical Review D |
Abbreviated Journal |
Phys. Rev. D |
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Volume |
100 |
Issue |
9 |
Pages |
094039 - 19pp |
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Keywords |
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Abstract |
We present a novel analysis of the gluon gap equation, where its full nonlinear structure is duly taken into account. In particular, while in previous treatments the linearization of this homogeneous integral equation introduced an indeterminacy in the scale of the corresponding mass, the current approach determines it uniquely, once the value of the gauge coupling at a given renormalization point is used as input. A crucial ingredient for this construction is the “kinetic term” of the gluon propagator, whose form is not obtained from the complicated equation governing its evolution, but is rather approximated by suitable initial Ansatze, which are subsequently improved by means of a systematic iterative procedure. The multiplicative renormalization of the central equation is carried out following an approximate method, which is extensively employed in the studies of the standard quark gap equation. This approach amounts to the effective substitution of the vertex renormalization constants by kinematically simplified form factors of the three- and four-gluon vertices. The resulting numerical interplay, exemplified by the infrared suppression of the three-gluon vertex and the mild enhancement of the four-gluon vertex, is instrumental for obtaining positive-definite and monotonically decreasing running gluon masses. The resulting gluon propagators, put together from the gluon masses and kinetic terms obtained with this method, match rather accurately the data obtained from large-volume lattice simulations. |
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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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Amer Physical Soc |
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Language |
English |
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ISSN |
2470-0010 |
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Notes |
WOS:000498877900002 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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IFIC @ pastor @ |
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4208 |
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