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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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Amer Physical Soc |
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English |
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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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Amer Physical Soc |
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2470-0010 |
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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 |
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ISSN |
2470-0010 |
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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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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 |
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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 |
2470-0010 |
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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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| 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 |
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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Corporate Author |
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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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Abbreviated Series Title |
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Series Volume |
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ISSN |
2470-0010 |
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Expedition |
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Conference |
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Notes |
WOS:000498877900002 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
4208 |
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Author |
Souza, E.V.; Ferreira, M.N.; Aguilar, A.C.; Papavassiliou, J.; Roberts, C.D.; Xu, S.S. |
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Title |
Pseudoscalar glueball mass: a window on three-gluon interactions |
Type |
Journal Article |
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Year |
2020 |
Publication |
European Physical Journal A |
Abbreviated Journal |
Eur. Phys. J. A |
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Volume |
56 |
Issue |
1 |
Pages |
25 - 7pp |
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Keywords |
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Abstract |
In pure-glue QCD, gluon-gluon scattering in the J(PC) = 0(-+) channel is described by a very simple equation, especially if one considers just the leading contribution to the scattering kernel. Of all components in this kernel, only the three-gluon vertex, V-mu nu rho, is poorly constrained by contemporary analyses; hence, calculations of 0(-+) glueball properties serve as a clear window onto the character and form of V-mu nu rho. This is important given that many modern calculations of V-mu nu rho predict the appearance of an infrared suppression in the scalar function which comes to modulate the bare vertex after the nonperturbative resummation of interactions. Such behaviour is a peculiar prediction; but we find that the suppression is essential if one is to achieve agreement with lattice-QCD predictions for the 0(-+) glueball mass. Hence, it is likely that this novel feature of V-mu nu rho is real and has observable implications for the spectrum, decays and interactions of all QCD bound-states. |
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Address |
[Souza, E. V.] Fed Inst Educ Sci & Technol Piaui, BR-64605500 Picos, Piaui, Brazil, Email: emanuel.veras@ifpi.edu.br; |
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Publisher |
Springer |
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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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 |
1434-6001 |
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:000513948400001 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
4291 |
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| Permanent link to this record |
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Author |
Aguilar, A.C.; De Soto, F.; Ferreira, M.N.; Papavassiliou, J.; Rodriguez-Quintero, J.; Zafeiropoulos, S. |
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Title |
Gluon propagator and three-gluon vertex with dynamical quarks |
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 |
2 |
Pages |
154 - 17pp |
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Keywords |
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Abstract |
We present a detailed analysis of the kinetic and mass terms associated with the Landau gauge gluon propagator in the presence of dynamical quarks, and a comprehensive dynamical study of certain special kinematic limits of the three-gluon vertex. Our approach capitalizes on results from recent lattice simulations with (2+1) domain wall fermions, a novel nonlinear treatment of the gluon mass equation, and the nonperturbative reconstruction of the longitudinal three-gluon vertex from its fundamental Slavnov-Taylor identities. Particular emphasis is placed on the persistence of the suppression displayed by certain combinations of the vertex form factors at intermediate and low momenta, already known from numerous pure Yang-Mills studies. One of our central findings is that the inclusion of dynamical quarks moderates the intensity of this phenomenon only mildly, leaving the asymptotic low-momentum behavior unaltered, but displaces the characteristic “zero crossing” deeper into the infrared region. In addition, the effect of the three-gluon vertex is explored at the level of the effective gauge coupling, whose size is considerably reduced with respect to its counterpart obtained from the ghost-gluon vertex. The main upshot of the above considerations is the further confirmation of the tightly interwoven dynamics between the two- and three-point sectors of QCD. |
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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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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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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:000517203200001 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
4314 |
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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 |
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 |
[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 |
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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: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.; 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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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. |
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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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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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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 |
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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.; De Soto, F.; Ferreira, M.N.; Papavassiliou, J.; Rodriguez-Quintero, J. |
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Title |
Infrared facets of the three-gluon vertex |
Type |
Journal Article |
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Year |
2021 |
Publication |
Physics Letters B |
Abbreviated Journal |
Phys. Lett. B |
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Volume |
818 |
Issue |
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Pages |
136352 - 7pp |
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Keywords |
QCD; Three-gluon vertex; Lattice QCD; Schwinger-Dyson equations |
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Abstract |
We present novel lattice results for the form factors of the quenched three-gluon vertex of QCD, in two special kinematic configurations that depend on a single momentum scale. We consider three form factors, two associated with a classical tensor structure and one without tree-level counterpart, exhibiting markedly different infrared behaviors. Specifically, while the former display the typical suppression driven by a negative logarithmic singularity at the origin, the latter saturates at a small negative constant. These exceptional features are analyzed within the Schwinger-Dyson framework, with the aid of special relations obtained from the Slavnov-Taylor identities of the theory. The emerging picture of the underlying dynamics is thoroughly corroborated by the lattice results, both qualitatively as well as quantitatively. |
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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: jose.rodriguez@dfaie.uhu.es |
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Thesis |
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Publisher |
Elsevier |
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 |
0370-2693 |
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:000662629500036 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
4865 |
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