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Author |
Aguilar, A.C.; Binosi, D.; Papavassiliou, J. |
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Title |
Renormalization group analysis of the gluon mass equation |
Type |
Journal Article |
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Year |
2014 |
Publication |
Physical Review D |
Abbreviated Journal |
Phys. Rev. D |
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Volume |
89 |
Issue |
8 |
Pages |
085032 - 19pp |
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Keywords |
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Abstract |
We carry out a systematic study of the renormalization properties of the integral equation that determines the momentum evolution of the effective gluon mass in pure Yang-Mills theory, without quark effects taken into account. A detailed, all-order analysis of the complete kernel appearing in this particular equation, derived in the Landau gauge, reveals that the renormalization procedure may be accomplished through the sole use of ingredients known from the standard perturbative treatment of the theory, with no additional assumptions. However, the subtle interplay of terms operating at the level of the exact equation gets distorted by the approximations usually employed when evaluating the aforementioned kernel. This fact is reflected in the form of the obtained solutions, for which the deviations from the correct behavior are best quantified by resorting to appropriately defined renormalization-group invariant quantities. This analysis, in turn, provides a solid guiding principle for improving the form of the kernel, and furnishes a well-defined criterion for discriminating between various possibilities. Certain renormalization-group inspired Ansatze for the kernel are then proposed, and their numerical implications are explored in detail. One of the solutions obtained fulfills the theoretical expectations to a high degree of accuracy, yielding a gluon mass that is positive definite throughout the entire range of physical momenta, and displays in the ultraviolet the so-called “power-law” running, in agreement with standard arguments based on the operator product expansion. Some of the technical difficulties thwarting a more rigorous determination of the kernel are discussed, and possible future directions are briefly mentioned. |
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Address |
[Aguilar, A. C.] 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 |
1550-7998 |
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Conference |
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Notes |
WOS:000335236500008 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
1780 |
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Author |
Aguilar, A.C.; Binosi, D.; Ibañez, D.; Papavassiliou, J. |
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Title |
New method for determining the quark-gluon vertex |
Type |
Journal Article |
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Year |
2014 |
Publication |
Physical Review D |
Abbreviated Journal |
Phys. Rev. D |
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Volume |
90 |
Issue |
6 |
Pages |
065027 - 26pp |
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Keywords |
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Abstract |
We present a novel nonperturbative approach for calculating the form factors of the quark-gluon vertex in terms of an unknown three-point function, in the Landau gauge. The key ingredient of this method is the exact all-order relation connecting the conventional quark-gluon vertex with the corresponding vertex of the background field method, which is Abelian-like. When this latter relation is combined with the standard gauge technique, supplemented by a crucial set of transverse Ward identities, it allows the approximate determination of the nonperturbative behavior of all 12 form factors comprising the quark-gluon vertex, for arbitrary values of the momenta. The actual implementation of this procedure is carried out in the Landau gauge, in order to make contact with the results of lattice simulations performed in this particular gauge. The most demanding technical aspect involves the approximate calculation of the components of the aforementioned (fully dressed) three-point function, using lattice data as input for the gluon propagators appearing in its diagrammatic expansion. The numerical evaluation of the relevant form factors in three special kinematical configurations (soft-gluon and quark symmetric limit, zero quark momentum) is carried out in detail, finding qualitative agreement with the available lattice data. Most notably, a concrete mechanism is proposed for explaining the puzzling divergence of one of these form factors observed in lattice simulations. |
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Address |
[Aguilar, A. C.] Univ Estadual Campinas, UNICAMP, Inst Phys Gleb Wataghin, BR-13083859 Sao Paulo, Brazil |
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Amer Physical Soc |
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English |
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1550-7998 |
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Conference |
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Notes |
WOS:000342147700012 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
1932 |
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Author |
Aguilar, A.C.; Binosi, D.; Papavassiliou, J. |
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Title |
Yang-Mills two-point functions in linear covariant gauges |
Type |
Journal Article |
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Year |
2015 |
Publication |
Physical Review D |
Abbreviated Journal |
Phys. Rev. D |
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Volume |
91 |
Issue |
8 |
Pages |
085014 - 14pp |
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Keywords |
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Abstract |
In this paper we use two different but complementary approaches in order to study the ghost propagator of a pure SU(3) Yang-Mills theory quantized in the linear covariant gauges, focusing on its dependence on the gauge-fixing parameter xi in the deep infrared. In particular, we first solve the Schwinger-Dyson equation that governs the dynamics of the ghost propagator, using a set of simplifying approximations, and under the crucial assumption that the gluon propagators for xi > 0 are infrared finite, as is the case in the Landau gauge (xi = 0). Then we appeal to the Nielsen identities, and express the derivative of the ghost propagator with respect to xi in terms of certain auxiliary Green's functions, which are subsequently computed under the same assumptions as before. Within both formalisms we find that for xi > 0 the ghost dressing function approaches zero in the deep infrared, in sharp contrast to what happens in the Landau gauge, where it is known to saturate at a finite (nonvanishing) value. The Nielsen identities are then extended to the case of the gluon propagator, and the xi-dependence of the corresponding gluon masses is derived using as input the results obtained in the previous steps. The result turns out to be logarithmically divergent in the deep infrared; the compatibility of this behavior with the basic assumption of a finite gluon propagator is discussed, and a specific Ansatz is put forth, which readily reconciles both features. |
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Address |
[Aguilar, A. C.] Univ Estadual Campinas, 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 |
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Abbreviated Series Title |
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ISSN |
1550-7998 |
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Notes |
WOS:000352471500006 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
2189 |
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Author |
Aguilar, A.C.; Binosi, D.; Figueiredo, C.T.; Papavassiliou, J. |
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Title |
Unified description of seagull cancellations and infrared finiteness of gluon propagators |
Type |
Journal Article |
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Year |
2016 |
Publication |
Physical Review D |
Abbreviated Journal |
Phys. Rev. D |
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Volume |
94 |
Issue |
4 |
Pages |
045002 - 22pp |
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Keywords |
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Abstract |
We present a generalized theoretical framework for dealing with the important issue of dynamical mass generation in Yang-Mills theories, and, in particular, with the infrared finiteness of the gluon propagators, observed in a multitude of recent lattice simulations. Our analysis is manifestly gauge invariant, in the sense that it preserves the transversality of the gluon self-energy, and gauge independent, given that the conclusions do not depend on the choice of the gauge-fixing parameter within the linear covariant gauges. The central construction relies crucially on the subtle interplay between the Abelian Ward identities satisfied by the nonperturbative vertices and a special integral identity that enforces a vast number of “seagull cancellations” among the one-and two-loop dressed diagrams of the gluon Schwinger-Dyson equation. The key result of these considerations is that the gluon propagator remains rigorously massless, provided that the vertices do not contain (dynamical) massless poles. When such poles are incorporated into the vertices, under the pivotal requirement of respecting the gauge symmetry of the theory, the terms comprising the Ward identities conspire in such a way as to still enforce the total annihilation of all quadratic divergences, inducing, at the same time, residual contributions that account for the saturation of gluon propagators in the deep infrared. |
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Address |
[Aguilar, A. C.; Figueiredo, C. T.] Univ Campinas UNICAMP, Inst Phys Gleb Wataghin, BR-13083859 Campinas, SP, Brazil |
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Corporate Author |
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Thesis |
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Publisher |
Amer Physical Soc |
Place of Publication |
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Editor |
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Language |
English |
Summary Language |
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Original Title |
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Series Editor |
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Series Title |
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Abbreviated Series Title |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
2470-0010 |
ISBN |
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Expedition |
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Conference |
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Notes |
WOS:000380962400003 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
2772 |
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Author |
Aguilar, A.C.; Binosi, D.; Papavassiliou, J. |
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Title |
Schwinger mechanism in linear covariant gauges |
Type |
Journal Article |
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Year |
2017 |
Publication |
Physical Review D |
Abbreviated Journal |
Phys. Rev. D |
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Volume |
95 |
Issue |
3 |
Pages |
034017 - 16pp |
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Keywords |
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Abstract |
In this work we explore the applicability of a special gluon mass generating mechanism in the context of the linear covariant gauges. In particular, the implementation of the Schwinger mechanism in pure Yang-Mills theories hinges crucially on the inclusion of massless bound-state excitations in the fundamental nonperturbative vertices of the theory. The dynamical formation of such excitations is controlled by a homogeneous linear Bethe-Salpeter equation, whose nontrivial solutions have been studied only in the Landau gauge. Here, the form of this integral equation is derived for general values of the gauge-fixing parameter, under a number of simplifying assumptions that reduce the degree of technical complexity. The kernel of this equation consists of fully dressed gluon propagators, for which recent lattice data are used as input, and of three-gluon vertices dressed by a single form factor, which is modeled by means of certain physically motivated Ansatze. The gauge-dependent terms contributing to this kernel impose considerable restrictions on the infrared behavior of the vertex form factor; specifically, only infrared finite Ansatze are compatible with the existence of nontrivial solutions. When such Ansatze are employed, the numerical study of the integral equation reveals a continuity in the type of solutions as one varies the gauge-fixing parameter, indicating a smooth departure from the Landau gauge. Instead, the logarithmically divergent form factor displaying the characteristic “zero crossing,” while perfectly consistent in the Landau gauge, has to undergo a dramatic qualitative transformation away from it, in order to yield acceptable solutions. The possible implications of these results are briefly discussed. |
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Address |
[Aguilar, A. C.] Univ Estadual Campinas, UNICAMP, Inst Phys Gleb Wataghin, BR-13083859 Campinas, SP, Brazil |
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Corporate Author |
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Thesis |
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Publisher |
Amer Physical Soc |
Place of Publication |
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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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Expedition |
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Conference |
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Notes |
WOS:000394092900003 |
Approved |
no |
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Is ISI |
yes |
International Collaboration |
yes |
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Call Number |
IFIC @ pastor @ |
Serial |
2987 |
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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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Corporate Author |
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Thesis |
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Publisher |
Amer Physical Soc |
Place of Publication |
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English |
Summary Language |
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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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Expedition |
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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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Corporate Author |
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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 |
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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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Corporate Author |
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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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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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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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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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Language |
English |
Summary Language |
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Original Title |
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Abbreviated Series Title |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
2470-0010 |
ISBN |
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Area |
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Expedition |
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Conference |
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Notes |
WOS: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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