arXiv subjects

M. N. Ferreira

Publications and source records attributed to M. N. Ferreira.

33 records · Page 2Linked to original sources

arXiv2022

Theory and phenomenology of the three-gluon vertex

The three-gluon vertex is a fundamental ingredient of the intricate QCD dynamics, being inextricably connected to key nonperturbative phenomena, such as the emergence of a mass scale in the gauge sector of the theory. In this presentation, we review the main theoretical properties of the three-gluon vertex in the Landau gauge, obtained from the fruitful synergy between functional methods and lattice simulations. We pay particular attention to the manifestation and origin of the infrared suppression of its main form factors and the associated zero crossing. In addition, we discuss certain characteristic phenomenological applications that require this special vertex as input.

hep-ph↗

arXiv2022

Ghost dynamics from Schwinger-Dyson equations

We discuss the coupled dynamics of the ghost dressing function and the ghost-gluon vertex through the Schwinger-Dyson equations that they satisfy. In order to close the system of equations, we combine recent lattice data for the gluon propagator and an approximate STI-derived Ansatz for the general kinematics three-gluon vertex. The numerical solution of the resulting coupled system exhibits excellent agreement to lattice data, for both the ghost dressing function and the ghost-gluon vertex, and allows the determination of the coupling constant. Next, in the soft gluon limit the full three-gluon vertex appearing in the ghost-gluon equation reduces to a special projection that is tightly constrained by lattice simulations. Specializing the ghost-gluon Schwinger-Dyson equation to this limit provides a nontrivial consistency check on the approximations employed for the three-gluon interaction and shows that the latter has an important quantitative effect on the ghost-gluon vertex. Finally, our results stress the importance of eliminating artifacts when confronting lattice data with continuum predictions.

hep-ph↗

arXiv2021

Exploring smoking-gun signals of the Schwinger mechanism in QCD

In QCD, the Schwinger mechanism endows the gluons with an effective mass through the dynamical formation of massless bound-state poles that are longitudinally coupled. The presence of these poles affects profoundly the infrared properties of the interaction vertices, inducing crucial modifications to their fundamental Ward identities. Within this general framework, we present a detailed derivation of the non-Abelian Ward identity obeyed by the pole-free part of the three-gluon vertex in the soft-gluon limit, and determine the smoking-gun displacement that the onset of the Schwinger mechanism produces to the standard result. Quite importantly, the quantity that describes this distinctive feature coincides formally with the bound-state wave function that controls the massless pole formation. Consequently, this signal may be computed in two independent ways: by solving an approximate version of the pertinent Bethe-Salpeter integral equation, or by appropriately combining the elements that enter in the aforementioned Ward identity. For the implementation of both methods we employ two- and three-point correlation functions obtained from recent lattice simulations, and a partial derivative of the ghost-gluon kernel, which is computed from the corresponding Schwinger-Dyson equation. Our analysis reveals an excellent coincidence between the results obtained through either method, providing a highly nontrivial self-consistency check for the entire approach. When compared to the null hypothesis, where the Schwinger mechanism is assumed to be inactive, the statistical significance of the resulting signal is estimated to be three standard deviations.

hep-ph↗

arXiv2021

Ghost dynamics in the soft gluon limit

We present a detailed study of the dynamics associated with the ghost sector of quenched QCD in the Landau gauge, where the relevant dynamical equations are supplemented with key inputs originating from large-volume lattice simulations. In particular, we solve the coupled system of Schwinger-Dyson equations that governs the evolution of the ghost dressing function and the ghost-gluon vertex, using as input for the gluon propagator lattice data that have been cured from volume and discretization artifacts. In addition, we explore the soft gluon limit of the same system, employing recent lattice data for the three-gluon vertex that enters in one of the diagrams defining the Schwinger-Dyson equation of the ghost-gluon vertex. The results obtained from the numerical treatment of these equations are in excellent agreement with lattice data for the ghost dressing function, once the latter have undergone the appropriate scale-setting and artifact elimination refinements. Moreover, the coincidence observed between the ghost-gluon vertex in general kinematics and in the soft gluon limit reveals an outstanding consistency of physical concepts and computational schemes.

hep-ph↗

arXiv2021

Infrared facets of the three-gluon vertex

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.

hep-ph↗

arXiv2020

Gluon dynamics from an ordinary differential equation

We present a novel method for computing the nonperturbative kinetic term of the gluon propagator from an exactly solvable ordinary differential equation, whose origin is the fundamental Slavnov-Taylor identity satisfied by the three-gluon vertex, evaluated in a special kinematic limit. The main ingredients comprising the solution are a well-known projection of the three-gluon vertex, simulated on the lattice, and a particular derivative of the ghost-gluon kernel, whose approximate form is derived from a standard Schwinger-Dyson equation. Crucially, the physical requirement of a pole-free answer determines completely the form of the initial condition, whose value is calculated from a specific integral containing the same ingredients as the solution itself. This outstanding feature fixes uniquely, at least in principle, the form of the kinetic term, once the ingredients of the differential equation have been accurately evaluated. Furthermore, in the case where the gluon propagator has been independently accessed from the lattice, this property leads to the unambiguous 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. The systematic improvement of this approach through the detailed computation of one of its pivotal components is briefly outlined.

hep-ph↗

arXiv2020

Novel sum rules for the three-point sector of QCD

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.

hep-ph↗

arXiv2019

Gluon propagator and three-gluon vertex with dynamical quarks

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 renormalization-group invariant combination corresponding to 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.

hep-ph↗

arXiv2019

Pseudoscalar glueball mass: a window on three-gluon interactions

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, $V_{μνρ}$, is poorly constrained by contemporary analyses; hence, calculations of $0^{-+}$ glueball properties serve as a clear window onto the character and form of $V_{μνρ}$. This is important given that many modern calculations of $V_{μνρ}$ 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 such suppression is essential if one is to achieve agreement with lattice-QCD predictions for the $0^{-+}$ glueball mass. It is likely, therefore, that this novel feature of $V_{μνρ}$ is real and has observable implications for the spectrum, decays and interactions of all QCD bound-states.

nucl-th↗

arXiv2019

Gluon mass scale through nonlinearities and vertex interplay

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 {\it Ansätze}, 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.

hep-ph↗

arXiv2019

Nonperturbative structure of the ghost-gluon kernel

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 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 Ansätze 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 ghost-gluon vertex for arbitrary momenta, and, more importantly, pave the way towards the nonperturbative generalization of the Ball-Chiu construction for the longitudinal part of the three-gluon vertex.

hep-ph↗

arXiv2019

Nonperturbative Ball-Chiu construction of the three-gluon vertex

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 as well as Schwinger-Dyson equations, and good overall agreement is found. 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.

hep-ph↗

arXiv2018

Quark mass generation with Schwinger-Dyson equations

In this talk, we review some of the current efforts to understand the phenomenon of chiral symmetry breaking and the generation of a dynamical quark mass. To do that, we will use the standard framework of the Schwinger-Dyson equations. The key ingredient in this analysis is the quark-gluon vertex, whose non-transverse part may be determined exactly from the nonlinear Slavnov-Taylor identity that it satisfies. The resulting expressions for the form factors of this vertex involve not only the quark propagator, but also the ghost dressing function and the quark-ghost kernel. Solving the coupled system of integral equations formed by the quark propagator and the four form factors of the scattering kernel, we carry out a detailed study of the impact of the quark gluon 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. Particular attention is dedicated on the way that the correct renormalization group behavior of the dynamical quark mass is recovered, and in the extraction of the phenomenological parameters such as the pion decay constant.

hep-ph↗

arXiv2018

Quark gap equation with non-abelian Ball-Chiu vertex

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 non-transverse part may be determined exactly from the nonlinear Slavnov-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 Ansätze 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 here 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.

hep-ph↗

arXiv2018

Non-Abelian Ball-Chiu vertex for arbitrary Euclidean momenta

We determine the non-Abelian version of the four longitudinal 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. The potential phenomenological impact of these results is evaluated through the study of special renormalization-point-independent combinations, which quantify the strength of the interaction kernels appearing in the standard quark gap and Bethe-Salpeter equations.

hep-ph↗