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Aguilar, A. C., Ferreira, M. N., Figueiredo, C. T., & Papavassiliou, J. (2019). Gluon mass scale through nonlinearities and vertex interplay. Phys. Rev. D, 100(9), 094039–19pp.
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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Aguilar, A. C., Ambrosio, C. O., De Soto, F., Ferreira, M. N., Oliveira, B. M., Papavassiliou, J., et al. (2021). Ghost dynamics in the soft gluon limit. Phys. Rev. D, 104(5), 054028–18pp.
Abstract: 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.
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Aguilar, A. C., Ferreira, M. N., & Papavassiliou, J. (2022). Exploring smoking-gun signals of the Schwinger mechanism in QCD. Phys. Rev. D, 105(1), 014030–26pp.
Abstract: In Quantum Chromodynamics, 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 softgluon 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 BetheSalpeter 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 3 standard deviations.
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Aguilar, A. C., Binosi, D., & Papavassiliou, J. (2010). QCD effective charges from lattice data. J. High Energy Phys., 07(7), 002–24pp.
Abstract: We use recent lattice data on the gluon and ghost propagators, as well as the Kugo-Ojima function, in order to extract the non-perturbative behavior of two particular definitions of the QCD effective charge, one based on the pinch technique construction, and one obtained from the standard ghost-gluon vertex. The construction relies crucially on the definition of two dimensionful quantities, which are invariant under the renormalization group, and are built out of very particular combinations of the aforementioned Green's functions. The main non-perturbative feature of both effective charges, encoded in the infrared finiteness of the gluon propagator and ghost dressing function used in their definition, is the freezing at a common finite (non-vanishing) value, in agreement with a plethora of theoretical and phenomenological expectations. We discuss the sizable discrepancy between the freezing values obtained from the present lattice analysis and the corresponding estimates derived from several phenomenological studies, and attribute its origin to the difference in the gauges employed. A particular toy calculation suggests that the modifications induced to the non-perturbative gluon propagator by the gauge choice may indeed account for the observed deviation of the freezing values.
Keywords: Nonperturbative Effects; QCD
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Aguilar, A. C., Binosi, D., & Papavassiliou, J. (2012). Gluon mass through ghost synergy. J. High Energy Phys., 01(1), 050–32pp.
Abstract: In this work we compute, at the “one-loop-dressed” level, the nonperturbative contribution of the ghost loops to the self-energy of the gluon propagator, in the Landau gauge. This is accomplished within the PT-BFM formalism, where the contribution of the ghost-loops is inherently transverse, by virtue of the QED-like Ward identities satisfied in this framework. At the level of the “one-loop dressed” approximation, the ghost transversality is preserved by employing a suitable gauge-technique Ansatz for the longitudinal part of the full ghost-gluon vertex. Under the key assumption that the undetermined transverse part of this vertex is numerically subleading in the infrared, and using as nonperturbative input the available lattice data for the ghost dressing function, we show that the ghost contributions have a rather sizable effect on the overall shape of the gluon propagator, both for d = 3, 4. Then, by exploiting a recently introduced dynamical equation for the effective gluon mass, whose solutions depend crucially on the characteristics of the gluon propagator at intermediate energies, we show that if the ghost loops are removed from the gluon propagator then the gluon mass vanishes. These findings suggest that, at least at the level of the Schwinger-Dyson equations, the effects of gluons and ghosts are inextricably connected, and must be combined suitably in order to reproduce the results obtained in the recent lattice simulations.
Keywords: Nonperturbative Effects; QCD
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Aguilar, A. C., Binosi, D., & Papavassiliou, J. (2016). The gluon mass generation mechanism: A concise primer. Front. Phys., 11(2), 111203–18pp.
Abstract: We present a pedagogical overview of the nonperturbative mechanism that endows gluons with a dynamical mass. This analysis is performed based on pure Yang-Mills theories in the Landau gauge, within the theoretical framework that emerges from the combination of the pinch technique with the background field method. In particular, we concentrate on the Schwinger-Dyson equation satisfied by the gluon propagator and examine the necessary conditions for obtaining finite solutions within the infrared region. The role of seagull diagrams receives particular attention, as do the identities that enforce the cancellation of all potential quadratic divergences. We stress the necessity of introducing nonperturbative massless poles in the fully dressed vertices of the theory in order to trigger the Schwinger mechanism, and explain in detail the instrumental role of these poles in maintaining the Becchi-Rouet-Stora-Tyutin symmetry at every step of the mass-generating procedure. The dynamical equation governing the evolution of the gluon mass is derived, and its solutions are determined numerically following implementation of a set of simplifying assumptions. The obtained mass function is positive definite, and exhibits a power law running that is consistent with general arguments based on the operator product expansion in the ultraviolet region. A possible connection between confinement and the presence of an inflection point in the gluon propagator is briefly discussed.
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Aguilar, A. C., Binosi, D., Figueiredo, C. T., & Papavassiliou, J. (2018). Evidence of ghost suppression in gluon mass scale dynamics. Eur. Phys. J. C, 78(3), 181–15pp.
Abstract: In this work we study the impact that the ghost sector of pure Yang-Mills theories may have on the generation of a dynamical gauge boson mass scale, which hinges on the appearance of massless poles in the fundamental vertices of the theory, and the subsequent realization of the well-known Schwinger mechanism. The process responsible for the formation of such structures is itself dynamical in nature, and is governed by a set of Bethe-Salpeter type of integral equations. While in previous studies the presence of massless poles was assumed to be exclusively associated with the background-gauge three-gluon vertex, in the present analysis we allow them to appear also in the corresponding ghost-gluon vertex. The full analysis of the resulting Bethe-Salpeter system reveals that the contribution of the poles associated with the ghost-gluon vertex are particularly suppressed, their sole discernible effect being a slight modification in the running of the gluon mass scale, for momenta larger than a few GeV. In addition, we examine the behavior of the (background-gauge) ghost-gluon vertex in the limit of vanishing ghost momentum, and derive the corresponding version of Taylor's theorem. These considerations, together with a suitable Ansatz, permit us the full reconstruction of the pole sector of the two vertices involved.
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Aguilar, A. C., De Soto, F., Ferreira, M. N., Papavassiliou, J., Rodriguez-Quintero, J., & Zafeiropoulos, S. (2020). Gluon propagator and three-gluon vertex with dynamical quarks. Eur. Phys. J. C, 80(2), 154–17pp.
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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Aguilar, A. C., Ferreira, M. N., & Papavassiliou, J. (2020). Novel sum rules for the three-point sector of QCD. Eur. Phys. J. C, 80(9), 887–18pp.
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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Aguilar, A. C., Ferreira, M. N., & Papavassiliou, J. (2021). Gluon dynamics from an ordinary differential equation. Eur. Phys. J. C, 81(1), 54–20pp.
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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