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Aguilar, A. C., Binosi, D., & Papavassiliou, J. (2013). Gluon mass generation in the presence of dynamical quarks. Phys. Rev. D, 88(7), 074010–12pp.
Abstract: We study in detail the impact of dynamical quarks on the gluon mass generation mechanism, in the Landau gauge, for the case of a small number of quark families. As in earlier considerations, we assume that the main bulk of the unquenching corrections to the gluon propagator originates from the fully dressed quark-loop diagram. The nonperturbative evaluation of this diagram provides the key relation that expresses the unquenched gluon propagator as a deviation from its quenched counterpart. This relation is subsequently coupled to the integral equation that controls the momentum evolution of the effective gluon mass, which contains a single adjustable parameter; this constitutes a major improvement compared to the analysis presented in Aguilar et al. [Phys. Rev. D 86, 014032 (2012)], where the behavior of the gluon propagator in the deep infrared was estimated through numerical extrapolation. The resulting nonlinear system is then treated numerically, yielding unique solutions for the modified gluon mass and the quenched gluon propagator, which fully confirms the picture put forth recently in several continuum and lattice studies. In particular, an infrared finite gluon propagator emerges, whose saturation point is considerably suppressed, due to a corresponding increase in the value of the gluon mass. This characteristic feature becomes more pronounced as the number of active quark families increases, and can be deduced from the infrared structure of the kernel entering in the gluon mass equation.
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Ibañez, D., & Papavassiliou, J. (2013). Gluon mass generation in the massless bound-state formalism. Phys. Rev. D, 87(3), 034008–25pp.
Abstract: We present a detailed, all-order study of gluon mass generation within the massless bound-state formalism, which constitutes the general framework for the systematic implementation of the Schwinger mechanism in non-Abelian gauge theories. The main ingredient of this formalism is the dynamical formation of bound states with vanishing mass, which give rise to effective vertices containing massless poles; these latter vertices, in turn, trigger the Schwinger mechanism, and allow for the gauge-invariant generation of an effective gluon mass. This particular approach has the conceptual advantage of relating the gluon mass directly to quantities that are intrinsic to the bound-state formation itself, such as the “transition amplitude'' and the corresponding ”bound-state wave function.'' As a result, the dynamical evolution of the gluon mass is largely determined by a Bethe-Salpeter equation that controls the dynamics of the relevant wave function, rather than the Schwinger-Dyson equation of the gluon propagator, as happens in the standard treatment. The precise structure and field-theoretic properties of the transition amplitude are scrutinized in a variety of independent ways. In particular, a parallel study within the linear-covariant (Landau) gauge and the background-field method reveals that a powerful identity, known to be valid at the level of conventional Green's functions, also relates the background and quantum transition amplitudes. Despite the differences in the ingredients and terminology employed, the massless bound-state formalism is absolutely equivalent to the standard approach based on Schwinger-Dyson equations. In fact, a set of powerful relations allows one to demonstrate the exact coincidence of the integral equations governing the momentum evolution of the gluon mass in both frameworks.
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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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Horak, J., Ihssen, F., Papavassiliou, J., Pawlowski, J. M., Weber, A., & Wetterich, C. (2022). Gluon condensates and effective gluon mass. SciPost Phys., 13(2), 042–40pp.
Abstract: Lattice simulations along with studies in continuum QCD indicate that non-perturbative quantum fluctuations lead to an infrared regularisation of the gluon propagator in covariant gauges in the form of an effective mass-like behaviour. In the present work we propose an analytic understanding of this phenomenon in terms of gluon condensation through a dynamical version of the Higgs mechanism, leading to the emergence of color condensates. Within the functional renormalisation group approach we compute the effective potential of covariantly constant field strengths, whose non-trivial minimum is related to the color condensates. In the physical case of an SU(3) gauge group this is an octet condensate. The value of the gluon mass obtained through this procedure compares very well to lattice results and the mass gap arising from alternative dynamical scenarios.
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Horak, J., Papavassiliou, J., Pawlowski, J. M., & Wink, N. (2021). Ghost spectral function from the spectral Dyson-Schwinger equation. Phys. Rev. D, 104(7), 074017–16pp.
Abstract: We compute the ghost spectral function in Yang-Mills theory by solving the corresponding Dyson-Schwinger equation for a given input gluon spectral function. The results encompass both scaling and decoupling solutions for the gluon propagator input. The resulting ghost spectral function displays a particle peak at vanishing momentum and a negative scattering spectrum, whose infrared and ultraviolet tails are obtained analytically. The ghost dressing function is computed in the entire complex plane, and its salient features are identified and discussed.
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Aguilar, A. C., Ibañez, D., & Papavassiliou, J. (2013). Ghost propagator and ghost-gluon vertex from Schwinger-Dyson equations. Phys. Rev. D, 87(11), 114020–14pp.
Abstract: We study an approximate version of the Schwinger-Dyson equation that controls the nonperturbative behavior of the ghost-gluon vertex in the Landau gauge. In particular, we focus on the form factor that enters in the dynamical equation for the ghost dressing function, in the same gauge, and derive its integral equation, in the “one-loop dressed” approximation. We consider two special kinematic configurations, which simplify the momentum dependence of the unknown quantity; in particular, we study the soft gluon case and the well-known Taylor limit. When coupled with the Schwinger-Dyson equation of the ghost dressing function, the contribution of this form factor provides considerable support to the relevant integral kernel. As a consequence, the solution of this coupled system of integral equations furnishes a ghost dressing function that reproduces the standard lattice results rather accurately, without the need to artificially increase the value of the gauge coupling.
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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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Ferreira, M. N., & Papavassiliou, J. (2023). Gauge Sector Dynamics in QCD. Particles, 6(1), 312–363.
Abstract: The dynamics of the QCD gauge sector give rise to non-perturbative phenomena that are crucial for the internal consistency of the theory; most notably, they account for the generation of a gluon mass through the action of the Schwinger mechanism, the taming of the Landau pole, the ensuing stabilization of the gauge coupling, and the infrared suppression of the three-gluon vertex. In the present work, we review some key advances in the ongoing investigation of this sector within the framework of the continuum Schwinger function methods, supplemented by results obtained from lattice simulations.
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Binosi, D., & Papavassiliou, J. (2011). Gauge invariant Ansatz for a special three-gluon vertex. J. High Energy Phys., 03(3), 121–23pp.
Abstract: We construct a general Ansatz for the three-particle vertex describing the interaction of one background and two quantum gluons, by simultaneously solving the Ward and Slavnov-Taylor identities it satisfies. This vertex is known to be essential for the gauge-invariant truncation of the Schwinger-Dyson equations of QCD, based on the pinch technique and the background field method. A key step in this construction is the formal derivation of a set of crucial constraints (shown to be valid to all orders), relating the various form factors of the ghost Green's functions appearing in the aforementioned Slavnov-Taylor identity. When inserted into the Schwinger-Dyson equation for the gluon propagator, this vertex gives rise to a number of highly non-trivial cancellations, which are absolutely indispensable for the self-consistency of the entire approach.
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Gao, F., Papavassiliou, J., & Pawlowski, J. M. (2021). Fully coupled functional equations for the quark sector of QCD. Phys. Rev. D, 103(9), 094013–25pp.
Abstract: We present a comprehensive study of the quark sector of 2 + 1 flavor QCD, based on a self-consistent treatment of the coupled system of Schwinger-Dyson equations for the quark propagator and the full quark-gluon vertex in the one-loop dressed approximation. The individual form factors of the quark-gluon vertex are expressed in a special tensor basis obtained from a set of gauge-invariant operators. The sole external ingredient used as input to our equations is the Landau gauge gluon propagator with 2 + 1 dynamical quark flavors, obtained from studies with Schwinger-Dyson equations, the functional renormalization group approach, and large volume lattice simulations. The appropriate renormalization procedure required in order to self-consistently accommodate external inputs stemming from other functional approaches or the lattice is discussed in detail, and the value of the gauge coupling is accurately determined at two vastly separated renormalization group scales. Our analysis establishes a clear hierarchy among the vertex form factors. We identify only three dominant ones, in agreement with previous results. The components of the quark propagator obtained from our approach are in excellent agreement with the results from Schwinger-Dyson equations, the functional renormalization group, and lattice QCD simulation, a simple benchmark observable being the chiral condensate in the chiral limit, which is computed as (245 MeV)(3). The present approach has a wide range of applications, including the self-consistent computation of bound-state properties and finite temperature and density physics, which are briefly discussed.
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