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Aguilar, A. C., Ferreira, M. N., Figueiredo, C. T., & Papavassiliou, J. (2019). Nonperturbative Ball-Chiu construction of the three-gluon vertex. Phys. Rev. D, 99(9), 094010–30pp.
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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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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Nunes da Silva, T., Chinellato, D. D., Giannini, A. V., Takahashi, J., Ferreira, M. N., Denicol, G. S., et al. (2023). Prehydrodynamic evolution in large and small systems. Phys. Rev. C, 107(4), 044901–12pp.
Abstract: We extend our previous investigation of the effects of prehydrodynamic evolution on final-state observables in heavy-ion collisions [38] to smaller systems. We use a state-of-the-art hybrid model for the numerical simulations with optimal parameters obtained from a previous Bayesian study. By studying p-Pb collisions, we find that the effects due to the assumption of a conformal evolution in the prehydrodynamical stage are even more important in small systems. We also show that this effect depends on the time duration of the pre-equilibrium stage, which is further enhanced in small systems. Finally, we show that the recent proposal of a free-streaming with subluminal velocity for the pre-equilibrium stage, thus effectively breaking conformal invariance, can alleviate the contamination of final-state observables. Our study further reinforces the need for moving beyond conformal approaches in pre-equilibrium dynamics modeling, especially when extracting transport coefficients from hybrid models in the high-precision era of heavy-ion collisions.
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