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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., Brito, N., Ferreira, M. N., Papavassiliou, J., Oliveira, O., & Silva, P. J. (2024). Lattice determination of the Batalin-Vilkovisky function and the strong running interaction. Phys. Lett. B, 858, 139054–8pp.
Abstract: The Batalin-Vilkovisky function is a central component in the modern formulation of the background field method and the physical applications derived from it. In the present work we report on novel lattice results for this particular quantity, obtained by capitalizing on its equality with the Kugo-Ojima function in the Landau gauge. The results of the lattice simulation are in very good agreement with the predictions derived from a continuum analysis based on the corresponding Schwinger-Dyson equations. In addition, we show that an important relation connecting this function with the ghost propagator is fulfilled rather accurately. With the aid of these results, we carry out the first completely lattice-based determination of the process-independent strong running interaction, employed in a variety of phenomenological studies.
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Aguilar, A. C., De Soto, F., Ferreira, M. N., Papavassiliou, J., Pinto-Gomez, F., Rodríguez-Quintero, J., et al. (2024). Nonperturbative four-gluon vertex in soft kinematics. Phys. Lett. B, 858, 139065–7pp.
Abstract: We present a nonperturbative study of the form factor associated with the projection of the full four-gluon vertex on its classical tensor, for a set of kinematics with one vanishing and three arbitrary external momenta. The treatment is based on the Schwinger-Dyson equation governing this vertex, and a large-volume lattice simulation, involving ten thousand gauge field configurations. The key hypothesis employed in both approaches is the “planar degeneracy”, which classifies diverse configurations by means of a single variable, thus enabling their meaningful “averaging”. The results of both approaches show notable agreement, revealing a considerable suppression of the averaged form factor in the infrared. The deviations from the exact planar degeneracy are discussed in detail, and a supplementary variable is used to achieve a more accurate description. The effective charge defined through this special form factor is computed within both approaches, and the results obtained are in excellent agreement.
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Aguilar, A. C., De Soto, F., Ferreira, M. N., Papavassiliou, J., & Rodriguez-Quintero, J. (2021). Infrared facets of the three-gluon vertex. Phys. Lett. B, 818, 136352–7pp.
Abstract: 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.
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Athenodorou, A., Binosi, D., Boucaud, P., De Soto, F., Papavassiliou, J., Rodriguez-Quintero, J., et al. (2016). On the zero crossing of the three-gluon vertex. Phys. Lett. B, 761, 444–449.
Abstract: We report on new results on the infrared behavior of the three-gluon vertex in quenched Quantum Chromodynamics, obtained from large-volume lattice simulations. The main focus of our study is the appearance of the characteristic infrared feature known as 'zero crossing', the origin of which is intimately connected with the nonperturbative masslessness of the Faddeev-Popov ghost. The appearance of this effect is clearly visible in one of the two kinematic configurations analyzed, and its theoretical origin is discussed in the framework of Schwinger-Dyson equations. The effective coupling in the momentum subtraction scheme that corresponds to the three-gluon vertex is constructed, revealing the vanishing of the effective interaction at the exact location of the zero crossing.
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