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Aguilar, A. C., De Soto, F., Ferreira, M. N., Papavassiliou, J., Pinto-Gomez, F., Roberts, C. D., et al. (2023). Schwinger mechanism for gluons from lattice QCD. Phys. Lett. B, 841, 137906–8pp.
Abstract: Continuum and lattice analyses have revealed the existence of a mass-scale in the gluon two-point Schwinger function. It has long been conjectured that this expresses the action of a Schwinger mechanism for gauge boson mass generation in quantum chromodynamics (QCD). For such to be true, it is necessary and sufficient that a dynamically-generated, massless, colour-carrying, scalar gluon+gluon correlation emerges as a feature of the dressed three-gluon vertex. Working with results on elementary Schwinger functions obtained via the numerical simulation of lattice-regularised QCD, we establish with an extremely high level of confidence that just such a feature appears; hence, confirm the conjectured origin of the gluon mass scale.
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Binosi, D., Ibañez, D., & Papavassiliou, J. (2014). Nonperturbative study of the four gluon vertex. J. High Energy Phys., 09(9), 059–32pp.
Abstract: In this paper we study the nonperturbative structure of the SU(3) four-gluon vertex in the Landau gauge, concentrating on contributions quadratic in the metric. We employ an approximation scheme where “one-loop” diagrams are computed using fully dressed gluon and ghost propagators, and tree-level vertices. When a suitable kinematical configuration depending on a single momentum scale p is chosen, only two structures emerge: the tree-level four-gluon vertex, and a tensor orthogonal to it. A detailed numerical analysis reveals that the form factor associated with this latter tensor displays a change of sign (zero-crossing) in the deep infrared, and finally diverges logarithmically. The origin of this characteristic behavior is proven to be entirely due to the masslessness of the ghost propagators forming the corresponding ghost-loop diagram, in close analogy to a similar effect established for the three-gluon vertex. However, in the case at hand, and under the approximations employed, this particular divergence does not affect the form factor proportional to the tree-level tensor, which remains finite in the entire range of momenta, and deviates moderately from its naive tree-level value. It turns out that the kinematic configuration chosen is ideal for carrying out lattice simulations, because it eliminates from the connected Green's function all one-particle reducible contributions, projecting out the genuine one-particle irreducible vertex. Motivated by this possibility, we discuss in detail how a hypothetical lattice measurement of this quantity would compare to the results presented here, and the potential interference from an additional tensorial structure, allowed by Bose symmetry, but not encountered within our scheme.
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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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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.
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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.
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Xu, S. S., Cui, Z. F., Chang, L., Papavassiliou, J., Roberts, C. D., & Zong, H. S. (2019). New perspective on hybrid mesons. Eur. Phys. J. A, 55(7), 113–6pp.
Abstract: We introduce a novel approach to the hybrid-meson (valence-gluon+quark+antiquark) bound-state problem in relativistic quantum field theory. Exploiting the existence of strong two-body correlations in the gluon-quark, q(g) = [gq], and gluon-antiquark, (q) over bar (g) = [g (q) over bar] channels, we argue that a sound description of hybrids can be obtained by solving a coupled pair of effectively two-body equations; and, consequently, that hybrids may be viewed as highly correlated q(g)(q) over bar <-> q (q) over bar (g) bound states. Analogies may be drawn between this picture of hybrid structure and that of baryons, in which diquark (quark+quark) correlations play a key role. The potential of this formulation is illustrated by calculating the spectrum of light-quark isovector hybrid mesons.
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Aguilar, A. C. et al, & Papavassiliou, J. (2019). Pion and kaon structure at the electron-ion collider. Eur. Phys. J. A, 55(10), 190–15pp.
Abstract: Understanding the origin and dynamics of hadron structure and in turn that of atomic nuclei is a central goal of nuclear physics. This challenge entails the questions of how does the roughly 1 GeV mass-scale that characterizes atomic nuclei appear; why does it have the observed value; and, enigmatically, why are the composite Nambu-Goldstone (NG) bosons in quantum chromodynamics (QCD) abnormally light in comparison? In this perspective, we provide an analysis of the mass budget of the pion and proton in QCD; discuss the special role of the kaon, which lies near the boundary between dominance of strong and Higgs mass-generation mechanisms; and explain the need for a coherent effort in QCD phenomenology and continuum calculations, in exa-scale computing as provided by lattice QCD, and in experiments to make progress in understanding the origins of hadron masses and the distribution of that mass within them. We compare the unique capabilities foreseen at the electron-ion collider (EIC) with those at the hadron-electron ring accelerator (HERA), the only previous electron-proton collider; and describe five key experimental measurements, enabled by the EIC and aimed at delivering fundamental insights that will generate concrete answers to the questions of how mass and structure arise in the pion and kaon, the Standard Model's NG modes, whose surprisingly low mass is critical to the evolution of our Universe.
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Souza, E. V., Ferreira, M. N., Aguilar, A. C., Papavassiliou, J., Roberts, C. D., & Xu, S. S. (2020). Pseudoscalar glueball mass: a window on three-gluon interactions. Eur. Phys. J. A, 56(1), 25–7pp.
Abstract: 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-mu nu rho, is poorly constrained by contemporary analyses; hence, calculations of 0(-+) glueball properties serve as a clear window onto the character and form of V-mu nu rho. This is important given that many modern calculations of V-mu nu rho 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 the suppression is essential if one is to achieve agreement with lattice-QCD predictions for the 0(-+) glueball mass. Hence, it is likely that this novel feature of V-mu nu rho is real and has observable implications for the spectrum, decays and interactions of all QCD bound-states.
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Cui, Z. F., Ding, M., Morgado, J. M., Raya, K., Binosi, D., Chang, L., et al. (2022). Concerning pion parton distributions. Eur. Phys. J. A, 58(1), 10–14pp.
Abstract: Analyses of the pion valence-quark distribution function (DF), u(pi) (x; sigma), which explicitly incorporate the behaviour of the pion wave function prescribed by quantum chromodynamics (QCD), predict u(pi) (x similar or equal to 1; sigma) similar to (1 – x)(beta(sigma)), beta(sigma greater than or similar to m(p)) > 2, where mp is the proton mass. Nevertheless, more than forty years after the first experiment to collect data suitable for extracting the x similar or equal to 1 behaviour of up, the empirical status remains uncertain because some methods used to fit existing data return a result for up that violates this constraint. Such disagreement entails one of the following conclusions: the analysis concerned is incomplete; not all data being considered are a true expression of qualities intrinsic to the pion; or QCD, as it is currently understood, is not the theory of strong interactions. New, precise data are necessary before a final conclusion is possible. In developing these positions, we exploit a single proposition, viz. there is an effective charge which defines an evolution scheme for parton DFs that is all-orders exact. This proposition has numerous corollaries, which can be used to test the character of any DF, whether fitted or calculated.
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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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