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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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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., & 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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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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