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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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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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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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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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Cui, Z. F., Zhang, J. L., Binosi, D., De Soto, F., Mezrag, C., Papavassiliou, J., et al. (2020). Effective charge from lattice QCD. Chin. Phys. C, 44(8), 083102–10pp.
Abstract: Using lattice configurations for quantum chromodynamics (QCD) generated with three domain-wall fermions at a physical pion mass, we obtain a parameter-free prediction of QCD 's renormalisation-group-invariant process-independent effective charge, (alpha) over cap (k(2)). Owing to the dynamical breaking of scale invariance, evident in the emergence of a gluon mass-scale, m(0) = 0.43(1) GeV, this coupling saturates at infrared momenta: (alpha) over cap/pi = 0.97(4). Amongst other things: (alpha) over cap (k(2)) is almost identical to the process-dependent (PD) effective charge defined via the Bjorken sum rule; and also that PD charge which, employed in the one-loop evolution equations, delivers agreement between pion parton distribution functions computed at the hadronic scale and experiment. The diversity of unifying roles played by (alpha) over cap (k(2)) suggests that it is a strong candidate for that object which represents the interaction strength in QCD at any given momentum scale; and its properties support a conclusion that QCD is a mathematically well-defined quantum field theory in four dimensions.
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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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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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Binosi, D., & Papavassiliou, J. (2018). Coupled dynamics in gluon mass generation and the impact of the three-gluon vertex. Phys. Rev. D, 97(5), 054029–15pp.
Abstract: We present a detailed study of the subtle interplay transpiring at the level of two integral equations that are instrumental for the dynamical generation of a gluon mass in pure Yang-Mills theories. The main novelty is the joint treatment of the Schwinger-Dyson equation governing the infrared behavior of the gluon propagator and of the integral equation that controls the formation of massless bound-state excitations, whose inclusion is instrumental for obtaining massive solutions from the former equation. The self-consistency of the entire approach imposes the requirement of using a single value for the gauge coupling entering in the two key equations; its fulfilment depends crucially on the details of the three-gluon vertex, which contributes to both of them, but with different weight. In particular, the characteristic suppression of this vertex at intermediate and low energies enables the convergence of the iteration procedure to a single gauge coupling, whose value is reasonably close to that extracted from related lattice simulations.
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Binosi, D., Mezrag, C., Papavassiliou, J., Roberts, C. D., & Rodriguez-Quintero, J. (2017). Process-independent strong running coupling. Phys. Rev. D, 96(5), 054026–7pp.
Abstract: We unify two widely different approaches to understanding the infrared behavior of quantum chromodynamics (QCD), one essentially phenomenological, based on data, and the other computational, realized via quantum field equations in the continuum theory. Using the latter, we explain and calculate a process-independent running coupling for QCD, a new type of effective charge that is an analogue of the Gell-Mann-Low effective coupling in quantum electrodynamics. The result is almost identical to the process-dependent effective charge defined via the Bjorken sum rule, which provides one of the most basic constraints on our knowledge of nucleon spin structure. This reveals the Bjorken sum to be a near direct means by which to gain empirical insight into QCD's Gell-Mann-Low effective charge.
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Binosi, D., Ibañez, D., & Papavassiliou, J. (2012). All-order equation of the effective gluon mass. Phys. Rev. D, 86(8), 085033–21pp.
Abstract: We present the general derivation of the full nonperturbative equation that governs the momentum evolution of the dynamically generated gluon mass, in the Landau gauge. The entire construction hinges crucially on the inclusion of longitudinally coupled vertices containing massless poles of nonperturbative origin, which preserve the form of the fundamental Slavnov-Taylor identities of the theory. The mass equation is obtained from a previously unexplored version of the Schwinger-Dyson equation for the gluon propagator, particular to the pinch technique-background field method formalism, which involves a reduced number of two-loop dressed diagrams, thus simplifying the calculational task considerably. The two-loop contributions turn out to be of paramount importance, modifying the qualitative features of the full mass equation and enabling the emergence of physically meaningful solutions. Specifically, the resulting homogeneous integral equation is solved numerically, subject to certain approximations, for the entire range of physical momenta, yielding positive-definite and monotonically decreasing gluon masses.
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