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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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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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Pinto-Gomez, F., De Soto, F., Ferreira, M. N., Papavassiliou, J., & Rodriguez-Quintero, J. (2023). Lattice three-gluon vertex in extended kinematics: Planar degeneracy. Phys. Lett. B, 838, 137737–8pp.
Abstract: We present novel results for the three-gluon vertex, obtained from an extensive quenched lattice simulation in the Landau gauge. The simulation evaluates the transversely projected vertex, spanned on a special tensorial basis, whose form factors are naturally parametrized in terms of individually Bosesymmetric variables. Quite interestingly, when evaluated in these kinematics, the corresponding form factors depend almost exclusively on a single kinematic variable, formed by the sum of the squares of the three incoming four-momenta, q, r, and p. Thus, all configurations lying on a given plane in the coordinate system (q2, r2, p2) share, to a high degree of accuracy, the same form factors, a property that we denominate planar degeneracy. We have confirmed the validity of this property through an exhaustive study of the set of configurations satisfying the condition q2 = r2, within the range [0, 5 GeV]. This drastic simplification allows for a remarkably compact description of the main bulk of the data, which is particularly suitable for future numerical applications. A semi-perturbative analysis reproduces the lattice findings rather accurately, once the inclusion of a gluon mass has cured all spurious divergences.
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Papavassiliou, J. (2022). Emergence of mass in the gauge sector of QCD. Chin. Phys. C, 46(11), 112001–23pp.
Abstract: It is currently widely accepted that gluons, while massless at the level of the fundamental QCD Lagrangian, acquire an effective mass through the non-Abelian implementation of the classic Schwinger mechanism. The key dynamical ingredient that triggers the onset of this mechanism is the formation of composite massless poles inside the fundamental vertices of the theory. These poles enter the evolution equation of the gluon propagator and nontrivially affect the way the Slavnov-Taylor identities of the vertices are resolved, inducing a smoking-gun displacement in the corresponding Ward identities. In this article, we present a comprehensive review of the pivotal concepts associated with this dynamical scenario, emphasizing the synergy between functional methods and lattice simulations and highlighting recent advances that corroborate the action of the Schwinger mechanism in QCD.
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Mavromatos, N. E., & Papavassiliou, J. (2018). Singular lensing from the scattering on special space-time defects. Eur. Phys. J. C, 78(1), 68–15pp.
Abstract: It is well known that certain special classes of self-gravitating point-like defects, such as global (non gauged) monopoles, give rise to non-asymptotically flat space-times characterized by solid angle deficits, whose size depends on the details of the underlying microscopic models. The scattering of electrically neutral particles on such space-times is described by amplitudes that exhibit resonant behaviour when thescattering and deficit angles coincide. This, in turn, leads to ring-like structures where the cross sections are formally divergent (“singular lensing”). In this work, we revisit this particular phenomenon, with the twofold purpose of placing it in a contemporary and more general context, in view of renewed interest in the theory and general phenomenology of such defects, and, more importantly, of addressing certain subtleties that appear in the particular computation that leads to the aforementioned effect. In particular, by adopting a specific regularization procedure for the formally infinite Legendre series encountered, we manage to ensure the recovery of theMinkowski space-time, and thus the disappearance of the lensing phenomenon, in the nodefect limit, and the validity of the optical theorem for the elastic total cross section. In addition, the singular nature of the phenomenon is confirmed by means of an alternative calculation, which, unlike the original approach, makes no use of the generating function of the Legendre polynomials, but rather exploits the asymptotic properties of the Fresnel integrals.
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Ibañez, D., & Papavassiliou, J. (2013). Gluon mass generation in the massless bound-state formalism. Phys. Rev. D, 87(3), 034008–25pp.
Abstract: We present a detailed, all-order study of gluon mass generation within the massless bound-state formalism, which constitutes the general framework for the systematic implementation of the Schwinger mechanism in non-Abelian gauge theories. The main ingredient of this formalism is the dynamical formation of bound states with vanishing mass, which give rise to effective vertices containing massless poles; these latter vertices, in turn, trigger the Schwinger mechanism, and allow for the gauge-invariant generation of an effective gluon mass. This particular approach has the conceptual advantage of relating the gluon mass directly to quantities that are intrinsic to the bound-state formation itself, such as the “transition amplitude'' and the corresponding ”bound-state wave function.'' As a result, the dynamical evolution of the gluon mass is largely determined by a Bethe-Salpeter equation that controls the dynamics of the relevant wave function, rather than the Schwinger-Dyson equation of the gluon propagator, as happens in the standard treatment. The precise structure and field-theoretic properties of the transition amplitude are scrutinized in a variety of independent ways. In particular, a parallel study within the linear-covariant (Landau) gauge and the background-field method reveals that a powerful identity, known to be valid at the level of conventional Green's functions, also relates the background and quantum transition amplitudes. Despite the differences in the ingredients and terminology employed, the massless bound-state formalism is absolutely equivalent to the standard approach based on Schwinger-Dyson equations. In fact, a set of powerful relations allows one to demonstrate the exact coincidence of the integral equations governing the momentum evolution of the gluon mass in both frameworks.
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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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