On the dependence of the gauge-invariant field-strength correlators in QCD on the shape of the Schwinger string

Giacomo, A. Di; Meggiolaro, Enrico

doi:10.1016/s0370-2693(02)01909-3

Cited by 17 publications

(13 citation statements)

References 26 publications

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“…In Appendix C, we have also demonstrated that, in accordance with the lattice results of Ref. [115], the correlation length of nonperturbative-nonconfining interactions of the background fields decreases with the deformation of the path interconnecting the two points in the correlation function (120). Finally, as has been announced at the beginning of this Section, let us discuss a possible modification of the 4D dual Abelian Higgs model, which can allow for the existence of different correlation lengths of the functions D(x) and D 1 (x).…”

Section: Correlation Lengths Of the Stochastic Yang-mills Fieldssupporting

confidence: 89%

“…This calculation allows us to show that the correlation length of nonperturbative-nonconfining self-interactions of the background fields decreases with the deformation of that trajectory, in agreement with the lattice results of Ref. [115].…”

Section: Correlation Lengths Of the Stochastic Yang-mills Fieldssupporting

confidence: 89%

“…Rather, inclusion of the higher-twist contribution according to Equation (115), with the parameter λ given by Equation (116), yields for the full quantity…”

Section: Yang-mills Running Coupling With An Ir-stable Fixed Pointmentioning

confidence: 99%

“…In spite of the numerical support provided by the dedicated lattice simulations [41][42][43][44][45]71,115], the stochastic vacuum model needs also a theoretical support in the form of analytic studies of the two-point correlation function. Such calculations have been initially performed in various Abelian models, where confinement is provided by the monopole condensation.…”

Section: Correlation Lengths Of the Stochastic Yang-mills Fieldsmentioning

confidence: 99%

“…Lattice simulations [115] indicate that, if the path in the phase factors on the left-hand side of Equation (120) deviates from the straight-line one, the correlation function decreases. In this Appendix, we test this indication by analytically calculating function D 1 (x) for paths of various shapes.…”

Section: Appendix B Scalar Curvature In the Tolman-oppenheimer-volkomentioning

confidence: 99%

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World-Line Formalism: Non-Perturbative Applications

Bellettre

2016

Universe

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This review addresses the impact on various physical observables which is produced by confinement of virtual quarks and gluons at the level of the one-loop QCD diagrams. These observables include the quark condensate for various heavy flavors, the Yang-Mills running coupling with an infra-red stable fixed point, and the correlation lengths of the stochastic Yang-Mills fields. Other non-perturbative applications of the world-line formalism presented in the review are devoted to the determination of the electroweak phase-transition critical temperature, to the derivation of a semi-classical analogue of the relation between the chiral and the gluon QCD condensates, and to the calculation of the free energy of the gluon plasma in the high-temperature limit. As a complementary result, we demonstrate Casimir scaling of k-string tensions in the Gaussian ensemble of the stochastic Yang-Mills fields.Keywords: the world-line formalism; Wilson loops; analytic calculations of path integrals with the minimal-area surfaces; theoretical foundations of the stochastic vacuum model; confinement and chiral-symmetry breaking in QCD; gluonic bound states; Casimir scaling; the Yang-Mills running coupling; thermodynamics of the gluon plasma; electroweak phase transition Quark Condensate for Various Heavy FlavorsAs is well known, because of confinement in QCD, quarks and gluons do not exist as individual particles, but appear only in the form of bound states (for recent reviews, see [1,2]). The latter include mesons, baryons (as well as other possible quark bound states, such as tetra-and pentaquarks), glueballs, and the so-called hybrids consisting of a quark, an antiquark, and one or several gluons. Each bound state can be represented as an average of a certain operator over the Euclidean QCD vacuum. Since the vacuum state is gauge-invariant, only the gauge-invariant operators yield non-vanishing results once averaged over it. (This statement can be viewed as a corollary of the so-called Elitzur theorem [3,4], which states that a local gauge symmetry cannot be broken spontaneously.) For local composite operators, such asψψ or (F a µν ) 2 , gauge invariance holds automatically, and the mean values of these operators yield the QCD condensates [5,6]. Nevertheless, the quark and the gluon bound states are in general represented by the field operators which are defined at different points of the Euclidean space, so that a phase factor (also called a parallel transporter or a Schwinger string) interpolating between these points is required in order to provide gauge invariance of the full non-local operator. That is, the non-local gauge-invariant operators have, e.g., the formψ i (x)Φ ij xxwhere Φ ij xx and Φ ab xx are the phase factors transforming under the fundamental and the adjoint representations of SU(N), respectively, with i, j = 1, . . . , N and a, b = 1, . . . , N 2 − 1. (Throughout this review, we denote the number of colors by N.) Thus, the phase factors provide long-range correlations of color between individual quark...

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Section: Correlation Lengths Of the Stochastic Yang-mills Fieldssupporting

confidence: 89%

Section: Correlation Lengths Of the Stochastic Yang-mills Fieldssupporting

confidence: 89%

“…Rather, inclusion of the higher-twist contribution according to Equation (115), with the parameter λ given by Equation (116), yields for the full quantity…”

Section: Yang-mills Running Coupling With An Ir-stable Fixed Pointmentioning

confidence: 99%

Section: Correlation Lengths Of the Stochastic Yang-mills Fieldsmentioning

confidence: 99%

Section: Appendix B Scalar Curvature In the Tolman-oppenheimer-volkomentioning

confidence: 99%

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World-Line Formalism: Non-Perturbative Applications

Bellettre

2016

Universe

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Wilson-loop formalism for Reggeon exchange in soft high-energy scattering

Giordano

2012

J. High Energ. Phys.

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We derive a nonperturbative expression for the non-vacuum, qq-Reggeon-exchange contribution to the meson-meson elastic scattering amplitude at high energy and low momentum transfer, in the framework of QCD. Describing the mesons in terms of colourless qq dipoles, the problem is reduced to the two-fermion-exchange contribution to the dipole-dipole scattering amplitudes, which is expressed as a path integral, over the trajectories of the exchanged fermions, of the expectation value of a certain Wilson loop. We also show how the resulting expression can be reconstructed from a corresponding quantity in the Euclidean theory, by means of analytic continuation. Finally, we make contact with previous work on Reggeon exchange in the gauge/gravity duality approach.

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Asymptotic energy dependence of hadronic total cross sections from lattice QCD

Giordano

Meggiolaro

Moretti

2012

J. High Energ. Phys.

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The nonperturbative approach to soft high-energy hadron-hadron scattering, based on the analytic continuation of Wilson-loop correlation functions from Euclidean to Minkowskian theory, allows to investigate the asymptotic energy dependence of hadron-hadron total cross sections in lattice QCD. In this paper we will show, using best fits of the lattice data with proper functional forms satisfying unitarity and other physical constraints, how indications emerge in favor of a universal asymptotic high-energy behavior of the kind B log 2 s for hadronic total cross sections. *

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On the dependence of the gauge-invariant field-strength correlators in QCD on the shape of the Schwinger string

Abstract: We study, by numerical simulations on a lattice, the dependence of the gauge-invariant two-point field-strength correlators in QCD on the path used to perform the color parallel transport between the two points. (PACS code: 12.38.Gc) *

Cited by 17 publications

References 26 publications

World-Line Formalism: Non-Perturbative Applications

World-Line Formalism: Non-Perturbative Applications

Wilson-loop formalism for Reggeon exchange in soft high-energy scattering

Asymptotic energy dependence of hadronic total cross sections from lattice QCD

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