Studies of confinement: How the gluon propagates

Brown, N. N.; Pennington, M.R.

doi:10.1103/physrevd.39.2723

Cited by 131 publications

(168 citation statements)

References 38 publications

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“…The enhancement persists to k 2 ∼ 1-2 GeV 2 , where a perturbative analysis becomes quantitatively reliable. In the neighbourhood of k 2 = 0 the enhancement can be represented [ 3] as a regularisation of 1/k 4 as a distribution, and this behaviour is illustrated in Fig. 1.…”

Section: Gluon Propagatormentioning

confidence: 99%

“…Indeed, those Figure 1. G(k 2 )/k 2 from a solution [ 3] of the gluon DSE (dash-dot line) compared with the one-loop perturbative result (dashed line) and a fit (solid line) obtained following the method of Ref. [ 4]; i.e., requiring that the gluon propagator lead, via the quark DSE, to a good description of a range of hadron observables.…”

Section: Dyson-schwinger Equationsmentioning

confidence: 99%

“…[ 11]. It is a single, quantitative measure of whether or not a Schwinger function has a Lehmann representation, and has been used [ 12] to striking effect in QED 3 .) The chiral transition is completely characterised by two critical exponents: β, δ, which can be extracted from the behaviour of the chiral and thermal susceptibilities: [ 13] …”

Section: Chiral Phase Transition At µ =mentioning

confidence: 99%

“…It is adequate to consider a simple separable model [ 21] which preserves Goldstone's theorem and ensures the absence of a Lehmann representation for the quark propagator. This Ansatz has two parameters that can be fixed by requiring a good description of pion properties at T = 0 = µ; e.g., D 0 = 106/Λ 2 , Λ = 0.71 GeV yield f π = 93 MeV and − qq = (238 MeV) 3 . A feature of the model is that it admits a semi-algebraic analysis and at µ = 0, with these parameter values, it has second-order deconfinement and chiral symmetry restoration transitions at T c ∼ > 130 MeV, while for T = 0 these transitions are first-order at µ c = 330 MeV neglecting the effect of a diquark condensate.…”

Section: Diquarksmentioning

confidence: 99%

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Deconfinement and hadron properties at extremes of temperature and density

Blaschke

Roberts

1998

Nuclear Physics A

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After introducing essential, qualitative concepts and results, we discuss the application of Dyson-Schwinger equations to QCD at finite T and µ. We summarise the calculation of the critical exponents of two-light-flavour QCD using the chiral and thermal susceptibilities; and an algebraic model that elucidates the origin of an anticorrelation between the µ-and T -dependence of a range of meson properties. That model also provides an algebraic understanding of why the finite-T behaviour of bulk thermodynamic properties is mirrored in their µ-dependence, and why meson masses decrease with µ even though f π and − qq increase. The possibility of diquark condensation is canvassed. Its realisation is uncertain because it is contingent upon an assumption about the quark-quark scattering kernel that is demonstrably false in some applications; e.g., it predicts the existence of coloured diquarks in the strong interaction spectrum, which are not observed. DYSON-SCHWINGER EQUATIONSThe Dyson-Schwinger equations (DSEs) provide a Poincaré invariant, continuum approach to solving quantum field theories. There are many familiar examples, among them: the gap equation in superconductivity; and the Bethe-Salpeter equation (BSE) and covariant Fadde'ev equation, which describe relativistic 2-and 3-body bound states. The DSEs are a system of coupled integral equations and a truncation is necessary to obtain a tractable problem. The simplest truncation scheme is a weak-coupling expansion, which generates every diagram in perturbation theory. Hence, in the intelligent application of DSEs to QCD, there is always a tight constraint on the ultraviolet behaviour. That is crucial in extrapolating into the infrared, and in developing uniformly valid, efficacious, symmetry-preserving truncations.The task of development is not a purely numerical one, and neither is it always obviously systematic. For some, this last point diminishes the appeal of the approach. However, with growing community involvement and interest, the qualitatively robust results and intuitive understanding that the DSEs can provide is becoming clear. Indeed, those * A combined summary of two presentations,

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Section: Gluon Propagatormentioning

confidence: 99%

Section: Dyson-schwinger Equationsmentioning

confidence: 99%

Section: Chiral Phase Transition At µ =mentioning

confidence: 99%

Section: Diquarksmentioning

confidence: 99%

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Deconfinement and hadron properties at extremes of temperature and density

Blaschke

Roberts

1998

Nuclear Physics A

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“…Early studies of the Dyson-Schwinger equation for the gluon propagator in the Landau gauge concluded that the gluon propagator is highly singular in the infrared [6,7,8,9]. However, these studies neglected any contribution of the ghost fields, and moreover, required one to assume cancellations of certain leading terms in the equations.…”

Section: Introductionmentioning

confidence: 99%

Multiplicative renormalizability of gluon and ghost propagators in QCD

Bloch

2001

Phys. Rev. D

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We reformulate the coupled set of continuum equations for the renormalized gluon and ghost propagators in QCD, such that the multiplicative renormalizability of the solutions is manifest, independently of the specific form of full vertices and renormalization constants. In the Landau gauge, the equations are free of renormalization constants, and the renormalization point dependence enters only through the renormalized coupling and the renormalized propagator functions. The structure of the equations enables us to devise novel truncations with solutions that are multiplicatively renormalizable and agree with the leading order perturbative results. We show that, for infrared power law behaved propagators, the leading infrared behavior of the gluon equation is not solely determined by the ghost loop, as concluded in previous studies, but that the gluon loop, the three-gluon loop, the four-gluon loop, and even massless quarks also contribute to the infrared analysis. In our new Landau gauge truncation, the combination of gluon and ghost loop contributions seems to reject infrared power law solutions, but massless quark loops illustrate how additional contributions to the gluon vacuum polarization could reinstate these solutions. Moreover, a schematic study of the three-gluon and four-gluon loops shows that they too need to be considered in more detail before a definite conclusion about the existence of infrared power behaved gluon and ghost propagators can be reached.

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A Solution to Coupled Dyson–Schwinger Equations for Gluons and Ghosts in Landau Gauge

1998

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A truncation scheme for the Dyson Schwinger equations of QCD in Landau gauge is presented which implements the Slavnov Taylor identities for the 3-point vertex functions. Neglecting contributions from 4-point correlations such as the 4-gluon vertex function and irreducible scattering kernels, a closed system of equations for the propagators is obtained. For the pure gauge theory without quarks this system of equations for the propagators of gluons and ghosts is solved in an approximation which allows for an analytic discussion of its solutions in the infrared: The gluon propagator is shown to vanish for small spacelike momenta whereas the ghost propagator is found to be infrared enhanced. The running coupling of the non-perturbative subtraction scheme approaches an infrared stable fixed point at a critical value of the coupling, : c & 9.5. The gluon propagator is shown to have no Lehmann representation. The results for the propagators obtained here compare favorably with recent lattice calculations.1998 Academic Press

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Studies of confinement: How the gluon propagates

Cited by 131 publications

References 38 publications

Deconfinement and hadron properties at extremes of temperature and density

Deconfinement and hadron properties at extremes of temperature and density

Multiplicative renormalizability of gluon and ghost propagators in QCD

A Solution to Coupled Dyson–Schwinger Equations for Gluons and Ghosts in Landau Gauge

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