Concerning the quark condensate

Langfeld, Kurt; Markum, H.; Pullirsch, Rainer; Roberts, Craig D.; Schmidt, S.

doi:10.1103/physrevc.67.065206

Cited by 57 publications

(75 citation statements)

References 37 publications

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“…For example, it occurs as a parameter at leading order in chiral perturbation theory. It is a basic fact that only in the chiral limit is it possible to unambiguously define the gauge invariant vacuum quark condensate in terms of S(p) [32,36,37]. That such a definition is possible at all emphasises that gauge covariant quantities contain gauge invariant information.…”

Section: Dynamical Chiral Symmetry Breakingmentioning

confidence: 99%

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Hadron properties and Dyson–Schwinger equations

Roberts

2008

Progress in Particle and Nuclear Physics

184

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An overview of the theory and phenomenology of hadrons and QCD is provided from a DysonSchwinger equation viewpoint. Following a discussion of the definition and realisation of light-quark confinement, the nonperturbative nature of the running mass in QCD and inferences from the gap equation relating to the radius of convergence for expansions of observables in the current-quark mass are described. Some exact results for pseudoscalar mesons are also highlighted, with details relating to the U A (1) problem, and calculated masses of the lightest J = 0, 1 states are discussed. Studies of nucleon properties are recapitulated upon and illustrated: through a comparison of the ln-weighted ratios of Pauli and Dirac form factors for the neutron and proton; and a perspective on the contribution of quark orbital angular momentum to the spin of a nucleon at rest. Comments on prospects for the future of the study of quarks in hadrons and nuclei round out the contribution.

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Section: Dynamical Chiral Symmetry Breakingmentioning

confidence: 99%

“…8 Harking back to Sect. 2, it is interesting to note that considered as a function of current-quark mass the dressed-quark propagator possesses a spectral representation [36], confinement and DCSB notwithstanding.…”

Section: Dynamical Chiral Symmetry Breakingmentioning

confidence: 99%

Hadron properties and Dyson–Schwinger equations

Roberts

2008

Progress in Particle and Nuclear Physics

184

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“…[6,46,47] provides a context for Eqs. (37) - (40), and a connection between our reasoning and that used in other frameworks to calculate the quark condensate.…”

Section: Closer To Qcdmentioning

confidence: 99%

Dynamical chiral symmetry breaking and a critical mass

et al. 2007

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On a bounded, measurable domain of non-negative current-quark mass, realistic models of QCD's gap equation can simultaneously admit two inequivalent dynamical chiral symmetry breaking (DCSB) solutions and a solution that is unambiguously connected with the realisation of chiral symmetry in the Wigner mode. The Wigner solution and one of the DCSB solutions are destabilised by a current-quark mass and both disappear when that mass exceeds a critical value. This critical value also bounds the domain on which the surviving DCSB solution possesses a chiral expansion. This value can therefore be viewed as an upper bound on the domain within which a perturbative expansion in the current-quark mass around the chiral limit is uniformly valid for physical quantities. For a pseudoscalar meson constituted of equal mass current-quarks, it corresponds to a mass m 0 − ∼ 0.45 GeV. In our discussion we employ properties of the two DCSB solutions of the gap equation that enable a valid definition of qq in the presence of a nonzero current-mass. The behaviour of this condensate indicates that the essentially dynamical component of chiral symmetry breaking decreases with increasing current-quark mass.

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“…[24], with the results presented in Table I. The vacuum quark condensate reported in that table is obtained from the trace of the chiral-limit dressed-quark propagator [25,26] and the chiral-limit leptonic decay constant is determined from the Gell-Mann-Oakes-Renner relation: [Remember, the renormalisation point is removed to infinity when using Eq. (13).]…”

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confidence: 99%

Sketching the Bethe-Salpeter Kernel

2009

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An exact form is presented for the axial-vector Bethe-Salpeter equation, which is valid when the quark-gluon vertex is fully dressed. A Ward-Takahashi identity for the Bethe-Salpeter kernel is derived therefrom and solved for a class of dressed quark-gluon vertex models. The solution provides a symmetry-preserving closed system of gap and vertex equations. The analysis can be extended to the vector equation. This enables a comparison between the responses of pseudoscalarand scalar meson masses to nonperturbatively dressing the quark-gluon vertex. The result indicates that dynamical chiral symmetry breaking enhances spin-orbit splitting in the meson spectrum.

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Concerning the quark condensate

Cited by 57 publications

References 37 publications

Hadron properties and Dyson–Schwinger equations

Hadron properties and Dyson–Schwinger equations

Dynamical chiral symmetry breaking and a critical mass

Sketching the Bethe-Salpeter Kernel

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