Dyson–Schwinger Equations: A Tool for Hadron Physics

Maris, Pieter; Roberts, C. D.

doi:10.1142/s0218301303001326

Cited by 613 publications

(725 citation statements)

References 152 publications

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“…[27], which has served as an archetype for numerous efficacious applications, as can be seen, e.g., from Refs. [28,29,30,31]. [11,33], "data" -numerical simulations of unquenched lattice-QCD [34].…”

Section: Confinementmentioning

confidence: 99%

Hadron properties and Dyson–Schwinger equations

Roberts

2008

Progress in Particle and Nuclear Physics

186

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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: Confinementmentioning

confidence: 99%

Hadron properties and Dyson–Schwinger equations

Roberts

2008

Progress in Particle and Nuclear Physics

186

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“…Here, we are using a 2-parameter model for the effective interaction [8], fitted to give a value for the chiral condensate of (240 MeV) 3 and f π = 131 MeV. This effective running coupling, with Λ QCD = 0.234 GeV and N f = 4, is shown in Fig.…”

Section: Rainbow-ladder Truncationmentioning

confidence: 99%

“…Refs. [1,2,3] and references therein. Provided that the (effective) quark-quark interaction reduces to the perturbative running coupling in the ultraviolet region, it is also straightforward to reproduce the asymptotic behavior of Eqs.…”

Section: Quark Propagatormentioning

confidence: 99%

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QCD modeling of hadron physics

Maris

Tandy

2006

Nuclear Physics B - Proceedings Supplements

103

120

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We review recent developments in the understanding of meson properties as solutions of the Bethe-Salpeter equation in rainbow-ladder truncation. Included are recent results for the pseudoscalar and vector meson masses and leptonic decay constants, ranging from pions up to cc bound states; extrapolation to bb states is explored. We also present a new and improved calculation of Fπ(Q 2 ) and an analysis of the πγγ transition form factor for both π(140) and π(1330). Lattice-QCD results for propagators and the quark-gluon vertex are analyzed, and the effects of quark-gluon vertex dressing and the three-gluon coupling upon meson masses are considered. DYSON-SCHWINGER EQUATIONS OF QCDThe Dyson-Schwinger equations [DSEs] are the equations of motion of a quantum field theory. They form an infinite hierarchy of coupled integral equations for the Green's functions (n-point functions) of the theory. Bound states (mesons, baryons) appear as poles in the Green's functions. Thus, a study of the poles in n-point functions using the set of DSEs will tell us something about hadrons. For recent reviews on the DSEs and their use in hadron physics, see Refs. [1,2,3]. Quark propagatorThe exact DSE for the quark propagator is 1where D µν (q = k − p) is the renormalized dressed gluon propagator, and Γ i ν (k, p) is the renormalized dressed quark-gluon vertex. The notation k stands for Λ d 4 k/(2π) 4 . For divergent integrals a translationally invariant regularization is necessary; the regularization scale Λ is to be removed at the end of all calculations, after renormalization, and will be suppressed henceforth.1 We use Euclidean metric {γµ, γν } = 2δµν , γ † µ = γµ andThe solution of Eq. (1) can be written asrenormalized according to S(p) −1 = i / p + m(µ) at a sufficiently large spacelike µ 2 , with m(µ) the current quark mass at the scale µ. Both the propagator, S(p), and the vertex, Γ i µ depend on the quark flavor, although we have not indicated this explicitly. The renormalization constants Z 2 and Z 4 depend on the renormalization point and on the regularization mass-scale, but not on flavor: in our analysis we employ a flavor-independent renormalization scheme. MesonsBound states correspond to poles in n-point functions: for example a meson appears as a pole in the 2-quark, 2-antiquark Green's function G (4) = 0|q 1 q 2q1q2 |0 . In the vicinity of a meson, i.e. in the neighborhood of P 2 = −M 2 with M being the meson mass, such a Green's function behaves likewhere P is the total 4-momentum of the meson, p o and p i are the momenta of the outgoing quark and incoming quark respectively, and similarly for k i and k o . Momentum conservation relates these momenta:

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“…In recent years there has been significant progress in the study of the spectrum of hadrons, as well as their non-perturbative structure and form factors, through approaches that are manifestly covariant and which accommodate both dynamical chiral symmetry breaking (DCSB) and quark confinement [1]. Covariance provides efficient and unambiguous access to form factors [2,3,4] and parton distribution functions [5].…”

Section: Introductionmentioning

confidence: 99%

Consequences of fully dressing quark–gluon vertex function with two-point gluon lines

Matevosyan

Thomas

Tandy

2007

J. Phys. G: Nucl. Part. Phys.

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We extend recent studies of the effects of quark-gluon vertex dressing upon the solutions of the Dyson-Schwinger equation for the quark propagator. A momentum delta function is used to represent the dominant infrared strength of the effective gluon propagator so that the resulting integral equations become algebraic. The guark-gluon vertex is constructed from the complete set of diagrams involving only 2-point gluon lines. The additional diagrams, including those with crossed gluon lines, are shown to make an important contribution to the DSE solutions for the quark propagator, because of their large color factors and the rapid growth in their number.

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Dyson–Schwinger Equations: A Tool for Hadron Physics

Cited by 613 publications

References 152 publications

Hadron properties and Dyson–Schwinger equations

Hadron properties and Dyson–Schwinger equations

QCD modeling of hadron physics

Consequences of fully dressing quark–gluon vertex function with two-point gluon lines

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