Dyson–Schwinger equations furnish a Poincare covariant framework within which to study hadrons. A particular feature is the existence of a nonperturbative, symmetry preserving truncation that enables the proof of exact results. The gap equation reveals that dynamical chiral symmetry breaking is tied to the long-range behavior of the strong interaction, which is thereby constrained by observables, and the pion is precisely understood, and seen to exist simultaneously as a Goldstone mode and a bound state of strongly dressed quarks. The systematic error associated with the simplest truncation has been quantified, and it underpins a one-parameter model efficacious in describing an extensive body of mesonic phenomena. Incipient applications to baryons have brought successes and encountered challenges familiar from early studies of mesons, and promise a covariant field theory upon which to base an understanding of contemporary large momentum transfer data.

Dyson–Schwinger Equations: A Tool for Hadron Physics

https://www.ge.infn.it/jlab12/IT/files/0612014-C.F..pdf

Nucleon electromagnetic form factors

The ratio of the proton elastic electromagnetic form factors, GEp/GMp, was obtained by measuring Pt and P, the transverse and longitudinal recoil proton polarization components, respectively, for the elastic epepreaction in the four-momentum transfer squared range of 0.5 to 3.5 GeV2. In the single-photon exchange approximation, GEp/GMp is directly proportional to Pt/P. The simultaneous measurement of Pt and P in a polarimeter reduces systematic uncertainties. The results for GEp/GMp show a systematic decrease with increasing Q2, indicating for the first time a definite difference in the distribution of charge and magnetization in the proton. The data have been reanalyzed and their systematic uncertainties have become significantly smaller than those reported previously. (Less)

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Proton elastic form-factor ratios to Q**2 = 3.5-GeV**2 by polarization transfer

Baryons as relativistic three-quark bound states

We survey contemporary studies of hadrons and strongly interacting quarks using QCD's Dyson-Schwinger equations, addressing: aspects of confinement and dynamical chiral symmetry breaking; the hadron spectrum; hadron elastic and transition form factors, from small- to large-Q^2; parton distribution functions; the physics of hadrons containing one or more heavy quarks; and properties of the quark gluon plasma.

Collective perspective on advances in Dyson-Schwinger Equation QCD

The influence of the nuclear medium upon the internal structure of a composite nucleon is examined. The interaction with the medium is assumed to depend on the relative distances between the quarks in the nucleon consistent with the notion of color neutrality, and to be proportional to the nucleon density. In the resulting description the nucleon in matter is a superposition of the ground state (free nucleon) and radial excitations. The effects of the nuclear medium on the electromagnetic and weak nucleon form factors and the nucleon structure function are computed using a light-front constituent quark model. Further experimental consequences are examined by considering the electromagnetic nuclear response functions. The effects of color neutrality supply small but significant corrections to predictions of observables. {copyright} {ital 1996 The American Physical Society.}

Role of color neutrality in nuclear physics: Modifications of nucleonic wave functions

Nucleon form factors are calculated on ${q}^{2}\ensuremath{\in}[0,3]{\mathrm{GeV}}^{2}$ using an ansatz for the nucleon's Faddeev amplitude motivated by quark-diquark solutions of the relativistic Faddeev equation. Only the scalar diquark is retained, and it and the quark are confined. A good description of the data requires a nonpointlike diquark correlation with an electromagnetic radius of $0.8{r}_{\ensuremath{\pi}}.$ The composite, nonpointlike nature of the diquark is crucial. It provides for diquark-breakup terms that are of greater importance than the diquark photon absorption contribution.

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Nucleon form factors and a nonpointlike diquark

Inclusive quasielastic response functions are calculated for electron scattering in a relativistic model including momentum dependent scalar and vector mean fields. The momentum dependence of the mean fields is taken from Dirac optical fits to proton nucleus scattering and is important in describing data at momentum transfers of 1 GeV/c or larger. Our simple model is applicable for quasielastic scattering over a large range of momentum transfers.

Relativistic models for quasielastic (e,e') at large momentum transfers.

The Dyson-Schwinger equation framework is employed to obtain expressions for the electromagnetic nucleon form factor. In generalized impulse approximation the form factor depends on the dressed quark propagator, the dressed quark-photon vertex, which is crucial to ensuring current conservation, and the nucleon Faddeev amplitude. The approach manifestly incorporates the large space-like-q{sup 2} renormalization group properties of QCD and allows a realistic extrapolation to small space-like-q{sup 2}. This extrapolation allows one to relate experimental data to the form of the quark-quark interaction at small space-like-q{sup 2}, which is presently unknown. The approach provides a means of unifying, within a single framework, the treatment of the perturbative and nonperturbative regimes of QCD. The wealth of experimental nucleon form factor data, over a large range of q{sup 2}, ensures that this application will provide an excellent environment to test, improve and extend our approach.

M. R. Frank

Papers

Role of color neutrality in nuclear physics: Modifications of nucleonic wave functions

Nucleon form factors and a nonpointlike diquark

Relativistic models for quasielastic (e,e') at large momentum transfers.

Electromagnetic nucleon form factors