Recent Advances in Dyson-Schwinger Studies

There have been many demonstrations of the utility of the Dyson-Schwinger equations of QCD as a systematic, phenomenological framework for describing the perturbative and non-perturbative dynamics of hadrons in terms of Euclidean Green functions of quarks and gluons. Still, there remain some unanswered questions regarding the theoretical underpinnings of the approach. I review several studies that are shedding light on how these questions might be resolved and review predictions for some exotic meson states.Comment: Plenary talk at N-Star 2002. 5 pages, 3 figure

Current Conservation in the Covariant Quark-Diquark Model of the Nucleon

The description of baryons as fully relativistic bound states of quark and glue reduces to an effective Bethe-Salpeter equation with quark-exchange interaction when irreducible 3-quark interactions are neglected and separable 2-quark (diquark) correlations are assumed. This covariant quark-diquark model of baryons is studied with the inclusion of the quark substructure of the diquark correlations. In order to maintain electromagnetic current conservation it is then necessary to go beyond the impulse approximation. A conserved current is obtained by including the coupling of the photon to the exchanged quark and direct ``seagull'' couplings to the diquark structure. Adopting a simple dynamical model of constituent quarks and exploring various parametrisations of scalar diquark correlations, the nucleon Bethe-Salpeter equation is solved and the proton and neutron electromagnetic form factors are calculated numerically. The resulting magnetic moments are still about 50% too small, the improvements necessary to remedy this are discussed. The results obtained in this framework provide an excellent description of the electric form factors (and charge radii) of the proton, up to a photon momentum transfer of 3.5GeV^2, and the neutron.Comment: 30 Pages, LaTeX2e, revised version, minor modifiactions to the text, some phrases eliminated, some remarks adde

Non-diffractive mechanisms in the ϕ\phi meson photoproduction on nucleons

We examine the non-diffractive mechanisms in the $\phi$ meson photoproduction from threshold up to a few GeV using an effective Lagrangian in a constituent quark model. The new data from CLAS at large angles can be consistently accounted for in terms of {\it s}- and {\it u}-channel processes. Isotopic effects arising from the reactions $\gamma p\to \phi p$ and $\gamma n\to \phi n$, are investigated by comparing the cross sections and polarized beam asymmetries. Our result highlights an experimental means of studying non-diffractive mechanisms in $\phi$ meson photoproduction.Comment: 4 eps figures, version accepted by Phys. Lett.

Electromagnetic form factors of light vector mesons

The electromagnetic form factors G_E(q^2), G_M(q^2), and G_Q(q^2), charge radii, magnetic and quadrupole moments, and decay widths of the light vector mesons rho^+, K^{*+} and K^{*0} are calculated in a Lorentz-covariant, Dyson-Schwinger equation based model using algebraic quark propagators that incorporate confinement, asymptotic freedom, and dynamical chiral symmetry breaking, and vector meson Bethe-Salpeter amplitudes closely related to the pseudoscalar amplitudes obtained from phenomenological studies of pi and K mesons. Calculated static properties of vector mesons include the charge radii and magnetic moments: r_{rho+} = 0.61 fm, r_{K*+} = 0.54 fm, and r^2_{K*0} = -0.048 fm^2; mu_{rho+} = 2.69, mu_{K*+} = 2.37, and mu_{K*0} = -0.40. The calculated static limits of the rho-meson form factors are similar to those obtained from light-front quantum mechanical calculations, but begin to differ above q^2 = 1 GeV^2 due to the dynamical evolution of the quark propagators in our approach.Comment: 8 pages of RevTeX, 5 eps figure

Spin Information from Vector-Meson Decay in Photoproduction

For the photoproduction of vector mesons, all single and double spin observables involving vector meson two-body decays are defined consistently in the $\gamma N$ center of mass. These definitions yield a procedure for extracting physically meaningful single and double spin observables that are subject to known rules concerning their angle and energy evolution. As part of this analysis, we show that measuring the two-meson decay of a photoproduced $\rho$ or $\phi$ does not determine the vector meson's vector polarization, but only its tensor polarization. The vector meson decay into lepton pairs is also insensitive to the vector meson's vector polarization, unless one measures the spin of one of the leptons. Similar results are found for all double spin observables which involve observation of vector meson decay. To access the vector meson's vector polarization, one therefore needs to either measure the spin of the decay leptons, make an analysis of the background interference effects or relate the vector meson's vector polarization to other accessible spin observables.Comment: 22 pages, 3 figure

Nucleonic resonance excitations with linearly polarized photon in γp→ωp\gamma p\to \omega p

In this work, an improved quark model approach to the $\omega$ meson photo-production with an effective Lagrangian is presented. The {\it t}-channel {\it natural}-parity exchange is taken into account through the Pomeron exchange, while the {\it unnatural}-parity exchange is described by the $\pi^0$ exchange. With a very limited number of parameters, the available experimental data in the low energy regime can be consistently accounted for. We find that the beam polarization observables show sensitivities to some {\it s}-channel individual resonances in the $SU(6)\otimes O(3)$ quark model symmetry limit. Especially, the two resonances $P_{13}(1720)$ and $F_{15}(1680)$, which belong to the representation $[{\bf 56, ^2 8}, 2, 2, J]$, have dominant contributions over other excited states. Concerning the essential motivation of searching for "missing resonances" in meson photo-production, this approach provides a feasible framework, on which systematic investigations can be done.Comment: 16 pages, Revtex, 9 eps figures, to appear in PR