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

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

Multipole analysis of spin observables in vector meson photoproduction

A multipole analysis of vector meson photoproduction is formulated as a generalization of the pseudoscalar meson case. Expansion of spin observables in the multipole basis and behavior of these observables near threshold and resonances are examined.Comment: 15 pages, latex, 2 figure

Valence-quark distributions in the pion

We calculate the pion's valence-quark momentum-fraction probability distribution using a Dyson-Schwinger equation model. Valence-quarks with an active mass of 0.30 GeV carry 71% of the pion's momentum at a resolving scale q_0=0.54 GeV = 1/(0.37 fm). The shape of the calculated distribution is characteristic of a strongly bound system and, evolved from q_0 to q=2 GeV, it yields first, second and third moments in agreement with lattice and phenomenological estimates, and valence-quarks carrying 49% of the pion's momentum. However, pointwise there is a discrepancy between our calculated distribution and that hitherto inferred from parametrisations of extant pion-nucleon Drell-Yan data.Comment: 8 pages, 3 figures, REVTEX, aps.sty, epsfig.sty, minor corrections, version to appear in PR

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