Quenched lattice-QCD data on the dressed-quark Schwinger function can be correlated with dressed-gluon data via a rainbow gap equation so long as that equation's kernel possesses enhancement at infrared momenta above that exhibited by the gluon alone. The required enhancement can be ascribed to a dressing of the quark-gluon vertex. The solutions of the rainbow gap equation exhibit dynamical chiral symmetry breaking and are consistent with confinement. The gap equation and related, symmetry-preserving ladder Bethe-Salpeter equation yield estimates for chiral and physical pion observables that suggest these quantities are materially underestimated in the quenched theory: || by a factor of two and f_pi by 30%.Comment: 9 pages, LaTeX2e, REVTEX4, 6 figure

Abstract. 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.

The electromagnetic form factors GE(q 2 ), GM (q 2 ), and GQ(q 2 ), charge radii, magnetic and quadrupole moments, and decay widths of the light vector mesons ρ + , 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 π and K mesons. Calculated static properties of vector mesons include the charge radii and magnetic moments: r 2 ρ+ 1/2 = 0.61 fm, r 2 K * + 1/2 = 0.54 fm, and r 2 K * 0 = -0.048 fm 2 ; µρ+ = 2.69, µ K * + = 2.37, and µ K * 0 = -0.40. The calculated static limits of the ρ-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.

We consider the solution of the Bethe-Salpeter equation in the Euclidean metric for a q q vector meson in the circumstance where the dressed quark propagators have timelike complex conjugate mass poles. This approximates features encountered in recent QCD modeling via the Dyson-Schwinger equations; the absence of real mass poles simulates quark confinement. The analytic continuation in the total momentum necessary to reach the mass shell for a meson sufficiently heavier than 1 GeV leads to the quark poles being within the integration domain for two variables in the standard approach. Through Feynman integral techniques, we show how the analytic continuation can be implemented in a way suitable for a practical numerical solution. We show that the would-be q q width to the meson generated from one quark pole is exactly canceled by the effect of the conjugate partner pole; the meson mass remains real and there is no spurious q q production threshold. The ladder kernel we employ is consistent with one-loop perturbative QCD and has a two-parameter infrared structure found to be successful in recent studies of the light SU͑3͒ meson sector.