Independent of assumptions about the form of the quark-quark scattering kernel K, we derive the explicit relation between the flavor-nonsinglet pseudoscalar-meson Bethe-Salpeter amplitude ⌫ H and the dressed-quark propagator in the chiral limit. In addition to a term proportional to ␥ 5 , ⌫ H necessarily contains qualitatively and quantitatively important terms proportional to ␥ 5 ␥• P and ␥ 5 ␥•kk•P, where P is the total momentum of the bound state. The axial-vector vertex contains a bound state pole described by ⌫ H , whose residue is the leptonic decay constant for the bound state. The pseudoscalar vertex also contains such a bound state pole and, in the chiral limit, the residue of this pole is related to the vacuum quark condensate. The axial-vector Ward-Takahashi identity relates these pole residues, with the Gell-Mann-Oakes-Renner relation a corollary of this identity. The dominant ultraviolet asymptotic behavior of the scalar functions in the meson Bethe-Salpeter amplitude is fully determined by the behavior of the chiral limit quark mass function, and is characteristic of the QCD renormalization group. The rainbow-ladder Ansatz for K, with a simple model for the dressed-quarkquark interaction, is used to illustrate and elucidate these general results. The model preserves the one-loop renormalization group structure of QCD. The numerical studies also provide a means of exploring procedures for solving the Bethe-Salpeter equation without a three-dimensional reduction. ͓S0556-2813͑97͒04112-5͔

The masses and decay constants of the light vector mesons ρ/ω, φ and K ⋆ are studied within a ladder-rainbow truncation of the coupled Dyson-Schwinger and Bethe-Salpeter equations of QCD with a model 2-point gluon function. The approach is consistent with quark and gluon confinement, reproduces the correct one-loop renormalization group behavior of QCD, generates dynamical chiral symmetry breaking, and preserves the relevant Ward identities. The one phenomenological parameter and two current quark masses are fixed by requiring that the calculated f π , m π and m K are correct. The resulting f K is within 3% of the experimental value. For the vector mesons, all eight transverse covariants are included and the dominant ones are identified; the complete angle dependence of the amplitudes is also retained. The calculated values for the masses m ρ , m φ and m K ⋆ are within 5%, while the decay constants f ρ , f φ and f K ⋆ for electromagnetic and leptonic decays are within 10% of the experimental values.

Dyson-Schwinger equations furnish a Poincaré 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.

Independent of assumptions about the form of the quark-antiquark scattering kernel we derive the explicit relation between the pion Bethe-Salpeter amplitude, Gamma_pi, and the quark propagator in the chiral limit; Gamma_pi necessarily involves a non-negligible gamma_5 gamma.P term (P is the pion four-momentum). We also obtain exact expressions for the pion decay constant, f_pi, and mass, both of which depend on Gamma_pi; and demonstrate the equivalence between f_pi and the pion Bethe-Salpeter normalisation constant in the chiral limit. We stress the importance of preserving the axial-vector Ward-Takahashi identity in any study of the pion itself, and in any study whose goal is a unified understanding of the properties of the pion and other hadronic bound states.Comment: 11 pages, LaTeX, elsart.st

The rainbow truncation of the quark Dyson-Schwinger equation is combined with the ladder Bethe-Salpeter equation for the meson amplitudes and the dressed quark-photon vertex in a self-consistent Poincaré-invariant study of the pion and kaon electromagnetic form factors in impulse approximation. We demonstrate explicitly that the current is conserved in this approach and that the obtained results are independent of the momentum partitioning in the Bethe-Salpeter amplitudes. With model gluon parameters previously fixed by the condensate, the pion mass and decay constant, and the kaon mass, the charge radii and spacelike form factors are found to be in good agreement with the experimental data.

We perform no-core full configuration calculations for a set of light nuclei including 16 O with a realistic NN interaction, JISP16. We obtain ground-state energies and their uncertainties through exponential extrapolations that we demonstrate are reliable in 2 H, 3 H, and 4 He test cases where fully converged results are obtained directly. We find that 6 He, 6 Li, and 8 He are underbound by about 600 keV, 560 keV, and 1.7 MeV, respectively. 12 C is overbound by about 1.7 MeV and 16 O is overbound by about 16 MeV. The first excited 0 + states in 12 C and 16 O are also evaluated but their uncertainties are significantly larger than the uncertainties for the ground states.

We explore the analytic structure of the gluon and quark propagators of Landau gauge QCD from numerical solutions of the coupled system of renormalized Dyson-Schwinger equations and from fits to lattice data. We find sizable negative norm contributions in the transverse gluon propagator indicating the absence of the transverse gluon from the physical spectrum. A simple analytic structure for the gluon propagator is proposed. For the quark propagator we find evidence for a mass-like singularity on the real timelike momentum axis, with a mass of 350 to 500 MeV. Within the employed Green's functions approach we identify a crucial term in the quark-gluon vertex that leads to a positive definite Schwinger function for the quark propagator.

The rainbow truncation of the quark Dyson-Schwinger equation is combined with the ladder Bethe-Salpeter equation for the dressed quark-photon vertex to study the low-momentum behavior of the pion electromagnetic form factor. With model gluon parameters previously fixed by the pion mass and decay constant, the pion charge radius r π is found to be in excellent agreement with the data. When the often-used Ball-Chiu Ansatz is used to construct the quark-photon vertex directly from the quark propagator, less than half of r 2 π is generated. The remainder of r 2 π is seen to be attributable to the presence of the ρ-pole in the solution of the ladder Bethe-Salpeter equation.