We provide a snapshot of Dyson-Schwinger equation applications to the theory and phenomenology of hadrons. Exact results for pseudoscalar mesons are highlighted, with details relating to the U A (1) problem. Calculated masses of the lightest J = 0, 1 states are discussed. We recapitulate upon studies of nucleon properties and give a perspective on the… (More)
Dyson-Schwinger equations furnish a Poincaré covariant approach to hadron physics. They reveal that dynamical chiral symmetry breaking is tied to the long-range behaviour of the strong interaction and make predictions corroborated by modern lattice-QCD simulations. A hallmark in the contemporary use of DSEs is the existence of a nonperturbative, symmetry… (More)
Aspects of the dressed-quark-gluon vertex and their role in the gap and Bethe-Salpeter equations are briefly surveyed using an intuitive model. The model allows one to elucidate why a linear extrapolation to the chiral limit of extant lattice data on the dressed-quark mass-function overestimates this function and hence the value of the vacuum quark… (More)
We present a calculation of the three-quark core contribution to the mass of the ∆-resonance in a Poincaré-covariant Faddeev framework. A consistent setup for the dressed-quark propagator, the quark-quark and quark-'diquark' interactions is used, where all the ingredients are solutions of their respective Dyson-Schwinger or Bethe-Salpeter equations in… (More)
A strongly momentum-dependent dressed-quark mass function is basic to QCD. It is central to the appearance of a constituent-quark mass-scale and an existential prerequisite for Goldstone modes. Dyson-Schwinger equation (DSEs) studies have long emphasised this importance, and have proved that QCD's Goldstone modes are the only pseudoscalar mesons to possess… (More)
Starting from a one–body front–form equation with Lepage-Brodsky spinors we show, with a fair amount of new technology, how an integral equation in standard momentum space with Bjørken-Drell spinors can be obtained. The integral equation decouples for singlets and triplets.