Inside Mesons: Coupling Constants and Form Factors

In this work the dressed quark propagators and approximation schemes are guided by the Dyson-Schwinger equation (DSE) approach to non-perturbative QCD modeling of hadron physics. This covariant QCD phenomenology has proved to be quite efficient for low-mass mesons and their form factors. To expedite investigations we make use of a convenient parameterization of confining solutions of quark DSEs. The broad features are taken from the solution to a simple DSE model 3 that is extremely infrared dominant, produces a propagator with no mass-shell pole, and includes gluon-quark vertex dressing determined by the Ward identity. The resulting propagator is an entire function in the complex p-plane describing absolutely confined 4 dressed quarks in the presence of both explicit and dynamical breaking of chiral symmetry. Additional strength for the propagator at intermediate space-like momenta is necessary to represent solutions of more realistic DSE models. With the quark propagator written as S(p) = −iγ · pσV (p )+σS(p ), the following parameterization for flavor f = u/d, s captures the essential features 5,6 σ̄ S(x) = F(b f 1x)F(b f 3x) (