Approaching low-energy QCD with a gauged, nonlocal, constituent-quark model

We study the minimal constituent-quark model with momentum-dependent quark mass in the presence of SU(3)×{}SU(3) external gauge fields V_μ(x), A_μ(x), $S(x)$, and $P(x)$. The model generates vertex functions, for any number of external fields and pseudo Goldstone bosons coupling to quarks, saturating the Ward-Takahashi identities of QCD. Parameters in the O(p⁴) chiral Lagrangian are expressed in terms of the quark mass function Σ(p) and are surprisingly consistent with low-energy QCD. By use of the auxiliary-field method we discuss the relation of the model to the improved ladder approximation in QCD.