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 $V_{\mu }\mathrm{}\left(x\right)\mathrm{}$, $A_{\mu }\mathrm{}\left(x\right)\mathrm{}$, $S\left(x\right)\mathrm{}$, and $P\left(x\right)\mathrm{}$. 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 $O\left(p^4\right)$ chiral Lagrangian are expressed in terms of the quark mass function $\Sigma \mathrm{}\left(p\right)\mathrm{}$ 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.