Low energy QCD from an effective quark-quark interaction

Abstract

We consider a model truncation of QCD which is based on an effective quark-quark interaction. The truncation allows for a phenomenological description in a framework which maintains the global symmetries of QCD and permits a 1/Nc expansion. The applied truncation leads to the Schwinger-Dyson equation for the quark self energy in the rainbow approximation, which is solved numerically for a given model form of the gluon 2 point function D(q2). Meson bound states appear as solutions of the homogeneous ladder Bethe-Salpeter equation. This approach allows for a detailed and systematic investigation of nonperturbative phenomena at low and intermediate energies. A systematic chiral low energy expansion is performed leading to a model prediction of all the chiral coefficients (Gasser Leutwyler coefficients). We demonstrate how the UA(1) anomaly and the splitting between η and η′ can arise in this approach. It turns out that a necessary condition is a 1/q4 infrared singularity for the gluon 2 point function. Withi...