X iv : h ep - p h / 02 03 19 7 v 2 8 J an 2 00 3 Calculation of Chiral Lagrangian Coefficients

We present a systematic way to combine the global color model and the instanton liquid model to calculate the chiral Lagrangian coefficients. Our numerical results are in agreement well with the experimental values. Quantum chromodynamics (QCD) is successful to describe strong interaction in terms of basic force at high energy. However, the large coupling constant at low energy makes the perturbation theory break down. At low-energy scale, the freedoms of quarks and gluons realize themselves in hadronic level as mesons and baryons, which is characterized by chiral perturbation theory (χPT). [1, 2] The χPT can give a lot of satisfactory explanations for experimental data while the coefficients of the chiral expansion are input parameters and their values are determined from experimental observables. Since the present technique cannot derivate the chiral Lagrangian from QCD directly, a class of chiral invariant QCD based models are used in deriving the chiral Lagrangian which is characterized by the effective quark-quark interaction. The global colour model (GCM), which has provided a lot of successful descriptions of the long distance properties of strong interaction and the QCD vacuum as well as hadronic phenomena at low energy, is based on a trun-cation of QCD Lagragian preserves global colour gauge transformation and permits a large N c expansion. [3, 4, 5, 6] The instanton liquid model (ILM) of the QCD vacuum is based on a semiclassical approximation, in which all gauge configurations are replaced by an ensemble of topological nontrivial fields, instantons and anti-instantons.