Exploring the Chiral Regime of QCD in the Interacting Instanton Liquid Model

Since contemporary lattice QCD calculations have highlighted the need to understand the dependence of QCD observables on the quark mass, this paper presents the framework to investigate this dependence in the context of the Interacting Instanton Liquid Model (IILM). By computing the nucleon and pion masses for a wide range of quark masses, we show that the IILM reproduces the existing lattice data for pion masses in the range 450 - 730 MeV. We also show that in the low-pion mass regime, the nucleon mass dependence in this model is consistent with O(p^4) Chiral Perturbation Theory and O(p^3) Baryon Chiral Perturbation theory. The nucleon sigma-term extracted from this analysis is in qualitative agreement with but slightly below the result from recent lattice calculations. To further explore this model in the chiral regime, we show that the spectral density of the Dirac operator and the three-point scalar correlation function agree with the behavior expected from chiral perturbation theory for two flavors. In the IILM, we identify a characteristic quark energy scale, m*= 80 MeV, which governs the zero mode zone and thus the scale for instanton mediated chiral symmetry breaking, and discuss its physical significance