Effective chiral Lagrangian in the chiral limit from the instanton vacuum

Abstract

We study the effective chiral Lagrangian in the chiral limit from the instanton vacuum. Starting from the nonlocal effective chiral action, we derive the effective chiral Lagrangian, using the derivative expansion to order ${O(p}^{4})$ in the chiral limit. The low energy constants ${L}_{1},$ ${L}_{2},$ and ${L}_{3}$ are determined and compared with various models and the corresponding empirical data. The results are in a good agreement with the data. We also discuss the upper limit of the sigma meson, based on the present results.