Low Energy Constants of Chiral Perturbation Theory from the Instanton Vacuum

Abstract

In the framework of the instanton vacuum model we make expansion over the current mass $m$ and number of colors $N_c$ and evaluate ${\cal O}(1/N_c, m, m/N_c, m \ln m/N_c)$-corrections to the dynamical quark mass $M$, the quark condensate $<\bar qq>$, the pion mass $M_\pi$ and decay constant $F_\pi$. We found the SU(2) $\chi$PT low-energy constants $\bar l_3, \bar l_4$ in a good correspondence with the phenomenology and lattice calculations.