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 $\mathcal{O}(1/N_c,m,m/N_c,m\ln m/N_c)$-corrections to the dynamical quark mass $M$, the quark condensate $<\bar{q}q>$, 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.

Comments: Talk given at Baldin ISHEPP XIX, Dubna, September 29 - October 4, 2008. Few typos was corrected