Low energy constants of \chiPT from the instanton vacuum model

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. There are several sources of these corrections: meson loops, finite size of the instanton distribution and the quark-quark "tensor" interaction terms. In contrast to the expectations, we found that numerically the 1/N_c-corrections to dynamical mass are large and mostly come from meson loops. As a consequence, we have large 1/N_c-corrections to all the other quantities. To provide the values of $F_{\pi }(m=0),\text{ave}\bar{q}q(m=0)$ in agreement with \chiPT, we offer a new set of parameters \rho, R. Finally, we find the low-energy SU(2)_f chiral lagrangian constants ${\bar{l}}_3,{\bar{l}}_4$ in a rather good correspondence with the phenomenology.