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 ${\cal O}(1/N_c, m, m/N_c, m \ln m/N_c)$-corrections to the dynamical quark mass M, the quark condensate $<\bar qq>$, the pion mass M_πand decay constant F_π. 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 $F_π(m=0), \ave{\bar qq(m=0)}$ in agreement with \chiPT, we offer a new set of parameters ρ, 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.