Low energy constants ofχPTfrom 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 $\mathcal{O}(1/{N}_{c},m,m/{N}_{c},m\mathrm{ln}m/{N}_{c})$ corrections to the dynamical quark mass $M$, the quark condensate $⟨\overline{q}q⟩$, the pion mass ${M}_{\ensuremath{\pi}}$, and decay constant ${F}_{\ensuremath{\pi}}$. 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 ${F}_{\ensuremath{\pi}}(m=0)$, $⟨\overline{q}q(m=0)⟩$ in agreement with $\ensuremath{\chi}\mathrm{PT}$, we offer a new set of parameters $\ensuremath{\rho}$, $R$. Finally, we find the low-energy $SU(2{)}_{f}$ chiral Lagrangian constants ${\overline{l}}_{3},{\overline{l}}_{4}$ in a rather good correspondence with the phenomenology.