Low energy constants of \chiPT from the instanton vacuum model

TL;DR

This paper calculates low-energy constants of chiral perturbation theory using the instanton vacuum model, revealing significant 1/N_c corrections mainly from meson loops, and provides parameters aligning with phenomenology.

Contribution

It introduces a detailed expansion in the instanton vacuum model to evaluate corrections to key QCD quantities, offering new parameter sets consistent with chiral perturbation theory.

Findings

Large 1/N_c corrections mainly from meson loops.

Derived low-energy constants $ar l_3, ar l_4$ agree with phenomenology.

Provided parameter sets for $ ho$, $R$ matching chiral perturbation theory.

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. 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 $F_\pi(m=0), \ave{\bar qq(m=0)}$ 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.