Low Energy Constants of Chiral Perturbation Theory from the Instanton Vacuum

TL;DR

This paper calculates low-energy constants of chiral perturbation theory using the instanton vacuum model, providing results consistent with phenomenology and lattice data.

Contribution

It introduces a method to evaluate corrections to key quantities in QCD within the instanton vacuum framework, including low-energy constants.

Findings

SU(2) T low-energy constants 3, 4 match phenomenology and lattice results.

Calculated corrections to quark mass, condensate, pion mass, and decay constant.

Provides a consistent theoretical approach to low-energy QCD parameters.

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 $F_\pi$. 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.