QCD isospin breaking ChPT low-energy constants from the instanton vacuum

TL;DR

This paper calculates low-energy constants in Chiral Perturbation Theory using the instanton vacuum model, revealing the sensitivity of certain constants to instanton parameters and their small contribution to pion mass difference.

Contribution

It provides a novel evaluation of the ChPT low-energy constant l_7 within the instanton vacuum model, highlighting its dependence on instanton shape and parameters.

Findings

l_7 constant is sensitive to instanton shape and parameters

The value of l_7 suggests a small QCD contribution to pion mass difference

Results agree with previous order of magnitude estimates

Abstract

In the framework of the instanton vacuum model we evaluate the Chiral Perturbation Theory (ChPT) low-energy constants h_3,l_7. We found that in the instanton vacuum model the constant l_7 is very sensitive to the shape of the instanton and the instanton vacuum parameters. We evaluated the constant l_7 for two different zero-mode profiles and as a function of the average instanton size \rho and inter-instanton distance R. Our result agrees with an old "order of magnitude" estimate of this constant from [1]. The obtained value of l_7 implies that the pure QCD contribution to the pion mass difference is small, ~1% of the observed experimental value.