$\Delta S=1,2$ Effective Weak Chiral Lagrangian from the Instanton Vacuum

TL;DR

This paper derives the $ riangle S=1,2$ weak chiral Lagrangian using the instanton vacuum approach, highlighting the importance of momentum-dependent quark masses in refining low-energy constants relevant for chiral perturbation theory.

Contribution

It introduces a method to incorporate the $ riangle S=1,2$ weak Hamiltonian into the instanton vacuum framework, deriving the weak effective Lagrangian with improved low-energy constants.

Findings

Momentum-dependent quark mass improves low energy constants.

Enhanced ratio of $g_{8}/g_{27}$ constants.

Derived weak Lagrangian applicable in chiral perturbation theory.

Abstract

We study the effective weak chiral Lagrangian within the framework of the instanton vacuum. We incorporate the $\Delta S=1,2$ effective weak Hamiltonian into the effective low-energy QCD partition function defining the chiral symmetric quark-Goldstone boson interactions with the momentum-dependent dynamical quark mass. Employing the derivative expansion, we derive the corresponding weak effective Lagrangian in leading order with the low energy constants to be used e.g. in chiral perturbation theory. We find that the momentum-dependent dynamical quark mass plays an essential role in improving the low energy constants and their ratio $g_{8}/g_{27}$.