Multi-Instanton Effects in QCD Sum Rules for the Pion

TL;DR

This paper investigates multi-instanton effects on QCD sum rules for the pion within an instanton liquid model, showing gauge-dependent differences and emphasizing the singular gauge's effectiveness at large distances.

Contribution

It demonstrates that multi-instanton contributions can be effectively approximated by single-instanton effects in the singular gauge within the QCD sum rule framework.

Findings

Singular gauge provides better description of correlators at large distances.

Planar diagrams in leading order of 1/Nc are similar to single-instanton contributions.

Gauge choice significantly affects the modeling of instanton effects.

Abstract

Multi-instanton contributions to QCD sum rules for the pion are investigated within a framework which models the QCD vacuum as an instanton liquid. It is shown that in singular gauge the sum of planar diagrams in leading order of the $1/N_{c}$ expansion provides similar results as the effective single-instanton contribution. These effects are also analysed in regular gauge. Our findings confirm that at large distances the correlator functions are more adequately described in the singular gauge rather than in the regular one.