Quark Propagation in the Instantons of Lattice QCD

TL;DR

This study demonstrates that instantons in lattice QCD configurations are primarily responsible for the dynamical mass generation of quarks, with smeared gauge fields retaining key propagator features.

Contribution

It shows that instanton effects extracted via smearing reproduce the main features of the quark propagator, highlighting their role in mass generation.

Findings

Instanton-like objects dominate gauge fields after smearing.

Smeared configurations maintain characteristic propagator features.

Vacuum packing fraction exceeds phenomenological predictions.

Abstract

We quantitatively examine the extent to which instanton degress of freedom, contained within standard Monte-carlo generated gauge-field configurations, can maintain the characteristic features of the mass and renormalisation functions of the non-perturbative quark propagator. We use over-improved stout-link smearing to isolate instanton effects on the lattice. Using a variety of measures, we illustrate how gauge fields consisting almost solely of instanton-like objects are produced after only 50 sweeps of smearing. We find a full vacuum, with a packing fraction more than three times larger than phenomenological models predict. We calculate the overlap quark propagator on these smeared configurations, and find that even at high levels of smearing the majority of the characteristic features of the propagator are reproduced. We thus conclude that instantons contained within standard Monte-carlo generated gauge-field configurations are the degrees of freedom responsible for the dynamical generation of mass observed in lattice QCD.