Instanton dominance over $\alpha_s$ at low momenta from lattice QCD simulations at $N_f=0$, $N_f=2+1$ and $N_f=2+1+1$

TL;DR

This paper demonstrates that instanton effects dominate low-momentum gluon Green functions in lattice QCD simulations across various flavors, enabling the extraction of instanton parameters and lattice spacing through an instanton-based analysis.

Contribution

It introduces an instanton-based framework to analyze low-momentum gluon Green functions in lattice QCD, applicable to both quenched and unquenched simulations, and employs Gradient Flow to study instanton properties.

Findings

Instanton dominance observed in low-momentum gluon Green functions.

Gradient Flow effectively removes short-distance fluctuations, revealing instanton structures.

Instanton parameters are consistent across different lattice setups and flavor configurations.

Abstract

We report on an instanton-based analysis of the gluon Green functions in the Landau gauge for low momenta; in particular we use lattice results for $\alpha_s$ in the symmetric momentum subtraction scheme (${\rm MOM}$) for large-volume lattice simulations. We have exploited quenched gauge field configurations, $N_f=0$, with both Wilson and tree-level Symanzik improved actions, and unquenched ones with $N_f=2+1$ and $N_f=2+1+1$ dynamical flavors (domain wall and twisted-mass fermions, respectively). We show that the dominance of instanton correlations on the low-momenta gluon Green functions can be applied to the determination of phenomenological parameters of the instanton liquid and, eventually, to a determination of the lattice spacing. We furthermore apply the Gradient Flow to remove short-distance fluctuations. The Gradient Flow gets rid of the QCD scale, $\Lambda_{\rm QCD}$, and reveals that the instanton prediction extents to large momenta. For those gauge field configurations free of quantum fluctuations, the direct study of topological charge density shows the appearance of large-scale lumps that can be identified as instantons, giving access to a direct study of the instanton density and size distribution that is compatible with those extracted from the analysis of the Green functions.