Lattice QCD analysis for Faddeev-Popov eigenmodes in terms of gluonic momentum components in the Coulomb gauge

TL;DR

This study explores how gluonic momentum components affect Faddeev-Popov eigenmodes and the confining potential in Coulomb gauge lattice QCD, revealing the critical role of infrared gluons in confinement.

Contribution

It provides new insights into the relationship between gluon momentum components and Faddeev-Popov eigenmodes, emphasizing the importance of infrared gluons in confinement mechanisms.

Findings

Near-zero Faddeev-Popov eigenmodes enhance Coulomb energy.

Ultraviolet gluon cuts do not significantly change the spectrum.

Infrared gluons are essential for confinement and eigenmode structure.

Abstract

We analyze the relation between Faddeev-Popov eigenmodes and gluon-momentum components in the Coulomb gauge using SU(3) lattice QCD. In the Coulomb gauge, the color-Coulomb energy is largely enhanced by near-zero Faddeev-Popov eigenmodes, which would lead to the confining potential. By the ultraviolet-momentum gluon cut, the color-Coulomb energy and the Faddeev-Popov spectrum are almost unchanged. In contrast to the ultraviolet insensitivity, the color-Coulomb energy and the Faddeev-Popov eigenmodes drastically change by infrared-momentum gluon cut. Without infrared gluons, the color-Coulomb energy tends to become non-confining, and near-zero Faddeev-Popov eigenmodes vanish. We also investigate the full FP eigenmodes, and find that infrared gluons widely influence both high and low Faddeev-Popov eigenmodes.