Lattice QCD analysis for instantaneous interquark potential in generalized Landau gauge

TL;DR

This study explores how the instantaneous interquark potential in SU(3) lattice QCD varies across generalized Landau gauges, revealing a gauge-dependent linear potential component that approximates the physical potential in an intermediate gauge.

Contribution

It demonstrates the continuous gauge dependence of the instantaneous potential and identifies an intermediate gauge where it closely matches the physical interquark potential.

Findings

Instantaneous potential lacks linear part in Landau gauge.

Linear part of potential grows towards Coulomb gauge.

Intermediate $oldsymbol{ extlambda_C}$-gauge reproduces physical potential.

Abstract

Using generalized Landau gauge, we study the continuous change of gluon properties from the Landau gauge toward the Coulomb gauge in SU(3) lattice QCD. We investigate "instantaneous interquark potential", which is defined by the spatial correlation of the temporal link-variable $U_4$ and is an interesting gauge-dependent concept. In the Coulomb gauge, the instantaneous potential is expressed by the Coulomb plus linear potential, where the slope is, however, 2-3 times as large as the physical string tension. In the Landau gauge, the instantaneous potential has no linear part. We find that the linear part is continuously growing by varying gauge from the Landau gauge toward the Coulomb gauge. We also find that the instantaneous potential approximately reproduces the physical interquark potential in a specific intermediate gauge, $\lambda_C$-gauge. This $\lambda_C$-gauge is expected to be a useful gauge for modeling effective theories such as the quark potential model.