Instantaneous interquark potential in generalized Landau gauge in SU(3) lattice QCD: a possible gauge for the quark potential model

TL;DR

This study explores how the instantaneous interquark potential varies across different gauges in SU(3) lattice QCD, identifying an intermediate gauge that reproduces the physical potential and may support quark potential models.

Contribution

It introduces a generalized Landau gauge framework that interpolates between Landau and Coulomb gauges, revealing an intermediate gauge where the potential aligns with the physical interquark potential.

Findings

Instantaneous potential lacks linear part in Landau gauge.

In Coulomb gauge, the potential shows a Coulomb plus linear form with a large slope.

An intermediate gauge, called '$\lambda_C$-gauge', reproduces the physical potential.

Abstract

We investigate "instantaneous interquark potential", an interesting gauge-dependent quantity defined from the spatial correlator $<\mathrm{Tr} [U_4^\dagger(s)U_4(s')]>$ of the temporal link-variable $U_4$, in detail in generalized Landau gauge using SU(3) quenched lattice QCD. While the instantaneous potential has no linear part in the Landau gauge, in the Coulomb gauge, it is expressed by the Coulomb plus linear potential, where the slope is 2-3 times larger than the physical string tension, and the lowest energy state is considered to be a gluon-chain state. Using the generalized Landau gauge, we find that the instantaneous potential can be continuously described between the Landau and the Coulomb gauges, and it approximately reproduces the physical interquark potential in a specific intermediate gauge, which we call "$\lambda_C$-gauge". This $\lambda_C$-gauge is expected to provide a quark-potential-model picture, where dynamical gluons do not appear. We also investigate $T$-length terminated Polyakov-line correlator and its corresponding "finite-time potential" in generalized Landau gauge.