Instantaneous Interquark Potential in Generalized Landau Gauge in SU(3) Lattice QCD: A Linkage between the Landau and the Coulomb Gauges

TL;DR

This study explores how instantaneous interquark potentials in SU(3) lattice QCD vary across generalized Landau gauges, revealing a continuous transition from no linear potential in Landau gauge to a Coulomb-like potential with a larger slope near Coulomb gauge.

Contribution

It demonstrates the gauge dependence of instantaneous interquark potentials and establishes a continuous description between Landau and Coulomb gauges in lattice QCD.

Findings

Instantaneous potential has no linear part in Landau gauge.

In Coulomb gauge, the potential is Coulomb plus a linear term with a slope 2-3 times larger than the physical string tension.

The potential transitions smoothly between gauges, with the linear part rapidly increasing near Coulomb gauge.

Abstract

We investigate in detail "instantaneous interquark potentials", interesting gauge-dependent quantities defined from the spatial correlators of the temporal link-variable $U_4$, in generalized Landau gauge using SU(3) quenched lattice QCD. The instantaneous Q$\bar{\rm Q}$ potential has no linear part in the Landau gauge, and it is expressed by the Coulomb plus linear potential in the Coulomb gauge, where the slope is 2-3 times larger than the physical string tension. Using the generalized Landau gauge, we find that the instantaneous potential can be continuously described between the Landau and the Coulomb gauges, and its linear part rapidly grows in the neighborhood of the Coulomb gauge. We also investigate the instantaneous 3Q potential in the generalized Landau gauge, and obtain similar results to the Q$\bar{\rm Q}$ case. $T$-length terminated Polyakov-line correlators and their corresponding "finite-time potentials" are also investigated in generalized Landau gauge.