Gauge Dependence of ccbar Potential from Nambu-Bethe-Salpeter Wave Function in Lattice QCD

TL;DR

This study investigates how the extracted $car{c}$ potentials from lattice QCD depend on the choice of gauge, comparing Coulomb and Landau gauges, and finds gauge-dependent discrepancies at large distances due to excited-state contamination.

Contribution

It introduces a systematic comparison of gauge dependence in $car{c}$ potentials using the HAL QCD method with charm quark mass determination, highlighting the impact of gauge choice on potential behavior.

Findings

Central potentials agree at short distances in both gauges.

Discrepancies appear at large distances due to excited-state contamination.

Landau gauge shows less suppression of excited states, affecting potential linearity.

Abstract

We study the gauge dependence of $c\bar{c}$ potentials extracted from Nambu-Bethe-Salpeter (NBS) wave functions. The potentials are obtained using the HAL QCD potential method, with an extension introduced by Kawanai and Sasaki for self-consistent determination of the charm quark mass. A systematic comparison is conducted between results obtained in the Coulomb and Landau gauges. The numerical calculations are performed using 2+1 flavor QCD gauge configurations with the charm quark treated in the quenched approximation. We find that the central potentials in both gauges show excellent agreement at short distances but exhibit discrepancies at large distances. We attribute these discrepancies to insufficient suppression of excited-state contamination in the Landau gauge, which affects the linear-rising behavior of the potential at large distance.