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

Tianchen Zhang, Noriyoshi Ishii

Published 2025-02-10Version 1

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.