Roles of the quark field in the infrared lattice Coulomb gauge and Landau gauge QCD

TL;DR

This study investigates the infrared behavior of the effective coupling in QCD under different gauges and fermion configurations, revealing gauge-dependent suppression and the influence of quark fields on ghost propagators and confinement indicators.

Contribution

It provides a comparative analysis of the infrared effective coupling in Coulomb and Landau gauges using unquenched lattice configurations with different fermions, highlighting the impact of quark fields.

Findings

Infrared effective coupling in Coulomb gauge matches recent JLab results.

Infrared suppression observed in Landau gauge coupling.

Quark effects reduce ghost propagator fluctuations and bring the Kugo-Ojima parameter closer to 1.

Abstract

The effective coupling of QCD is measured by using the gauge configurations produced by the MILC collaboration in which the Kogut Susskind (KS) fermion is incorporated and by using that produced by the QCDOC collaboration in which the domain wall fermion (DWF) is incorporated. We fix the gauge to the Landau gauge and to the Coulomb gauge. The infrared effective coupling in the Coulomb gauge agrees with the recent extraction at JLab, but that in the Landau gauge shows infrared suppression. The suppression is expected to be due to the color anti-symmetric ghost propagator which in the unquenched configurations has stronger infrared singularity than the color diagonal ghost propagator. The Coulomb form factor in the infrared depends on the kind of the fermion incorporated in the system and the temperature. The quark has the effect of quenching randomness and the fluctuation of the color anti-symmetric ghost propagator is reduced in the unquenched configuration, and the Kugo-Ojima parameter c is closer to 1 in the unquenched configuration than in the quenched configuration.