Coulomb-gauge ghost and gluon propagators in SU(3) lattice Yang-Mills theory

TL;DR

This paper investigates the momentum dependence of ghost and gluon propagators in SU(3) lattice Coulomb gauge theory, revealing strong lattice artifacts and complex scale dependences that challenge existing theoretical expectations.

Contribution

It provides a detailed joint analysis of ghost and gluon propagators across different lattice cutoffs, highlighting the strong lattice artifacts and the unusual scale dependence of the D_{44} gluon propagator.

Findings

Lattice artifacts are significant at high momenta for both propagators.

The scale dependence a(beta) runs faster than two-loop predictions but slower than heavy quark potential analysis.

Residual gauge-fixing affects the D_{44} gluon propagator, posing interpretative challenges.

Abstract

We study the momentum dependence of the ghost propagator and of the space and time components of the gluon propagator at equal time in pure SU(3) lattice Coulomb gauge theory carrying out a joint analysis of data collected independently at RCNP Osaka and Humboldt University Berlin. We focus on the scaling behavior of these propagators at beta=5.8,...,6.2 and apply a matching technique to relate the data for the different lattice cutoffs. Thereby, lattice artifacts are found to be rather strong for both instantaneous gluon propagators at large momentum. As a byproduct we obtain the respective lattice scale dependences a(beta) for the transversal gluon and the ghost propagator which indeed run faster with beta than two-loop running, but slightly slower than what is known from the Necco-Sommer analysis of the heavy quark potential. The abnormal a(beta) dependence as determined from the instantaneous time-time gluon propagator, D_{44}, remains a problem, though. The role of residual gauge-fixing influencing D_{44} is discussed.