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

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 the Research Center for Nuclear Physics, Osaka and Humboldt University, Berlin. We focus on the scaling behavior of these propagators at $\ensuremath{\beta}=5.8,\dots{},6.2$ 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 a large momentum. As a byproduct we obtain the respective lattice scale dependences $a(\ensuremath{\beta})$ for the transversal gluon and the ghost propagator which indeed run faster with $\ensuremath{\beta}$ than two-loop running, but slightly slower than what is known from the Necco-Sommer analysis of the heavy quark potential. The abnormal $a(\ensuremath{\beta})$ 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.