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 $\beta =5.8,\dots ,6.2$ 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 $a(\beta )$ 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.

• Received 8 March 2009

DOI:https://doi.org/10.1103/PhysRevD.79.114504