Measuring the aspect ratio renormalization of anisotropic-lattice gluons

Using tadpole-improved actions we investigate the consistency between different methods of measuring the aspect ratio renormalization of anisotropic-lattice gluons for bare aspect ratios ${\chi }_0=4,6,10\mathrm{}$ and inverse lattice spacing in the range $a_s^{-1}=660\mathrm{}–840$ MeV. The tadpole corrections to the action, which are established self-consistently, are defined for two cases, mean link tadpoles in the Landau gauge and gauge invariant mean plaquette tadpoles. Parameters in the latter case exhibited no dependence on the spatial lattice size L, while in the former, parameters showed only a weak dependence on L easily extrapolated to $L=\infty .$ The renormalized anisotropy ${\chi }_R$ was measured using both the torelon dispersion relation and the sideways potential method. There is general agreement between these approaches, but there are discrepancies which are evidence for the presence of lattice artifact contributions. For the torelon these are estimated to be $O\left({\alpha }_S{a}_s^2{/R}^2\right),$ where R is the flux-tube radius. We also present some new data that suggest that rotational invariance is established more accurately for the mean-link action than the plaquette action.