Measuring the aspect ratio renormalization of anisotropic-lattice gluons

TL;DR

This paper investigates the consistency of different methods for measuring the aspect ratio renormalization of anisotropic-lattice gluons using tadpole-improved actions, finding good agreement and suggesting improved rotational invariance with mean-link actions.

Contribution

It compares methods of measuring anisotropy renormalization and shows that mean-link tadpole improvement yields more accurate rotational invariance than plaquette-based methods.

Findings

Good agreement between torelon dispersion and sideways potential methods.

Discrepancies are within 3-4%, consistent with lattice artifacts.

Mean-link actions improve rotational invariance over plaquette actions.

Abstract

Using tadpole inproved 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 and inverse lattice spacing in the range a_s^{-1}=660-840 MeV. The tadpole corrections to the action, which are established self-consistently, are defined for two cases, mean link tadpoles in 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. We found good agreement between these different approaches. Any discrepancy was at worst 3-4% which is consistent with the effect of lattice artifacts that for the torelon we estimate as O(\a_Sa_s^2/R^2) where R is the flux-tube radius. We also present some new data that suggests that rotational invariance is established more accurately for the mean-link action than the plaquette action.