Improved gauge action on an anisotropic lattice II - Anisotropy parameter in the medium coupling region -

TL;DR

This paper calculates the quantum correction of the anisotropy parameter for improved lattice gauge actions in the medium coupling region, revealing different $eta$ dependences and applying the link integration method near the confined phase.

Contribution

It provides the first detailed calculation of the anisotropy parameter $ta$ for improved actions at medium coupling, highlighting differences from standard actions and perturbative results.

Findings

$ta$ remains nearly constant for Iwasaki and DBW2 actions across $eta$ range.

$ta$ increases as $eta$ decreases for Symanzik action, with a steeper slope than perturbative predictions.

Application of link integration method reduces gauge field fluctuations near the confined phase.

Abstract

The quantum correction of the anisotropy parameter, $\eta$, is calculated for $\xi=2$ and 3 in the $\beta$ region where numerical simulations such as hadron spectroscopy are currently carried out, for the improved actions composed of plaquette and rectangular 6-link loops. The $\beta$ dependences of $\eta$ for the renormalization group improved actions are quite different from those of the standard and Symanzik actions. In Iwasaki and DBW2 actions, $\eta$ stays almost constant in a wide range of $\beta$, which also differs from the one-loop perturbative result, while in the case of Symanzik action, it increases as $\beta$ decreases, which is qualitatively similar to the perturbative result, but the slope is steeper. In the calculation of the $\eta$ parameter close to and in the confined phase, we have applied the link integration method to suppress the fluctuation of the gauge fields. Some technical details are summarized.