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

Abstract

The quantum correction of the anisotropy parameter, $η$, is calculated for $ξ=2$ and 3 in the $β$ 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 $β$ dependences of $η$ for the renormalization group improved actions are quite different from those of the standard and Symanzik actions. In Iwasaki and DBW2 actions, $η$ stays almost constant in a wide range of $β$, which also differs from the one-loop perturbative result, while in the case of Symanzik action, it increases as $β$ decreases, which is qualitatively similar to the perturbative result, but the slope is steeper. In the calculation of the $η$ 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.