Universality and scaling behavior of RG gauge actions

TL;DR

This study investigates universality and scaling of RG-improved gauge actions, specifically Iwasaki and DBW2, in SU(3) Yang–Mills by comparing $T_{c}$ and glueball masses using the scale $r_{0}$. It demonstrates universality of $T_{c}r_{0}$ with the Wilson action and finds that Iwasaki exhibits superior scaling compared to Wilson, while DBW2 shows pronounced lattice artefacts and positivity violations. The authors compute $r_{0}/a$ and perform a continuum extrapolation yielding $T_{c}r_{0}=0.7498(50)$ for the RG actions, and assess $\,\alpha_{q\overline{q}}(\mu)$ from the static force, highlighting action-dependent artefacts and the limits of tree-level improvement. Glueball masses $m_{0^{++}}$ and $m_{2^{++}}$ are measured but remain inconclusive due to large errors caused by positivity violations, underscoring the need for variance-reduction techniques. Overall, the results support careful $r_{0}$-based scale setting and observables-specific assessments when employing RG actions in future unquenched lattice QCD studies.

Abstract

We study universality and scaling properties of RG gauge actions (Iwasaki and DBW2). In the first part we consider the critical temperature T_{c} and compute the reference energy scale r_{0} for critical couplings β_{c} corresponding to N_{t}=3,4,6,8. The universality of T_{c}r_{0} between Iwasaki and Wilson action is confirmed and the scaling behavior of the Iwasaki action is found to be better than the one for the Wilson action. The results for the DBW2 action show larger lattice artefacts. A continuum value T_{c}r_{0}=0.7498(50) is extracted. We compute also the glueball masses for the states 0^{++} and 2^{++}, investigate the scaling of m_{0^{++}}r_{0} and m_{2^{++}}r_{0} and point out practical problems which are due to the violation of positivity present in the RG actions.

Figures (16)

• Figure 1: $T_{c}/\sqrt{\sigma}$ as function of $1/N_{t}^2$ for different actions, from Niedermayer:2000yx. By "RG improved" is meant here the Iwasaki action.
• Figure 2: The effective potential as function of $t$ for $r\approx r_{0}$ ($r_{0}/a\sim 4-5$) for the Wilson action and for the RG-improved Iwasaki and DBW2 action.
• Figure 3: The force at tree level for several actions.
• Figure 4: Parametrization of $r_{0}/a$ for the Iwasaki action, eq. (\ref{['fit_iwasaki']}), using the tree-level improved definition of the force.
• Figure 5: Parametrization of $r_{0}/a$ for the DBW2 action, eq. (\ref{['fit_dbw2']}), using the tree-level improved definition of the force.