Glueballs from Improved Lattice Actions

TL;DR

This paper evaluates the effectiveness of improved lattice actions in accurately computing low-lying glueball masses and the hadronic scale in SU(3) gauge theory, utilizing anisotropic lattices for efficiency.

Contribution

It demonstrates that improved lattice actions combined with anisotropic lattices effectively reduce finite-spacing artifacts in glueball mass calculations.

Findings

Accurate low-lying glueball masses obtained.

Effective removal of finite-spacing artifacts demonstrated.

Enhanced measurement efficiency using anisotropic lattices.

Abstract

The low-lying glueball masses and the hadronic scale $r_0$ are computed in lattice SU(3) gauge theory with the aim of establishing the effectiveness of the improved action approach in removing finite-spacing artifacts. The use of anisotropic lattices in which the temporal spacing is much smaller than that in the spatial directions allows much more efficient glueball mass measurements.

Full text

Glueballs and hybrid mesons are presently of great interest theoretically and experimentally. The lattice formulation of QCD provides an ideal setting in which to carry out theoretical studies of such systems from first principles using sophisticated numerical simulations. In order to extract the physical properties of glueballs and hybrid mesons from such simulations, systematic errors from the finite lattice spacing $a$ must be removed or made acceptably small. There are two approaches to accomplishing this: (1) using finer grids or (2) using improved actions on coarse grids. The first approach is much simpler and has been used in almost all previous glueball and hybrid meson studies. However, this approach requires vast computational power. As the grid is made finer, many more lattice sites are needed to maintain the physical volume of the system. The simulation costs rise typically as $1/a^{6}$ as $a$ is decreased. Because of this, lattice studies of glueballs have in the past been dominated by large collaborations using some of the world’s fastest supercomputers.

Here, we show that the second approach, the use of improved actions, can be used to study glueballs much more efficiently. Improved actions have smaller lattice spacing errors, and hence, permit the use of much coarser lattices which can be simulated using modern computer workstations. The key to the success of the improvement program is the reliable determination of the couplings of the interactions terms in the action. Much effort over the past decade has been directed towards this problem. Recently, two competing methods have emerged, one which uses block-renormalization group transformations, another which advocates a judicious combination of mean field theory and perturbation theory. In this work, we use the latter approach.

A novel feature of our calculations is the use of anisotropic lattices in which the temporal spacing $a_{t}$ is much smaller than the spacing $a_{s}$ in the spatial directions. This allows much more efficient glueball mass measurements by exploiting the enhanced signal-to-noise of the glueball correlation functions at smaller temporal separations. Mean-field link renormalization[2] is crucial for maintaining the proper renormalized anisotropy $a_{t}/a_{s}$.

Our results are shown in Fig. 1. The scalar glueball mass from the improved action exhibits dramatically reduced cutoff contamination compared to the Wilson action. Finite-$a_{s}$ errors are seen to be small for the tensor and pseudo-vector glueballs, although differences between the $E^{++}$ and $T_{2}^{++}$ representations indicate small violations of rotational invariance, especially for large $a_{s}$. These results clearly show that glueballs can be studied without the use of supercomputers, provided that simulations are carried out using improved actions on anisotropic lattices.