Efficient glueball simulations on anisotropic lattices

TL;DR

This paper demonstrates that an improved, anisotropic lattice action enables efficient and accurate extraction of the low-lying glueball spectrum in quenched QCD on coarse lattices, by combining smeared/fuzzed operator construction with a variational approach and careful scale setting via the static potential. Key contributions include precise determinations of the tensor $2^{++}$ and pseudovector $1^{+-}$ glueball masses in physical units, and a detailed continuum-extrapolation strategy that shows large efficiency gains over Wilson-action simulations. Finite-volume effects are shown to be negligible, while the scalar glueball remains the main source of discretization uncertainty, motivating ongoing action development. Collectively, the work provides a robust framework for glueball spectroscopy on anisotropic lattices and sets the stage for exploring heavier states and mixings with non-glueball degrees of freedom.

Abstract

Monte Carlo results for the low-lying glueball spectrum using an improved, anisotropic action are presented. Ten simulations at lattice spacings ranging from 0.2 to 0.4 fm and two different anisotropies have been performed in order demonstrate the advantages of using coarse, anisotropic lattices to calculate glueball masses. Our determinations of the tensor (2++) and pseudovector (1+-) glueball masses are more accurate than previous Wilson action calculations.

Figures (14)

• Figure 1: The four Wilson loop shapes in each channel used to form the lattice glueball operators. The complete set of 24 operators was formed by computing linear combinations of each of these loops rotated and translated across the lattice on six different sets of smoothed links. Where a loop shape occurs twice, it is used in two different projections into the appropriate irreducible representation.
• Figure 2: Effective mass plot showing the results of a single-exponential fit to the Wilson loop for $V(\vec{r})$ with $\vec{r}/a_s=(2,2,2)$, $\beta=2.4$, and $\xi=3$. The $t_{\rm min}-t_{\rm max}$ region of the fit is also indicated.
• Figure 3: The static-quark potential $V(\vec{r})$ expressed in terms of the hadronic scale $r_0$. This plot includes measurements from the $\beta=2.2$, $2.4$, and $2.6$ simulations for $\xi=3$, and the $\beta=2.2$ and $2.4$ simulations for $\xi=5$. Lattice spacing errors are seen to be small.
• Figure 4: Effective mass plot showing the results of a single-exponential fit to the glueball correlation function for the $A_1^{++}$ channel for $\beta=2.6$ and $\xi=3$. The $t_{\rm min}-t_{\rm max}$ region of the fit is also indicated.
• Figure 5: Effective mass plot showing the results of a single-exponential fit to the glueball correlation function for the $T_1^{+-}$ channel for $\beta=2.6$ and $\xi=3$.