Glueball Spectrum and Matrix Elements on Anisotropic Lattices

TL;DR

The paper addresses predicting glueball production by calculating glueball-to-vacuum matrix elements of local gluonic operators on anisotropic lattices. It introduces two complementary operator constructions (Type-I and Type-II) with Symanzik and tadpole improvements, performs finite-volume tests, and conducts continuum extrapolations to obtain renormalized scalar, pseudoscalar, and tensor matrix elements. The study reports updated glueball masses across multiple channels and provides nonperturbative estimates for the relevant matrix elements s, p, and t, contributing to the understanding of glueball structure and their role in hadronic decays. These results inform phenomenology related to J/ψ radiative decays and glueball identification in experiments.

Abstract

The glueball-to-vacuum matrix elements of local gluonic operators in scalar, tensor, and pseudoscalar channels are investigated numerically on several anisotropic lattices with the spatial lattice spacing ranging from 0.1fm - 0.2fm. These matrix elements are needed to predict the glueball branching ratios in $J/ψ$ radiative decays which will help identify the glueball states in experiments. Two types of improved local gluonic operators are constructed for a self-consistent check and the finite volume effects are studied. We find that lattice spacing dependence of our results is very weak and the continuum limits are reliably extrapolated, as a result of improvement of the lattice gauge action and local operators. We also give updated glueball masses with various quantum numbers.

Figures (16)

• Figure 1: Wilson loops used in making the Type-I gluonic operators.
• Figure 2: The clover-shape combinations of spatial plaquette and rectangle, which are used to derive the gauge field strength $F_{\mu\nu}$ on the lattice. Here $i$ and $j$ are the indices of the spatial direction.
• Figure 3: Wilson loops used in making the smeared glueball operators.
• Figure 4: Finite-volume effects of glueball masses at $\beta=2.4$, $\xi=5$. Each point shows the fractional change $\delta_G(L) = 1-M(L)/\bar{M}$ of the glueball mass, where $M(L)$ is the glueball mass measured on the lattice $L^3\times T$ with $L = 8,12,$ and 16, and $\bar{M}$ is the average values over those from different lattices. The errorbars come from the statistical errors of $M(L)$. The lattice labels $L$ are shown along the horizontal axis, and the labels along the vertical axis are the irreps of lattice symmetry group. The solid lines indicates $\delta_G=0$, and the dotted lines above the solid lines indicates $\delta_G = 0.02$, and the dotted line lines below the solid lines indicate $\delta_G = -0.02$.
• Figure 5: Masses of $PC=++$ glueballs in terms of $r_0$ against the lattice spacing square $(a_s/r_0)^2$. The calculated values are plotted in points, and the curves are the best fits.