Wave functions of $SU(3)$ pure gauge glueballs on the lattice

TL;DR

This study investigates the wave functions of $SU(3)$ pure gauge glueballs using lattice methods, identifying ground and excited states, and analyzing their spatial structures to enhance understanding of glueball internal composition.

Contribution

It provides a detailed lattice calculation of glueball wave functions, distinguishing ground and excited states, and examines their radial structures with improved methods.

Findings

Ground state radial wave functions are approximately Gaussian.

Tensor glueballs are roughly twice as large as scalar ones.

First excited states show clear radial nodes, indicating radial excitations.

Abstract

The Bethe-Salpeter wave functions of $SU(3)$ pure gauge glueballs are revisited in this study. The ground and the first excited states of scalar and tensor glueballs are identified unambiguously by using the variational method on the basis of large operator sets. We calculate their wave functions in the Coulomb gauge and use two lattices with different lattice spacings to check the discretization artifacts. For ground states, the radial wave functions are approximately Gaussian and the size of the tensor is twice as large as that of the scalar. For the first excited states, the radial nodes are clearly observed for both the scalar and the tensor glueballs, such that they can be interpreted as the first radial excitations. These observations may shed light on the theoretical understanding of the inner structure of glueballs.