High Spin Glueballs from the Lattice

TL;DR

This paper develops numerical techniques to analyze higher spin glueballs on the lattice, applying them to compute the spectrum of SU(2) gauge theory in 2+1 dimensions and clarifying the spin assignments of certain states.

Contribution

It introduces methods to rotate Wilson loops arbitrarily on the lattice and applies them to accurately determine the glueball spectrum and spin labels in 2+1 dimensions.

Findings

Corrected the spin assignment of the 0^- glueball to 4^-

Identified the lightest 'J=1' state as spin 3

Demonstrated how rotation symmetry is recovered in the continuum

Abstract

We discuss the principles underlying higher spin glueball calculations on the lattice. For that purpose, we develop numerical techniques to rotate Wilson loops by arbitrary angles in lattice gauge theories close to the continuum. As a first application, we compute the glueball spectrum of the SU(2) gauge theory in 2+1 dimensions for both parities and for spins ranging from 0 up to 4 inclusive. We measure glueball angular wave functions directly, decomposing them in Fourier modes and extrapolating the Fourier coefficients to the continuum. This allows a reliable labelling of the continuum states and gives insight into the way rotation symmetry is recovered. As one of our results, we demonstrate that the D=2+1 SU(2) glueball conventionally labelled as J^P = 0^- is in fact 4^- and that the lightest ``J=1'' state has, in fact, spin 3.