Glueballs in Flatland

TL;DR

This paper investigates glueball states in 2+1 dimensional pure gauge theory using an extended Isgur-Paton model and lattice calculations, questioning traditional spin assignments and providing new lattice operator methods.

Contribution

It extends the Isgur-Paton model with curvature and mixing, and develops novel lattice operators to better identify glueball states in 2+1 dimensions.

Findings

Masses from lattice agree with the extended model.

Proximity of spin 4 state challenges spin 0 assignment.

New lattice operators reduce rotational ambiguities.

Abstract

The pure gauge theory in 2+1 dimensions is explored, through both a phenomenological model and a lattice calculation. The Isgur-Paton model is extended to include a curvature term and various mixing mechanisms. The method of inferential statistics is used to extract the parameters of best fit and to compare the likelihoods of the various models when compared to existing lattice data. The conventional assignment of spin 0 to the pseudoscalar state is called into question by the proximity of a spin 4 state in the model, which motivates calculating the mass of the spin 4 state on the lattice. Novel lattice operators are constructed from a matrix of effective Greens functions which attempt to overcome the lattice rotational ambiguities. Correlation functions are presented for the channels with even J, and effective masses extracted. The resulting masses compare well with the extended Isgur-Paton model.