Spin Resolution of Glueballs in 2+1 Dimensional Lattice Gauge Theory

TL;DR

This paper introduces a new lattice operator construction method to resolve spin ambiguities in 2+1 dimensional lattice gauge theory, enabling more accurate identification of glueball states' spins.

Contribution

It proposes a technique to generate lattice operators at non-standard angles, improving spin resolution beyond the modulo 4 ambiguity in traditional methods.

Findings

Masses for spin 0, 2, and 4 states were calculated and compared.

Results show good agreement for spins 0 and 2 with previous data.

The spin 4 state mass matches that of a spin 0 state, suggesting possible misidentification.

Abstract

Conventional lattice gauge theory assigns the lowest spin compatible with the symmetry channel of a given operator to the state coupling to that operator. Operators on a cubic lattice, however, are only defined on angles of pi/2, hence states with spin equal modulo 4 may overlap significantly. This paper explores a new technique for generating lattice operators that may be placed onto the lattice at angles other than pi/2, thereby resolving this modulo 4 ambiguity. Calculations of the mass of states with spin equal t o 0, 2, and 4 are performed in the positive parity and charge conjugation channe l and compared to the spectrum from previous lattice calculations. These masses compare well for spin 0 and 2, and for spin 4 the mass agrees with a state conv entionally assigned spin 0, raising the possibility of mis-identification of the spin of states coupling to some traditional operators.