Glueball Regge Trajectories in (2+1) Dimensional Gauge Theories

TL;DR

This study calculates glueball masses in (2+1)D SU(2) gauge theory, revealing a linear Regge trajectory with a low intercept, suggesting complex high-energy scattering behavior beyond simple Regge pole dominance.

Contribution

It provides the first detailed computation of glueball Regge trajectories in (2+1)D gauge theories, including continuum extrapolation and implications for high-energy scattering.

Findings

Glueball spectrum forms a straight Regge trajectory.

The trajectory's slope is between adjoint-string and flux-tube models.

Intercept is approximately -1, indicating non-Pomeron-like high-energy behavior.

Abstract

We compute glueball masses for even spins ranging from 0 to 6, in the D=2+1 SU(2) lattice gauge theory. We do so over a wide range of lattice spacings, and this allows a well-controlled extrapolation to the continuum limit. When the resulting spectrum is presented in the form of a Chew-Frautschi plot we find that we can draw a straight Regge trajectory going through the lightest glueballs of spin 0, 2, 4 and 6. The slope of this trajectory is small and turns out to lie between the predictions of the adjoint-string and flux-tube glueball models. The intercept we find, \alpha_0 ~ -1, is much lower than is needed for this leading trajectory to play a `Pomeron-like' role of the kind it is often believed to play in D=3+1. We elaborate the Regge theory of high energy scattering in 2 space dimensions, and we conclude, from the observed low intercept, that high-energy glueball scattering is not dominated by the leading Regge pole exchange, but rather by a more complex singularity structure in the region 0 <= Re{\lambda} <= 1/2 of the complex angular momentum \lambda plane. We show that these conclusions do not change if we go to larger groups, SU(N>2), and indeed to SU(\infty), and we contrast all this with our very preliminary calculations in the D=3+1 SU(3) gauge theory.