Glueball Regge trajectories in (2+1)-dimensional gauge theories Original Research Article

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, α0∼−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⩽Reλ⩽1/2 of the complex angular momentum λ plane. We show that these conclusions do not change if we go to larger groups, SU(N>2), and indeed to SU(∞), and we contrast all this with our very preliminary calculations in the D=3+1 SU(3) gauge theory.