Particle theory

Abstract:

We calculate the lowest glueball masses and the string tension for both Manton's action and for Symanzik's tree-level improved action. We do so on large lattices and for small lattice spacings using techniques recently employed in an extensive investigation of the Wilson plaquette action. Comparing all these results we find that the ratios of the lightest masses are universal to a high degree of accuracy. In particular, we confirm that on large volumes the tensor glueball is heavier than the scalar glueball: m[2+]{reversed tilde equals}1.5 m[0+]. We repeat these calculations for larger lattice spacings and find that the string tension follows 2-loop perturbation theory more closely in the case of these alternative actions than in the case of the standard plaquette action. Our attempt to repeat the analysis with Wilson's block-spin improved action foundered on the strong breakdown of positivity apparent in the calculated correlation functions. In all cases which we were able to study the observed violations of scaling are in the same direction. This suggests that the causes of the scaling violations observed with Wilson's plaquette action are "semi-universal". It also weakens the implication of the observed universality for the question of how close we are to the continuum limit. © 1988.

Abstract:

We use lattice gauge theory simulation to evaluate the spectrum in pure gauge theory with an SU(2) colour group. Glueball states in all representations of the cubic group Oh are investigated. We compare our results for small spatial volumes with the analytic hamiltonian results of Koller and van Baal and with our large lattice results. © 1988.

Abstract:

We calculate glueball masses and the string tension on lattices as large as 204 and at couplings as small as β= 6 g2=6.2. To be able to do so we construct wave-functionals that maintain a good overlap with the long-distance physics as the lattice spacing is made small. Our calculations strongly indicate that the lightest glueball is the 0++ and that the next highest levels are a nearly degenerate 2++ and 0-+ at roughly 1.6m[0++]. In addition there is a 1+- just below 2m[0++]. The mass of the scalar is about 3.5 times the square root of the string tension. We find that this ratio is consistent with being independent of β for β≥5.9 (in contrast to its strong variation at lower β) and that this appears tobe so at a statistically significant level. The ratio of the 2++ and 0++ glueball masses is also consistent with being independent of β. © 1988.