R.R. Horgan

Measuring the aspect ratio renormalization of anisotropic-lattice gluons

Using tadpole-improved actions we investigate the consistency between different methods of measuring the aspect ratio renormalization of anisotropic-lattice gluons for bare aspect ratios {chi}{sub 0}=4,6,10 and inverse lattice spacing in the range a{sub s}{sup -1}=660--840 MeV. The tadpole corrections to the action, which are established self-consistently, are defined for two cases, mean link tadpoles in the Landau gauge and gauge invariant mean plaquette tadpoles. Parameters in the latter case exhibited no dependence on the spatial lattice size L, while in the former, parameters showed only a weak dependence on L easily extrapolated to L={infinity}. The renormalized anisotropy {chi}{sub R} was measured using both the torelon dispersion relation and the sideways potential method. There is general agreement between these approaches, but there are discrepancies which are evidence for the presence of lattice artifact contributions. For the torelon these are estimated to be O({alpha}{sub S}a{sub s}{sup 2}/R{sup 2}), where R is the flux-tube radius. We also present some new data that suggest that rotational invariance is established more accurately for the mean-link action than the plaquette action.

QCD PRESSURE AND THE TRACE ANOMALY

Abstract Exact relations between the QCD thermal pressure and the trace anomaly are derived. These are used, first, to prove the equivalence of the thermodynamic and the hydrodynamic pressure in equilibrium in the presence of the trace anomaly, closing a gap in previous arguments. Second, in the temporal axial gauge a formula is derived which expresses the thermal pressure in terms of a Dyson-resummed two-point function. This overcomes the infrared problems encountered in the conventional perturbation-theory approach.

Spin effects in heavy hybrid mesons on an anisotropic lattice

Abstract We present a quenched calculation of lowest bottomonium hybrid states on an anisotropic lattice with Landau mean-link tadpole improvement, using the improved NRQCD Hamiltonian. We investigate the quark-spin s =0,1 sectors which contain both the non-exotic 1 −− and the exotic 1 −+ , and demonstrate their degeneracy in the case of the lowest order Hamiltonian. Both states are found at around 1.6 GeV above the ϒ ground state. We examine the spin-splitting for several hybrid states (1 −− , 1 −+ , 0 −+ , 2 −+ ) which is due to the −c 1 σ · B /2m b term in the NRQCD Hamiltonian, all other terms having negligible effect. The spin splittings are well resolved outside errors and are surprisingly large. We investigate their dependence on c 1 for several values of c 1 . We calculate one contribution to these splittings using the Born-Oppenheimer picture for hybrids and show that the observed size of the effect is plausibly explained by mixing with hybrid states with more than one constituent gluon.

Exclusive heavy-meson production and the Z0 width

Abstract We calculate in lowest order QCD perturbation theory the production from Z0 decay and e+e− annihilation of two mesons, each containing a heavy quark. With reasonable assumptions about the vertex functions that couple mesons to quarks, we find that the rates for these final states are strongly enhanced. Present-day knowledge even allows these rates to be so large that the Z0 may be too wide to be detected in p p collisions, with disastrous consequences also for event rates at e+e− colliders.

Non-Relativistic QCD for Heavy Quark Systems

Abstract We employ a non-relativistic version of QCD (NRQCD) to study heavy q q bound states in the lowest approximation without fine structure. We use gluon configurations on a 63×48 lattice at β=6.2 from the UKQCD Collaboration. For a bare quark mass near that of the b-quark (Ma=1.6) we obtain the bound state masses for the S-, P- and both types of D-waves. We also detect signals for two types of hybriges ( q q g states). The results are sufficiently accurate to confirm that the values of the D-wave mass from both D-waves coincide thus indicating that the cubical invariance of the lattice is restored to full rotational invariance to a good approximation. We also study S- and P-wave masses for values of the range of bare quark mass Ma=1.0, 1.3, 1.6 and 1.9. The results confirm the idea that the S/P-splitting is relatively insensitive to the value of the bare quark mass.

Production of unusual mesons in photon-photon collisions

Abstract The cross-section for the production of unusual mesons, such as (bc) or (bc), in photon-photon collisions is obtained in a high energy approximation. For a 100 + 100 GeV e + e − collider, the cross section is estimated to be about one unit of R for (bc) and (bc).

Y spectrum from NRQCD with improved action

We explore the effect of higher order operators in the non-relativistic formulation of QCD (NRQCD). We calculated masses in the bb-spectrum using quenched gauge configurations at β = 6.0 and two different NRQCD actions which have been corrected to order mv4 and mv6. The two-point functions are calculated in a gauge invariant fashion. We find the general structure of the spectrum to be the same in the two cases. Using the 1P - 13S1 splitting we determine the inverse lattice spacings to be 2.44(4) GeV and 2.44(5) GeV for the mv4 and mv6 actions, respectively. We do observe shifts in the spin splittings. The hyperfine splitting is reduced by approximately 4 MeV, while the fine splitting is down by up to 10 MeV, albeit with large statistical errors.

Improved Langevin methods for spin systems

Abstract We investigate methods for variance reduction and the elimination of systematic error in a Fourier accelerated Langevin scheme for general spin models. We present results for the SU(3)×SU(3)/SU(3) model in two dimensions that are consistent with those from multi-grid methods. From a study of lattices of sizes up to 64 × 64 and for correlation lengths up to 8 lattice spacings we argue that the timing for the Langevin method makes it comparable to multi-grid for a given level of error.

NRQCD on an anisotropic lattice

Abstract We present preliminary results for the ϒ spectrum on an anisotropic lattice using the improved O ( mv 6 ) NRQCD Hamiltonian. We find that accurate results can be obtained in moderate computer times and that they agree with earlier results on an isotropic lattice.

Heavy hybrids from NRQCD

We present a quenched lattice calculation for the lowest lying