M. Teper

An Improved Method for Lattice Glueball Calculations

Abstract We present a simple iterative method for obtaining glueball wave functionals of the appropriate physical size as one decreases the lattice spacing. We test the method in SU (2) for 2.1 ⩽ β ⩽ 2.5 and find a gain in computer time over previous methods, that can be several orders of magnitude. The method appears to make possible reliable, large lattice calculations of excited glueball masses and significantly extends the range of bare couplings where reliable glueball calculations can be performed.

The glueball spectrum in SU(3)

We study the glueball spectrum for pure gauge SU(3) using lattice-gauge-theory simulation. We investigate a range of β-values from 5.9 to 6.2, a range of sizes of spatial lattice from 103 to 203, all JPC possibilities, states of different momentum, etc. We are able to conclude that our results are relevant to the continuum limit of pure gauge QCD. We obtain glueball masses (in units of Keff which is about 0.44 GeV.): 3.5(2) and 6.3(4) for 0++, 5.3(2) for 2++, 5.3(2) for 0−+, 6.9(5) for 1+− and 6.6(10) for 2+−.

The SU(3) topological susceptibility at zero and finite temperature: A lattice Monte Carlo evaluation

We extend previous calculations of the zero-temperature topological susceptibility, χt, to larger lattices (up to 204) and smaller lattice spacings (up to β=6.2). Using a new technique we are able to achieve a precise control of finite size corrections. We confirm, with much greater systematic and statistical precision, that the dimensionless ratio χt/K2 is independent of β for β⩾5.7. This enables us to extract χt in physical units and we find χt=(179±4 MeV)4 - statistical error only - which is in striking agreement with the Witten-Veneziano calculation. We also investigate the previously observed fact that χt is suppressed as the temperature is raised through the deconfining transition. We find that χt is in fact discontinuous at the phase transition and that its temperature dependence is otherwise weak as long as it remains in a single well-defined phase.

Towards the Continuum Limit of SU(2) Lattice Gauge Theory

Abstract We study the approach to the continuum limit of SU(2) lattice gauge theory by accurately calculating several physical quantities on lattices up to 204 and for couplings up to β=4/g2=2.6. We find that the dependence of mass ratios on the lattice spacing weakens as the spacing decreases, although the two-loop relation between the spacing and g2 is not yet attained for β⩽2.6. We find glueball masses, and the string tension to be roughly in the ratio m(2−):m(0−):m(2+):m(0+):√K≈7:6.5:5.5:3.8:1 for the smallest lattice spacings.

On the mass spectrum of the SU(2) Higgs model in 2+1 dimensions

Abstract We calculate the masses of the low-lying states with quantum numbers J PC = 0 ++ , 1 −− in the Higgs and confinement regions of the three-dimensional SU(2) Higgs model, which plays an important role in the description of the thermodynamic properties of the standard model at finite temperatures. We extract the masses from correlation functions of gauge-invariant operators which are calculated by means of a lattice Monte Carlo simulation. The projection properties of our lattice operators onto the lowest states are greatly improved by the use of smearing techniques. We also consider cross correlations between various operators with the same quantum numbers. From these the mass eigenstates are determined by means of a variational calculation. In the symmetric phase, we find that some of the ground-state masses are about 30% lighter than those reported from previous simulations. We also obtain the masses of the first few excited states in the symmetric phase. Remarkable among these is the occurrence of a 0 ++ state composed almost entirely of gauge degrees of freedom. The mass of this state, as well as that of its first excitations, is nearly identical to the corresponding glueball states in three-dimensional SU(2) pure gauge theory, indicating an approximate decoupling of the pure gauge sector from the Higgs sector of the model. We perform a detailed study of finite-size effects and extrapolate the lattice mass spectrum to the continuum.We calculate the masses of the low-lying states with quantum numbers

The k=2 string tension in four-dimensional SU(N) gauge theories

J^{PC}=0^{++},1^{--}

The scalar and tensor glueball masses in lattice gauge theory

in the Higgs and confinement regions of the three-dimensional SU(2) Higgs model, which plays an important r\^ole in the description of the thermodynamic properties of the standard model at finite temperatures. We extract the masses from correlation functions of gauge-invariant operators which are calculated by means of a lattice Monte Carlo simulation. The projection properties of our lattice operators onto the lowest states are greatly improved by the use of smearing techniques. We also consider cross correlations between various operators with the same quantum numbers. From these the mass eigenstates are determined by means of a variational calculation. In the symmetric phase, we find that some of the ground state masses are about 30\% lighter than those reported from previous simulations. We also obtain the masses of the first few excited states in the symmetric phase. Remarkable among these is the occurrence of a

The finite-temperature phase transition of SU (2) gauge fields in 2 + 1 dimensions

0^{++}

The glueball spectrum and scaling in SU(3) lattice gauge theory

state composed almost entirely of gauge degrees of freedom. The mass of this state, as well as that of its first excitations, is nearly identical to the corresponding glueball states in three-dimensional SU(2) pure gauge theory, indicating an approximate decoupling of the pure gauge sector from the Higgs sector of the model. We perform a detailed study of finite size effects and extrapolate the lattice mass spectrum to the continuum.

The confining string and its tension for SU(2) gauge fields in 2 + 1 dimensions

Abstract We calculate the k =2 string tension in SU (4) and SU (5) gauge theories in 3+1 dimensions, and compare it to the k =1 fundamental string tension. We find, from the continuum extrapolation of our lattice calculations, that σ k =2 / σ f =1.40±0.08 in the SU (4) gauge theory, and that σ k =2 / σ f =1.56±0.10 in SU (5). We remark upon the way this might constrain the dynamics of confinement and the intriguing implications it might have for the mass spectrum of SU ( N ) gauge theories. We also note that these results agree closely with the MQCD-inspired conjecture that the SU ( N ) string tension varies as σ k ∝ sin( πk / N ).