Urs M. Heller

QCD spectrum with three quark flavors

We present results from a lattice hadron spectrum calculation using three flavors of dynamical quarks -- two light and one strange -- and quenched simulations for comparison. These simulations were done using a one-loop Symanzik improved gauge action and an improved Kogut-Susskind quark action. The lattice spacings, and hence also the physical volumes, were tuned to be the same in all the runs to better expose differences due to flavor number. Lattice spacings were tuned using the static quark potential, so as a by-product we obtain updated results for the effect of sea quarks on the static quark potential. We find indications that the full QCD meson spectrum is in better agreement with experiment than the quenched spectrum. For the 0{sup ++} (a{sub 0}) meson we see a coupling to two pseudoscalar mesons, or a meson decay on the lattice.

Scaling and Asymptotic Scaling in the SU(2) Gauge Theory

Abstract We determine the critical couplings for the deconfinement phase transition in SU(2) gauge theory on Nτ × Nσ3 lattices with Nτ = 8 and 16 and Nσ varying between 16 and 48. A comparison with string tension data shows scaling of the ratio Tc/√σ in the entire coupling regime s = 2.30−2.75, while the individual quantities still exhibit large scaling violations. We find Tc/√σ = 0.69(2). We also discuss in detail the extrapolation of T c /Λ MS and √σ/Λ MS to the continuum limit. Our result, which is consistent with the above ratio, is T c /Λ MS =1.23(11) and √σ/Λ MS =1.79(12) . We also comment upon corresponding results for SU(3) gauge theory and four-flavour QCD.

Spatial string tension in the deconfined phase of (3+1)-dimensional SU(2) gauge theory

We present results of a detailed investigation of the temperature dependence of the spatial string tension in SU(2) gauge theory. We show, for the first time, that the spatial string tension is scaling on the lattice and thus is non-vanishing in the continuum limit. It is temperature independent below Tc and rises rapidly above. For temperatures larger than 2Tc we find a scaling behaviour consistent with sigma_s(T) = 0.136(11) g^4(T) T^2, where g(T) is the 2-loop running coupling constant with a scale parameter determined as Lambda_T = 0.076(13) Tc.

Accurate scale determinations for the Wilson gauge action

Accurate determinations of the physical scale of a lattice action are required to check scaling and take the continuum limit. We present a high statistics study of the static potential for the SU(3) Wilson gauge action on coarse lattices (5.54 ⩽ β ⩽ 6.0). Using an improved analysis procedure we determine the string tension and the Sommer scale ro (and related quantities) to I% accuracy, including all systematic errors. Combining our results with earlier ones on finer lattices, we present parameterizations of these quantities that should be accurate to about 1 % for 5.6 ⩽ β S 6.5. We estimate the A-parameter of quenched QCD to be ΛGMs = 247(16) MeV.

Moments of nucleon light cone quark distributions calculated in full lattice QCD

Moments of the quark density, helicity, and transversity distributions are calculated in unquenched lattice QCD. Calculations of proton matrix elements of operators corresponding to these moments through the operator product expansion have been performed on the 16{sup 3} x 32 lattices for Wilson fermions at Beta=5.6 using configurations from the SESAM collaboration and at Beta = 5.5 using configurations from SCRI. One-loop perturbative renormalization corrections are included. At quark masses accessible in present calculations, there is no statistically significant difference between quenched and full QCD results, indicating that the contributions of quark-antiquark excitations from the Dirac Sea are small. Close agreement between calculations with cooled configurations containing essentially only instantons and the full gluon configurations indicates that quark zero modes associated with instantons play a dominant role. Naive linear extrapolation of the full QCD calculation to the physical pion mass yields results inconsistent with experiment. Extrapolation to the chiral limit including the physics of the pion cloud can resolve this discrepancy and the requirements for a definitive chiral extrapolation are described.

Unquenched gluon propagator in Landau gauge

[...] Using lattice quantum chromodynamics ~QCD! we perform an unquenched calculation of the gluon propagator in Landau gauge. We use configurations generated with the AsqTad quark action by the MILC collaboration for the dynamical quarks and compare the gluon propagator of quenched QCD ~i.e., the pure Yang-Mills gluon propagator! with that of 211 flavor QCD. The effects of the dynamical quarks are clearly visible and lead to a significant reduction of the nonperturbative infrared enhancement relative to the quenched case.

Monte Carlo renormalisation group studies of SU(3) lattice gauge theory

Results are reported of Monte Carlo renormalisation group studies of the approach to asymptotic scaling in SU(3) lattice gauge theory. By comparing measurements on 8 4 and 16 4 lattices, estimates are obtained for the shift, [Delta][beta], in the fundamental plaquette coupling, [beta9, corresponding to a change of length scale by a factor of 2. The definitions of block link variables contain a free parameter whose value can be optimised to minimise the transient flow to a renormalised trajectory. Our results, at [beta] = 6.0, 6.3 and 6.6, are consistent with those obtained previously with the improved ratio method, which is also briefly discussed. In both methods simulation is performed only with the standard Wilson action. An important feature of the results is the appearance of a pronounced dip in [Delta][beta] which implies that in the presently accesible range of [beta] the asymptotic value is approached from below, and its onset is delayed.

Study of chiral symmetry in quenched QCD using the overlap Dirac operator

We compute fermionic observables relevant to the study of chiral symmetry in quenched QCD using the overlap Dirac operator for a wide range of fermion mass. We use analytical results to disentangle the contribution from exact zero modes and simplify our numerical computations. Details concerning the numerical implementation of the overlap Dirac operator are presented. {copyright} {ital 1999} {ital The American Physical Society}

A study of practical implementations of the overlap Dirac operator in four dimensions

Abstract We study three practical implementations of the overlap Dirac operator D 0 = 1 2 [1+γϵ( H w )] in four dimensions. Two implementations are based on different representations of ϵ( H w ) as a sum over poles. One of them is a polar decomposition and the other is an optimal fit to a ratio of polynomials. The third one is obtained by representing ϵ( H w ) using Gegenbauer polynomials and is referred to as the fractional inverse method. After presenting some spectral properties of the Hermitian operator H 0 = γ 5 D 0 , we study its spectrum in a smooth SU(2) instanton properties of the with the aim of comparing the three implementations of D 0 . We also present some results in SU(2) gauge field backgrounds generated at β = 2.5 on an 8 4 lattice. Chiral properties have been numerically verified.

Quark Spectra, Topology, and Random Matrix Theory

Quark spectra in QCD are linked to fundamental properties of the theory including the identification of pions as the Goldstone bosons of spontaneously broken chiral symmetry. The lattice overlap Dirac operator provides a nonperturbative, ultraviolet-regularized description of quarks with the correct chiral symmetry. Properties of the spectrum of this operator and their relation to random matrix theory are studied here. In particular, the predictions from chiral random matrix theory in topologically nontrivial gauge field sectors are tested for the first time. {copyright} {ital 1999} {ital The American Physical Society}