Cooling for instantons and the Wrath of Nahm

The dynamics of instantons and anti-instantons in lattice QCD can be studied by analysing the action and topological charge of configurations as they approach a self-dual or anti-self-dual state, i.e. a state in which S/S_0=|Q|. We use cooling to reveal the semi-classical structure of the configurations we study. Improved actions which eliminate discretization errors up to and including O(a^4) are used to stabilise instantons as we cool for several thousand sweeps. An analogously improved lattice version of the continuum field-strength tensor is used to construct a topological charge free from O(a^4) discretization errors. Values of the action and topological charge obtained with these improved operators approach mutually-consistent integer values to within a few parts in 10^4 after several hundred cooling sweeps. Analysis of configurations with |Q| \approx 1 and |Q| \approx 2 supports the hypothesis that a self-dual |Q|=1 configuration cannot exist on the 4-torus.Comment: 5 pages, 4 figures, talk presented at the workshop on Lattice Hadron Physics, Cairns Australia, July 200

More on SU(3) Lattice Gauge Theory in the Fundamental--Adjoint Plane

We present further evidence for the bulk nature of the phase transition line in the fundamental--adjoint action plane of SU(3) lattice gauge theory. Computing the string tension and some glueball masses along the thermal phase transition line of finite temperature systems with $N_t=4$, which was found to join onto the bulk transition line at its endpoint, we find that the ratio $\sqrt{\sigma} / T_c$ remains approximately constant. However, the mass of the $0^{++}$ glueball decreases as the endpoint of the bulk transition line is approached, while the other glueball masses appear unchanged. This is consistent with the notion that the bulk transition line ends in a critical endpoint with the continuum limit there being a $\phi^4$ theory with a diverging correlation length only in the $0^{++}$ channel.Comment: 4 pages, uuencoded, gziped postscript file. To appear in the Proceedings of LATTICE'95, Melbourne, Australia, 11-15 July, 199

Autocorrelation in Updating Pure SU(3) Lattice Gauge Theory by the use of Overrelaxed Algorithms

We measure the sweep-to-sweep autocorrelations of blocked loops below and above the deconfinement transition for SU(3) on a $16^4$ lattice using 20000-140000 Monte-Carlo updating sweeps. A divergence of the autocorrelation time toward the critical $\beta$ is seen at high blocking levels. The peak is near $\beta$ = 6.33 where we observe 440 $\pm$ 210 for the autocorrelation time of $1\times 1$ Wilson loop on $2^4$ blocked lattice. The mixing of 7 Brown-Woch overrelaxation steps followed by one pseudo-heat-bath step appears optimal to reduce the autocorrelation time below the critical $\beta$. Above the critical $\beta$, however, no clear difference between these two algorithms can be seen and the system decorrelates rather fast.Comment: 4 pages of A4 format including 6-figure

Non-perturbative Renormalization of Lattice Operators

We briefly review and compare three methods (one perturbative, one based on Ward Identities and one non-perturbative) for the calculation of the renormalization constants of lattice operators. The following results are presented: (a) non perturbative renormalization of the operators with light quarks; (b) the renormalization constants with a heavy (charm) quark mass and its KLM improvement; (c) the non perturbative determination of the mixing of the $\Delta S = 2$ operator.Comment: 9 pages, uuencoded PS file, 8 figures included, 1 tabl

Proposal for Topologically Unquenched QCD

A proposal is presented for simulating an improvement on quenched QCD with dynamical fermions which interact with the gluon configuration only via the topological index of the latter. Strengths and shortcomings of the method are discussed and it is argued that the approximation - though being crude - shares some qualitative aspects of full QCD which relate to the issue of chiral symmetry breaking.Comment: latex, 13pp, material rearranged and better focused, final version to appear in Phys. Rev.

Gauge Boson Masses in the 3-d, SU(2) Gauge-Higgs Model

We study gauge boson propagators in the symmetric and symmetry broken phases of the 3-d, $SU(2)$ gauge-Higgs model. Correlation functions for the gauge fields are calculated in Landau gauge. They are found to decay exponentially at large distances leading to a non-vanishing mass for the gauge bosons. We find that the W-boson screening mass drops in the symmetry broken phase when approaching the critical temperature. In the symmetric phase the screening mass stays small and is independent of the scalar--gauge coupling (the hopping parameter). Numerical results coincide with corresponding calculations performed for the pure gauge theory. We find $m_w = 0.35(1)g^2T$ in this phase which is consistent with analytic calculations based on gap equations. This is, however, significantly smaller than masses extracted from gauge invariant vector boson correlation functions. As internal consistency check we also have calculated correlation functions for gauge invariant operators leading to scalar and vector boson masses. Finite lattice size effects have been systematically analyzed on lattices of size $L^2\times L_z$ with $L=4-24$ and $L_z = 16 - 128$.Comment: 20 pages, LaTeX2e File, 8 Postscript figure

Properties of hadron screening masses at small baryonic density

The properties of hadron screening masses around the deconfinement phase transition at finite baryonic density can be studied by evaluating the Taylor coefficients with respect to the iso-scalar and iso-vector chemical potentials. We simulate 2-flavour lattice QCD with staggered fermions on a 12*12*24*6 lattice with ma = 0.05 and 0.10 and report investigations of nucleon, pseudo-scalar and vector mesons. We present new, strong evidence that in the confining phase, the screening masses at vanishing chemical potential have significant temperature dependence, but the effect of the iso-scalar chemical potential is very small. Above the critical temperature, the second derivative terms of mesons rapidly increase as contrasted to the case of baryon. We also study the responses of the screening masses to an iso-vector chemical potential and discuss some of the issues related to the properties of hadron masses at finite density.Comment: 7 pages with 5 figures; added two new references, the title of article and the section 'Concluding Remarks' are slightly change

Scaling in the Positive Plaquette Model and Universality in SU(2) Lattice Gauge Theory

We investigate universality, scaling, the beta-function and the topological charge in the positive plaquette model for SU(2) lattice gauge theory. Comparing physical quantities, like the critical temperature, the string tension, glueball masses, and their ratios, we explore the effect of a complete suppression of a certain lattice artifact, namely the negative plaquettes, for SU(2) lattice gauge theory. Our result is that this modification does not change the continuum limit, i.e., the universality class. The positive plaquette model and the standard Wilson formulation describe the same physical situation. The approach to the continuum limit given by the beta-function in terms of the bare lattice coupling, however, is rather different: the beta-function of the positive plaquette model does not show a dip like the model with standard Wilson action.Comment: 35 pages, preprint numbers FSU-SCRI-94-71 and HU Berlin-IEP-94/1

Temperature dependence of instantons in QCD

We investigate the temperature dependence of the instanton contents of gluon fields, using unquenched lattice QCD and the cooling method. The instanton size parameter deduced from the correlation function decreases from 0.44fm below the phase-transition temperature $T_c$ ($\approx 150$MeV) to 0.33fm at 1.3 $T_c$. The instanton charge distribution is Poissonian above $T_c$, but it deviates from the convoluted Poisson at low temperature. The topological susceptibility decreases rapidly below $T_c$, showing the apparent restoration of the $U(1)_A$ symmetry already at $T \approx T_c$.Comment: 8 pages TEX, 3 Postscript figures available at http://www.krl.caltech.edu/preprints/MAP.htm

Reply to Isgur's Comments on Valence QCD

We reply to Nathan Isgur's critique that is directed at some of the conclusions drawn from the lattice simulation of valence QCD, regarding the valence quark model and effective chiral theories.Comment: 12 pages, 6 figure