String Tension and Thermodynamics with Tree Level and Tadpole Improved Actions

We calculate the string tension, deconfinement transition temperature and bulk thermodynamic quantities of the SU(3) gauge theory using tree level and tadpole improved actions. Finite temperature calculations have been performed on lattices with temporal extent N_tau = 3 and 4. Compared to calculations with the standard Wilson action on this size lattices we observe a drastic reduction of the cut-off dependence of bulk thermodynamic observables at high temperatures. In order to test the influence of improvement on long-distance observables at T_c we determine the ratio T_c/sqrt(sigma). For all actions, including the standard Wilson action, we find results which differ only little from each other. We do, however, observe an improved asymptotic scaling behaviour for the tadpole improved action compared to the Wilson and tree level improved actions.Comment: 20 pages, LaTeX2e File, 8 coloured Postscript figures, new analysis added, recent Wilson action string tension results included, figures replace

QCD Thermodynamics with Improved Actions

The thermodynamics of the SU(3) gauge theory has been analyzed with tree level and tadpole improved Symanzik actions. A comparison with the continuum extrapolated results for the standard Wilson action shows that improved actions lead to a drastic reduction of finite cut-off effects already on lattices with temporal extent $N_\tau=4$. Results for the pressure, the critical temperature, surface tension and latent heat are presented. First results for the thermodynamics of four-flavour QCD with an improved staggered action are also presented. They indicate similarly large improvement factors for bulk thermodynamics.Comment: Talk presented at LATTICE96(finite temperature) 4 pages, LaTeX2e file, 6 eps-file

SU(3) Latent Heat and Surface Tension from Tree Level and Tadpole Improved Actions

We analyze the latent heat and surface tension at the SU(3) deconfinement phase transition with tree level and tadpole improved Symanzik actions on lattices with temporal extent $N_\tau = 3$ and 4 and spatial extent $N_\sigma/ N_\tau = 4$, 6 and 8. In comparison to the standard Wilson action we do find a drastic reduction of cut-off effects already with tree level improved actions. On lattices with temporal extent $N_\tau=4$ results for the surface tension and latent heat obtained with a tree level improved action agree well with those obtained with a tadpole improved action. A comparison with $N_\tau=3$ calculations, however, shows that results obtained with tadpole action remain unaffected by cut-off effects even on this coarse lattice, while the tree level action becomes sensitive to the cut-off. For the surface tension and latent heat we find $\sigma_I/ T_c^3 = 0.0155~(16)$ and $\Delta\epsilon/T_c^4 = 1.40~(9)$, respectively.Comment: 11 pages, LaTeX2e File, 3 Postscript figure

Staggered Fermion Actions with Improved Rotational Invariance

We introduce a class of improved actions for staggered fermions which to O(p^4) and O(p^6), respectively, lead to rotationally invariant propagators. We discuss the resulting reduction of flavour symmetry breaking in the meson spectrum and comment on the improvement in the calculation of thermodynamic observables.Comment: 3 pages and 4 figures, Contribution to Lattice 97 (Poster Session), late

The Pressure in 2, 2+1 and 3 Flavour QCD

We calculate the pressure in QCD with two and three light quarks on a lattice of size 16^3x4 using tree level improved gauge and fermion actions. We argue that for temperatures T > 2T_c systematic effects due to the finite lattice cut-off and non-vanishing quark masses are below 15% in this calculation and give an estimate for the continuum extrapolated pressure in QCD with massless quarks. We find that the flavour dependence of the pressure is dominated by that of the Stefan-Boltzmann constant. Furthermore we perform a calculation of the pressure using 2 light (m_u,d/T=0.4) and one heavier quark (m_s/T = 1). In this case the pressure is reduced relative to that of three flavour QCD. This effect is stronger than expected from the mass dependence of an ideal Fermi gas.Comment: 13 pages, LaTeX2

The string tension in SU(N) gauge theory from a careful analysis of smearing parameters

We report a method to select optimal smearing parameters before production runs and discuss the advantages of this selection for the determination of the string tension.Comment: Contribution to Lat97 poster session, title was 'How to measure the string tension', 3 pages, 5 colour eps figure

3-d Lattice QCD Free Energy to Four Loops

We compute the expansion of the 3-d Lattice QCD free energy to four loop order by means of Numerical Stochastic Perturbation Theory. The first and second order are already known and are correctly reproduced. The third and fourth order coefficients are new results. The known logarithmic divergence in the fourth order is correctly identified. We comment on the relevance of our computation in the context of dimensionally reduced finite temperature QCD.Comment: 8 pages, 3 figures, latex typeset with JHEP3.cl

Equation of state for pure SU(3) gauge theory with renormalization group improved action

A lattice study of the equation of state for pure SU(3) gauge theory using a renormalization-group (RG) improved action is presented. The energy density and pressure are calculated on a $16^3\times 4$ and a $32^3\times 8$ lattice employing the integral method. Extrapolating the results to the continuum limit, we find the energy density and pressure to be in good agreement with those obtained with the standard plaquette action within the error of 3-4%.Comment: 17 pages, 14 figures, revte

Pade-related resummations of the pressure of quark-gluon plasma by approximate inclusion of g**6-terms

We perform various resummations of the hot QCD pressure based on the actual knowledge of the perturbation series which includes the g**6 ln(1/g) and part of the g**6 terms. Resummations are performed separately for the short- and long-distance parts. The g**6 term of the short-distance pressure is estimated on the basis on the known UV cutoff dependence of the long-distance part. The resummations are of the Pade and Borel-Pade type, using in addition the (Pade-)resummed expression for the squared screening mass mE**2 and for the EQCD coupling parameter gE**2. The resummed results depend weakly on the yet unknown g**6 terms and on the the short-range renormalization scale, at all temperatures. The dependence on the long-range renormalization scale is appreciable at low temperatures T < 1 GeV. The resulting dependence of pressure on temperature T is compatible with the results of the lattice calculations at low T.Comment: 25 pages, 15 double figures, 4 single figures, revtex4; thoroughly extended analysis; more figures; conclusions more clearly formulated; new references added; title slightly changed; accepted for publication in Phys.Rev.

Four loop stochastic perturbation theory in 3d SU(3)

Dimensional reduction is a key issue in finite temperature field theory. For example, when following the QCD Free Energy from low to high scales across the critical temperature, ultrasoft degrees of freedom can be captured by a 3d SU(3) pure gauge theory. For such a theory a complete perturbative matching requires four loop computations, which we undertook by means of Numerical Stochastic Perturbation Theory. We report on the computation of the pure gauge plaquette in 3d, and in particular on the extraction of the logarithmic divergence at order g^8, which had already been computed in the continuum.Comment: 3 pages, 2 figure, Lattice2003(nonzero