Employing a nonperturbative gauge invariant definition of the Debye screening mass m D in the effective field theory approach to finite temperature QCD, we use 3D lattice simulations to determine the leading O ͑g 2 ͒ and to estimate the next-to-leading O ͑g 3 ͒ corrections to m D in the high temperature region. The O ͑g 2 ͒ correction is large and modifies qualitatively the standard power-counting hierarchy picture of correlation lengths in high temperature QCD. [S0031-9007(97)04353-6] PACS numbers: 11.10. Wx, 11.15.Ha, 12.38.Mh QCD matter, a spatially and temporally extended system of matter described by the laws of quantum chromodynamics, goes at high temperatures into a quark-gluon plasma phase, in which color is no more confined and chiral symmetry is restored. An essential quantity, describing coherent static interactions in the plasma, is the inverse screening length of color electric fields, the Debye mass m D . The Debye mass enters in many essential characteristics of static properties of the plasma. Its numerical value is important for phenomenological discussions of formation of the quark-gluon plasma, for the analysis of J͞C and Y suppression in heavy ion collisions, for the computation of parton equilibration rates, etc. (see, e.g., [1]).The definition and computation of the Debye mass for Abelian QED plasma is well understood [2]. The electromagnetic current j m is a gauge-invariant quantity, and the Debye mass can be extracted from the two-point gauge invariant correlation function of j 0 in the plasma. There are no massless charged particles in QED, which allows an infrared-safe perturbative computation of the Debye mass in powers of the electromagnetic coupling e. This has been done to order e 5 [3]. The situation in QCD is much more complicated. First, the corresponding current in QCD, j a m , is not a gauge-invariant quantity. Second, there are massless charged gluons which give rise to infrared divergences and prevent the perturbative determination of the Debye mass beyond leading order.A nonperturbative gauge-invariant definition of the Debye mass in vectorlike theories with zero chemical potential was suggested in [4]. According to it, m D can be defined from the large distance exponential falloff of correlators of gauge-invariant time-reflection odd The aim of this Letter is a nonperturbative determination of the high temperature limit of the Debye mass, at T . a few 3 T c . We will see that the effective 3D approach to high temperature gauge theories, developed in [5][6][7] (for a review, see [8]) allows a simple and transparent gauge-invariant definition of the Debye mass [4], while 3D lattice Monte Carlo simulations provide an economical way to determine its value. The corrections to the leading result we shall find are numerically large; thus many computations in the phenomenology of quark-gluon plasma in heavy ion collisions should be reanalyzed.The theory we shall study is QCD with N f massless quark flavors and with the gauge group SU͑N͒ with N 2, 3. At high temperatures and zero...

We study a new method-maximal variance reduction-for reducing the variance of stochastic estimators for quark propagators. We find that while this method is comparable to the usual iterative inversion for light-light mesons, a considerable improvement is achieved for systems containing at least one infinitely heavy quark. Such systems are needed for heavy quark effective theory. As an illustration of the effectiveness of the method we present results for the masses of the ground state and excited states of Q q mesons and Q qq baryons. We compare these results with the experimental spectra involving b quarks.

We study numerically the phase structure of the Ginzburg-Landau model, with particular emphasis on mass measurements. There is no local gauge-invariant order parameter, but we find that there is a phase transition characterized by a vanishing photon mass. For type-I superconductors the transition is of first order. For type-II, a first-order transition is excluded by susceptibility analysis, but the photon correlation length is compatible with second-order critical behavior with ϳ 1 2 . The scalar mass, in contrast, does not show clear critical behavior in the type-II regime for V→ϱ, contrary to the conventional picture.

We study the finite temperature electroweak phase transition in an external hypercharge U(1) magnetic field H Y , using lattice Monte Carlo simulations. For sufficiently small fields, H Y /T 2 < ∼ 0.3, the magnetic field makes the first order transition stronger, but it still turns into a crossover for Higgs masses m H < ∼ 80 GeV. For larger fields, we observe a mixed phase analogous to a type I superconductor, where a single macroscopic tube of the symmetric phase, parallel to H Y , penetrates through the broken phase. For the magnetic fields and Higgs masses studied, we did not see indications of the expected Ambjørn-Olesen phase, which should be similar to a type II superconductor.