We present results on the QCD phase diagram for µ B ≤ πT . Our simulations are performed with an imaginary chemical potential µ = iµ I for which the fermion determinant is positive. On an 8 3 × 4 lattice with 2 flavors of staggered quarks, we map out the phase diagram and identify the (pseudo-)critical temperature T c (µ I ). For µ I /T ≤ π/3, this is an analytic function, whose Taylor expansion is found to converge rapidly, with truncation errors far smaller than statistical ones. The truncated series may then be continued to real µ, yielding the corresponding phase diagram for µ B < ∼ 500 MeV. This approach provides control over systematics and avoids reweighting. We compare it with other recent work.

We derive a static potential for a heavy quark-antiquark pair propagating in Minkowski time at finite temperature, by defining a suitable gauge-invariant Green's function and computing it to first non-trivial order in Hard Thermal Loop resummed perturbation theory. The resulting Debye-screened potential could be used in models that attempt to describe the "melting" of heavy quarkonium at high temperatures. We show, in particular, that the potential develops an imaginary part, implying that thermal effects generate a finite width for the quarkonium peak in the dilepton production rate. For quarkonium with a very heavy constituent mass M , the width can be ignored for T < ∼ g 2 M/12π, where g 2 is the strong gauge coupling; for a physical case like bottomonium, it could become important at temperatures as low as 250 MeV. Finally, we point out that the physics related to the finite width originates from the Landau-damping of low-frequency gauge fields, and could be studied non-perturbatively by making use of the classical approximation.

We present numerical results for the location of the chiral critical line at finite temperature and zero and non-zero baryon density for QCD with N f = 2 + 1 flavours of staggered fermions on lattices with temporal extent N t = 4. For degenerate quark masses, we compare our results obtained with the exact RHMC algorithm with earlier, inexact R-algorithm results and find a reduction of 25% in the critical quark mass, for which the first order phase transition changes to a smooth crossover. Extending our analysis to non-degenerate quark masses, we map out the chiral critical line up to the neighbourhood of the physical point, which we confirm to be in the crossover region. Our data are consistent with a tricritical point at (m u,d = 0, m s ∼500) MeV.We also investigate the shift of the critical line with finite baryon density, by simulating with an imaginary chemical potential for which there is no sign problem. We observe this shift to be very small or, conversely, the critical endpoint µ c (m u,d , m s ) to be extremely quark mass sensitive. Moreover, the sign of this shift is opposite to standard expectations. If confirmed on a finer lattice, it implies the absence of a critical endpoint for physical QCD at small chemical potential, or another revision of the QCD phase diagram. We critically examine earlier lattice determinations of the QCD critical point, and find them to be in no contradiction with our conclusion. Hence we argue that finer lattices are required to settle even the qualitative features of the QCD phase diagram.

We present results for the phase diagram of three flavor QCD for µ B < ∼ 500 MeV. Our simulations are performed with imaginary chemical potential µ I for which the fermion determinant is positive. Physical observables are then fitted by truncated Taylor series and continued to real chemical potential. We map out the location of the critical line T c (µ B ) with an accuracy up to terms of order (µ B /T ) 6 . We also give first results on a determination of the critical endpoint of the transition and its quark mass dependence. Our results for the endpoint differ significantly from those obtained by other methods, and we discuss possible reasons for this.

We review lattice QCD investigations at high temperature. After a short introduction to thermal QCD on the lattice, we report on the present understanding of the phase diagram and the equation of state, particularly in the presence of dynamical quarks. We discuss various screening lengths in the plasma phase, including results from dimensionally reduced QCD. We then summarize lattice data on quark-number susceptibilities and spectral densities, both of which are immediately relevant to the interpretation of heavy-ion experiments. A major section is devoted to simulations of QCD at small, yet phenomenologically important, values for the baryon density.

We use a perturbatively derived effective field theory and three-dimensional lattice simulations to determine the longest static correlation lengths in the deconfined QCD plasma phase at high temperatures (T > ∼ 2T c ) and finite densities (µ < ∼ 4T ). For vanishing chemical potential, we refine a previous determination of the Debye screening length, and determine the dependence of different correlation lengths on the number of massless flavours as well as on the number of colours. For non-vanishing but small chemical potential, the existence of Debye screening allows us to carry out simulations corresponding to the full QCD with two (or three) massless dynamical flavours, in spite of a complex action. We investigate how the correlation lengths in the different quantum number channels change as the chemical potential is switched on.Edinburgh 2000/09

Using combined strong coupling and hopping parameter expansions, we derive an effective three-dimensional theory from thermal lattice QCD with heavy Wilson quarks. The theory depends on traced Polyakov loops only and correctly reflects the centre symmetry of the pure gauge sector as well as its breaking by finite mass quarks. It is valid up to certain orders in the lattice gauge coupling and hopping parameter, which can be systematically improved. To its current order it is controlled for lattices up to N τ ∼ 6 at finite temperature. For nonzero quark chemical potentials, the effective theory has a fermionic sign problem which is mild enough to carry out simulations up to large chemical potentials. Moreover, by going to a flux representation of the partition function, the sign problem can be solved. As an application, we determine the deconfinement transition and its critical end point as a function of quark mass and all chemical potentials.

We calculate the masses of the low-lying states with quantum numbers J P C = 0 ++ , 1 −− in the Higgs and confinement regions of the three-dimensional SU(2) Higgs model, which plays an important rôle 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.