Lattice calculations at non-zero chemical potential: the QCD phase diagram

The so-called sign problem of lattice QCD prohibits Monte Carlo simulations at finite baryon density by means of importance sampling. Over the last few years, methods have been developed which are able to circumvent this problem as long as the quark chemical potential is m=T <~1. After a brief review of these methods, their application to a first principles determination of the QCD phase diagram for small baryon densities is summarised. The location and curvature of the pseudo-critical line of the quark hardon transition is under control and extrapolations to physical quark masses and the continuum are feasible in the near future. No definite conclusions can as yet be drawn regarding the existence of a critical end point, which turns out to be extremely quark mass and cut-off sensitive. Investigations with different methods on coarse lattices show the lightmass chiral phase transition to weaken when a chemical potential is switched on. If persisting on finer lattices, this would imply that there is no chiral critical point or phase transition for physical QCD. Any critical structure would then be related to physics other than chiral symmetry breaking

Debye Screening in the QCD plasma

Various definitions for the QCD Debye mass and its evaluation are reviewed in a non-perturabtive framework for the study of screening of general static sources. While it is possible to perturbatively integrate over scales $\sim T$ and thus construct a 3d effective theory, the softer scales $\sim gT$ and $\sim g^2T$ are strongly coupled for temperatures \lsim 10^7 GeV and require lattice simulations. Within the effective theory, a lattice treatment of screening at finite quark densities \mu \lsim 4/T is also possible.Comment: 12 pages, 4 figures. Invited talk at Strong and Electroweak Matter, Marseille, France, June 13-17, 200

The QCD phase diagram at low baryon density from lattice simulations

The QCD phase diagram as a function of temperature, T, and chemical potential for baryon number, mB, is still unknown today, due to the sign problem, which prohibits direct Monte Carlo simulations for non-vanishing baryon density. Investigations in models sharing chiral symmetry with QCD predict a phase diagram, in which the transition corresponds to a smooth crossover at zero density, but which is strengthened by chemical potential to turn into a first order transition beyond some second order critical point. This contribution reviews the lattice evidence in favour and against the existence of a critical point

Exploring the QCD phase diagram

Lattice simulations employing reweighting and Taylor expansion techniques have predicted a (m;T)-phase diagram according to general expectations, with an analytic quark-hadron crossover at m =0 turning into a first order transition at some critical chemical potential mE. By contrast, recent simulations using imgainary m followed by analytic continuation obtained a critical structure in the fmu;d;ms;T;mg parameter space favouring the absence of a critical point and first order line. I review the evidence for the latter scenario, arguing that the various raw data are not inconsistent with each other. Rather, the discrepancy appears when attempting to extract continuum results from the coarse (Nt =4) lattices simulated so far, and can be explained by cut-off effects. New (as yet unpublished) data are presented, which for Nf = 3 and on Nt = 4 confirm the scenario without a critical point. Moreover, simulations on finer Nt = 6 lattices show that even if there is a critical point, continuum extrapolation moves it to significantly larger values of mE than anticipated on coarse lattices