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 New (as yet unpublished) data are presented, which for Nf = 3 and on Nt = 4 confirm the scenario without a critical point.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

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

Fiddling with pasts : from tradition to heritage

Preprin

Towards a determination of the chiral critical surface of QCD

The chiral critical surface is a surface of second order phase transitions bounding the region of first order chiral phase transitions for small quark masses in the fmu;d;ms;mg parameter space. The potential critical endpoint of the QCD (T;m)-phase diagram is widely expected to be part of this surface. Since for m = 0 with physical quark masses QCD is known to exhibit an analytic crossover, this expectation requires the region of chiral transitions to expand with m for a chiral critical endpoint to exist. Instead, on coarse Nt = 4 lattices, we find the area of chiral transitions to shrink with m, which excludes a chiral critical point for QCD at moderate chemical potentials mB < 500 MeV. First results on finer Nt = 6 lattices indicate a curvature of the critical surface consistent with zero and unchanged conclusions. We also comment on the interplay of phase diagrams between the Nf = 2 and Nf = 2+1 theories and its consequences for physical QCD

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

The QCD phase diagram at zero and small baryon density

I review recent developments in determining the QCD phase diagram by means of lattice simulations. Since the invention of methods to side-step the sign problem a few years ago, a number of additional variants have been proposed, and progress has been made towards understanding some of the systematics involved. All available techniques agree on the transition temperature as a function of density in the regime mq/T <~1. There are by now four calculations with signals for a critical point, two of them at similar parameter values and with consistent results. However, it also emerges that the location of the critical point is exceedingly quark mass sensitive. At the same time sizeable finite volume, cut-off and step size effects have been uncovered, demanding additional investigations with exact algorithms on larger and finer lattices before quantitative conclusions can be drawn. Depending on the sign of these corrections, there is ample room for the eventual phase diagram to look as expected or also quite different, with no critical point at all