-
The QCD phase diagram at zero and small baryon density
(2005)
- 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.
-
QCD equation of state and dark matter
(2006)
- The QCD equation of state is not often discussed in cosmology. However, the relic density of weakly interacting massive particles (WIMPs) depends on the entropy and the expansion rate of the Universe when they freeze out, at a temperature in the range 400 MeV – 40GeV, where QCD corrections are still important. We use recent analytic and lattice calculations of the QCD pressure to produce a new equation of state suitable for use in relic density calculations. As an example, we show that relic densities calculated by the dark matter package DarkSUSY receive corrections of several per cent, within the observational accuracy of the Planck CMB mission, due for launch in 2007.
-
Strong coupling expansion for Yang-Mills theory at finite temperature
(2007)
- Euclidean strong coupling expansion of the partition function is applied to lattice Yang-Mills theory at finite temperature, i.e. for lattices with a compactified temporal direction. The expansions have a finite radius of convergence and thus are valid only for b <bc, where bc denotes the nearest singularity of the free energy on the real axis. The accessible temperature range is thus the confined regime up to the deconfinement transition. We have calculated the first few orders of these expansions of the free energy density as well as the screening masses for the gauge groups SU(2) and SU(3). The resulting free energy series can be summed up and corresponds to a glueball gas of the lowest mass glueballs up to the calculated order. Our result can be used to fix the lower integration constant for Monte Carlo calculations of the thermodynamic pressure via the integral method, and shows from first principles that in the confined phase this constant is indeed exponentially small. Similarly, our results also explain the weak temperature dependence of glueball screening masses below Tc, as observed in Monte Carlo simulations. Possibilities and difficulties in extracting bc from the series are discussed.
-
Twisted mass QCD at finite temperature
(2007)
- We discuss the use of Wilson fermions with twisted mass for simulations of QCD thermodynamics. As a prerequisite for a future analysis of the finite-temperature transition making use of automatic O(a) improvement, we investigate the phase structure in the space spanned by the hopping parameter k , the coupling b , and the twisted mass parameter m. We present results for Nf = 2 degenerate quarks on a 163×8 lattice, for which we investigate the possibility of an Aoki phase existing at strong coupling and vanishing m, as well as of a thermal phase transition at moderate gauge couplings and non-vanishing m.
-
Exploring the QCD phase diagram
(2007)
- 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 finite-temperature phase structure of lattice QCD with twisted-mass Wilson fermions
(2008)
- We report progress in our exploration of the finite-temperature phase structure of two-flavour lattice QCD with twisted-mass Wilson fermions and a tree-level Symanzik-improved gauge action for a temporal lattice size Nt = 8. Extending our investigations to a wider region of parameter space we gain a global view of the rich phase structure. We identify the finite temperature transition/ crossover for a non-vanishing twisted-mass parameter in the neighbourhood of the zerotemperature critical line at sufficiently high b . Our findings are consistent with Creutz’s conjecture of a conical shape of the finite temperature transition surface. Comparing with NLO lattice cPT we achieve an improved understanding of this shape.
-
Towards a determination of the chiral critical surface of QCD
(2009)
- 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
(2009)
- 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 low baryon density from lattice simulations
(2010)
- 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.
-
Effective theory for QCD at finite temperature and density from strong coupling expansion
(2011)
- QCD at finite temperature and denisty remains intractable by Monte Carlo simulations for quark chemical potentials m >∼T. It has been a long standing problem to derive effective theories from QCD which describe the phase structure of the former with controlled errors. We propose a solution to this problem by a combination of analytical and numerical methods. Starting from lattice QCD with in Wilson’s formulation, we derive an effective action in terms of Polyakov loops by means of combined strong coupling and hopping expansions. The theory correctly reflects the centre-symmetry in the pure gauge limit and its breaking through quarks. It is valid for heavy quarks and lattices up to Nt ∼ 6. Its sign problem can be solved and we are able to calculate the deconfinement transition of QCD with heavy quarks for all chemical potentials.
