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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.
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 New (as yet unpublished) data are presented, which for Nf = 3 and on Nt = 4 confirm the scenario without a critical point.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.
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.
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.
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.
We review our knowledge of the phase diagram of QCD as a function of temperature, chemical potential and quark masses. The presence of tricritical lines at imaginary chemical potential m = i p 3 T, with known scaling behaviour in their vicinity, puts constraints on this phase diagram, especially in the case of two light flavors. We show first results in our project to determine the finite-temperature behaviour in the Nf = 2 chiral limit.
A lot of effort in lattice simulations over the last years has been devoted to studies of the QCD deconfinement transition. Most state-of-the-art simulations use rooted staggered fermions, while Wilson fermions are affected by large systematic uncertainties, such as coarse lattices or heavy sea quarks. Here we report on an ongoing study of the transition, using two degenerate flavours of nonperturbatively O(a) improved Wilson fermions. We start with Nt = 12 and 16 lattices and pion masses of 600 to 450 MeV, aiming at chiral and continuum limits with light quarks.
LatticeQCD using OpenCL
(2011)
We perform a detailed study of the adjoint static potential in the pseudoparticle approach, which is a model for SU(2) Yang-Mills theory. We find agreement with the Casimir scaling hypothesis and there is clear evidence for string breaking. At the same time the potential in the fundamental representation is linear for large separations. Our results are in qualitative agreement with results from lattice computations.