Abstract
The transition temperature ( T c ) of QCD is determined by Symanzik improved gauge and stout-link improved staggered fermionic lattice simulations. We use physical masses both for the light quarks ( m u d ) and for the strange quark ( m s ). Four sets of lattice spacings ( N t = 4 , 6, 8 and 10) were used to carry out a continuum extrapolation. It turned out that only N t = 6 , 8 and 10 can be used for a controlled extrapolation, N t = 4 is out of the scaling region. Since the QCD transition is a non-singular cross-over there is no unique T c . Thus, different observables lead to different numerical T c values even in the continuum and thermodynamic limit. The peak of the renormalized chiral susceptibility predicts T c = 151 ( 3 ) ( 3 ) MeV , wheres T c -s based on the strange quark number susceptibility and Polyakov loops result in 24(4) MeV and 25(4) MeV larger values, respectively. Another consequence of the cross-over is the non-vanishing width of the peaks even in the thermodynamic limit, which we also determine. These numbers are attempted to be the full result for the T ≠ 0 transition, though other lattice fermion formulations (e.g. Wilson) are needed to cross-check them.
Highlights
The results presented in these works seem to confirm those of [2], in particular [4] concluded as: ”The preliminary results of the hotQCD collaboration indicate that the crossover region for both deconfinement and chiral symmetry restoration lie in the range T = (185-195) MeV”
Among other things one has to take into account that most lattice calculations are carried out with periodic boundary condition, which is convenient for the computations, but rather far from the experimental setup
An exploratory quenched study suggests [7] that critical temperatures with realistic boundary conditions can be up to 30 MeV larger than the values, which are measured in conventional lattice calculations
Summary
The primary role of zero temperature simulations is that they are used to convert the dimensionless temperature of the lattice to physical units. In [6] we had carried out zero temperature simulations at four different points with nonphysical light quark masses at each lattice spacing and made an extrapolation down to the physical point. In order to check the size of the systematics of these chiral extrapolations, we decided to carry out new simulations directly at the physical point for the same lattice spacings as in [6]. As it will be shown our approach of [6] was very accurate. Our code is ported to two types of architectures: Intel PC equipped with Graphical Processing Units (see [10]) and BlueGene/P
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