The QCD transition temperature:: Results with physical masses in the continuum limit

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(ud)) 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 not equal 0 transition, though other lattice fermion formulations (e.g. Wilson) are needed to cross-check them. (c) 2006 Elsevier B.V. All rights reserved.