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

The transition temperature (Tc) 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 (mud) and for the strange quark (ms). Four sets of lattice spacings (Nt=4, 6, 8 and 10) were used to carry out a continuum extrapolation. It turned out that only Nt=6, 8 and 10 can be used for a controlled extrapolation, Nt=4 is out of the scaling region. Since the QCD transition is a non-singular cross-over there is no unique Tc. Thus, different observables lead to different numerical Tc values even in the continuum and thermodynamic limit. The peak of the renormalized chiral susceptibility predicts Tc=151(3)(3)MeV, wheres Tc-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.