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

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.

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