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

TLDR

The QCD transition temperature is studied using Symanzik‑improved gauge and stout‑link improved staggered fermionic lattice simulations, and because the transition is a non‑singular cross‑over, no single Tc exists and different observables yield distinct Tc values. The study employs physical light and strange quark masses and performs a continuum extrapolation using four lattice spacings (Nt = 4, 6, 8, 10), with the Nt = 4 data excluded from the scaling region and future cross‑checks planned with Wilson fermions. The continuum‑extrapolated results show that only Nt = 6, 8, 10 are reliable, yielding a chiral‑susceptibility peak at Tc = 151 ± 3 ± 3 MeV, while strange‑quark‑number susceptibility and Polyakov‑loop observables give Tc values 24–25 MeV higher, and the cross‑over width remains finite even in the thermodynamic limit.

Abstract

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.