Chiral crossover in QCD at zero and non-zero chemical potentials

Abstract

We present results for pseudo-critical temperatures of QCD chiral crossovers at zero and non-zero values of baryon ($B$), strangeness ($S$), electric charge ($Q$), and isospin ($I$) chemical potentials $\hat{I}{¼}_{X=B,Q,S,I}$. The results were obtained using lattice QCD calculations carried out with two degenerate up and down dynamical quarks and a dynamical strange quark, with quark masses corresponding to physical values of pion and kaon masses in the continuum limit. By parameterizing pseudo-critical temperatures as $T_c(\hat{I}{¼}_X)=T_c(0)\left[1-\hat{I}{º}_2^X(\hat{I}{¼}_X/T_c(0){)}^2-\hat{I}{º}_4^X(\hat{I}{¼}_X/T_c(0){)}^4\right]$, we determined $\hat{I}{º}_2^X$ and $\hat{I}{º}_4^X$ from Taylor expansions of chiral observables in $\hat{I}{¼}_X$. We obtained a precise result for $T_c(0)=(156.5\pm 1.5)\mathrm{MeV}$. For analogous thermal conditions at the chemical freeze-out of relativistic heavy-ion collisions, i.e., $\hat{I}{¼}_S(T,\hat{I}{¼}_B)$ and $\hat{I}{¼}_Q(T,\hat{I}{¼}_B)$ fixed from strangeness-neutrality and isospin-imbalance, we found $\hat{I}{º}_2^B=0.012(4)$ and $\hat{I}{º}_4^B=0.000(4)$. For $\hat{I}{¼}_B\lesssim 300\mathrm{MeV}$, the chemical freeze-out takes place in the vicinity of the QCD phase boundary, which coincides with the lines of constant energy density of $0.42(6){GeV/fm}^3$ and constant entropy density of $3.7(5){\mathrm{fm}}^{-3}$.