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 ${\mu }_{X=B,Q,S,I}$. 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 $T_c({\mu }_X)=T_c(0)\left[1-{\kappa }_2^X({\mu }_X/T_c(0){)}^2-{\kappa }_4^X({\mu }_X/T_c(0){)}^4\right]$, we determined ${\kappa }_2^X$ and ${\kappa }_4^X$ from Taylor expansions of chiral observables in ${\mu }_X$. 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., ${\mu }_S(T,{\mu }_B)$ and ${\mu }_Q(T,{\mu }_B)$ fixed from strangeness-neutrality and isospin-imbalance, we found ${\kappa }_2^B=0.012(4)$ and ${\kappa }_4^B=0.000(4)$. For ${\mu }_B\lesssim 300\mathrm{MeV}$, 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 $3.7(5){\mathrm{fm}}^{-3}$.