We compare the lattice results on QCD phase diagram for two and three flavors with the hadron resonance gas model (HRGM) calculations. Lines of constant energy density $ϵ$ have been determined at different baryo-chemical potentials ${\mu }_B$. For the strangeness chemical potentials ${\mu }_S$, we use two models. In one model, we explicitly set ${\mu }_S=0$ for all temperatures and baryo-chemical potentials. This assignment is used in lattice calculations. In the other model, ${\mu }_S$ is calculated in dependence on $T$ and ${\mu }_B$ according to the condition of vanishing strangeness. We also derive an analytical expression for the dependence of $T_c$ on ${\mu }_B/T$ by applying Taylor expansion of $ϵ$. In both cases, we compare HRGM results on $T_c-{\mu }_B$ diagram with the lattice calculations. The agreement is excellent, especially when the trigonometric function of $ϵ$ is truncated up to the same order as done in lattice simulations. For studying the efficiency of the truncated Taylor expansion, we calculate the radius of convergence. For zero- and second-order radii, the agreement with lattice is convincing. Furthermore, we make predictions for QCD phase diagram for nontruncated expressions and physical masses. These predictions are to be confirmed by heavy-ion experiments and future lattice calculations with very small lattice spacing and physical quark masses.

• Received 22 December 2004

DOI:https://doi.org/10.1103/PhysRevD.71.054502