QCD phase diagram: A comparison of lattice and hadron resonance gas model calculations

Abstract

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 ${\ensuremath{\mu}}_{B}$. For the strangeness chemical potentials ${\ensuremath{\mu}}_{S}$, we use two models. In one model, we explicitly set ${\ensuremath{\mu}}_{S}=0$ for all temperatures and baryo-chemical potentials. This assignment is used in lattice calculations. In the other model, ${\ensuremath{\mu}}_{S}$ is calculated in dependence on $T$ and ${\ensuremath{\mu}}_{B}$ according to the condition of vanishing strangeness. We also derive an analytical expression for the dependence of ${T}_{c}$ on ${\ensuremath{\mu}}_{B}/T$ by applying Taylor expansion of $ϵ$. In both cases, we compare HRGM results on ${T}_{c}\ensuremath{-}{\ensuremath{\mu}}_{B}$ 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.