Lattice-based equation of state with a critical point from constant entropy contours and its comparison to effective QCD approaches

Abstract

In this work, we systematically assess the performance of a new method from [H. Shah et al., Phys. Rev. C 113, L012201] for locating the QCD critical point using constant-entropy contours by testing it against various effective QCD approaches. We demonstrate that, while the method yields spurious critical points in purely hadronic models (HRG) due to non-parabolic contour behavior at low temperatures ($T \lesssim 120$ MeV), it accurately reproduces the CP location in frameworks that feature a genuine phase transition and benchmarked against lattice QCD, such as Holographic Einstein-Maxwell-Dilaton, and Functional QCD approaches. Building on our previous determination of constant entropy contours using lattice data, we extend that analysis to construct a complete Lattice-based Equation of State (EoS) at finite density, which features a critical point at $(T, μ_B) \approx (114, 602)$ MeV. By integrating the extrapolated entropy density with respect to temperature, we reconstruct the pressure, baryon density, susceptibility, and speed of sound in the critical region, and analyze the focusing behavior of isentropic trajectories in the vicinity of the critical point.

Figures (13)

• Figure 1: Left panel: Entropy as a function of temperature for three representative baryon chemical potentials, with $\mu_1 < \mu_{B,c} < \mu_2$. Right panel: The corresponding constant-entropy trajectories in the $(T, \mu_B)$ plane. The blue star marks the location of the critical point, the shaded region indicates the spinodal domain, and the red dots highlight the spinodal points at $\mu_B = \mu_2$. Figure taken from Shah:2024img
• Figure 2: True (black, solid) vs truncated (blue, dashed) contours starting from different temperatures at zero $\mu_B$ for an ideal gas of massless quarks and gluons for both imaginary and real $\mu_B$.
• Figure 3: True contours (black, solid) shown against the extrapolated contours (blue, dashed) in an ideal hadron resonance gas model following Boltzmann statistics in the real and imaginary plane. The discrepancy in the extrapolated contours displays the invalidity of the parabolic approximation for the expansion in this case.
• Figure 4: Constant entropy contour expansion coefficient $\alpha_2$ and its temperature derivatives across various HRG-based models as functions of the temperature at vanishing $\mu_B$.
• Figure 5: Full (solid,black) vs truncated (blue,dashed) contours of constant entropy density in the excluded volume HRG model in the real baryon chemical potential plane, starting from different initial temperatures.