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

In this work, we systematically assess the performance of a new method from [H. Shah et al., ] 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 nonparabolic contour behavior at low temperatures ( T ≲ 120 MeV ), it accurately reproduces the critical point 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 ) ≈ ( 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.