Challenges in locating the QCD critical point via constant entropy density contours

A new method was proposed recently to investigate the location of the putative critical point of strongly interacting matter, governed by quantum chromodynamics. By approximating contours of constant entropy density at finite baryon chemical potential, the conditions for the existence of a critical point are solved. In this work, we analyze this method in the hadron resonance gas and Nambu--Jona-Lasinio models. We demonstrate that the prediction of the critical point in the HRG model is solely due to mesonic and baryonic degrees of freedom, and thus is not necessarily a signal of a critical point. We argue that such an expansion leads to a physically meaningful prediction only when applied near the critical point.