Searching for the QCD critical point through constant entropy density contours

TL;DR

The problem addressed is locating the QCD critical point in the phase diagram of strongly interacting matter. The authors propose a method that extrapolates lattice data at $\mu_B=0$ along contours of constant entropy density using a leading $\mathcal{O}(\mu_B^2)$ expansion with coefficients fixed by lattice inputs for $\chi_2^B$ and $s$. They identify the CP by inflection criteria and report CP locations around $(T_c, \mu_{B,c}) \approx (114 \pm 7\ \mathrm{MeV}, 602 \pm 62\ \mathrm{MeV})$ with parameterized input, and a cross-check around $(119.5, 556.5)\ \mathrm{MeV}$ from spline input, consistent within uncertainties. The results align with lattice QCD up to $\mu_B/T \le 3$ and underscore the need for higher-order terms and more precise coefficients to sharpen the endpoint, with implications for heavy-ion collision energies that can probe near-CP regions.

Abstract

We propose a novel method to locate the QCD critical point by constructing an expansion along contours of constant entropy density. Applying two independent analysis of lattice QCD data at zero baryon chemical potential, we find a critical point at $T_c = 114 \pm 7$ MeV and $μ_{B_c} = 602 \pm 62$ MeV for an expansion truncated at order $μ_B^2$. This approach is consistent with recent lattice QCD results up to $μ_B/T \leq 3$. A more precise determination of the required expansion coefficients from lattice simulations will be essential for reliably establishing the location of the QCD critical endpoint.

Figures (2)

• Figure 1: Left panel: Results for slices of constant $\mu_B/T$, with curves rescaled by different factors to prevent overlap and compared with available lattice QCD calctulations from Ref.Borsanyi:2021PRL. Right panel: Results at fixed baryon chemical potentials: $\mu_B = 450$ MeV (red, crossover), $\mu_B = 602$ MeV (blue, critical), and $\mu_B = 750$ MeV (orange, mixed phase). The blue circle marks the location of the critical point. In both panels, solid lines denote the mean lattice QCD parametrization, while shaded (translucent) bands represent the propagated uncertainty from Monte Carlo sampling.
• Figure 2: The location of the QCD critical point extracted using contours of constant entropy density extrapolated from lattice QCD results using either parametric forms (black point) or smoothing splines (blue point) for $s(T)$ and $\chi_2^B(T)$. The red and blue dashed ellipses denote the 68 % confidence regions reflecting uncertainties from the lattice input for the former and latter methods, respectively. The solid and dashed black curves represent the coexistence line and spinodal boundaries, respectively. The orange line shows the lower bound in temperature for the critical point based on heavy-ion freeze-out conditions translated to $\mu_Q = \mu_S = 0$ conditions Lysenko:2024cfoc. Green points denote chemical freeze-out parameters at various collision energies, while colored stars represent mean CP estimates from other theoretical Clarke:2024padetwoBasar:2024qcdHippert:2024bheFu:2020frgGunkel:2021dseGao:2021frg and data-driven Sorensen:2024fss approaches.