Finite density QCD equation of state: critical point and lattice-based $T'$-expansion

TL;DR

This paper introduces a new lattice-based equation of state for finite density QCD that incorporates a critical point and matches lattice results, aiding experimental searches for the QCD critical point.

Contribution

It develops a novel construction combining resummation of lattice QCD with critical behavior, providing a flexible family of equations of state with a tunable critical point.

Findings

Provides equations of state covering 0 ≤ μ_B ≤ 700 MeV and 25 MeV ≤ T ≤ 800 MeV.

Includes a critical point in the 3D Ising universality class within experimental reach.

Ensures stability and causality, extending previous parametric QCD EoS models.

Abstract

We present a novel construction of the QCD equation of state (EoS) at finite baryon density. Our work combines a recently proposed resummation scheme for lattice QCD results with the universal critical behavior at the QCD critical point. This allows us to obtain a family of equations of state in the range $0 \leq \mu_B \leq 700$ MeV and 25 MeV $\leq T \leq 800$ MeV, which match lattice QCD results near $\mu_B=0$ while featuring a critical point in the 3D Ising model universality class. The position of the critical point can be chosen within the range accessible to beam-energy scan heavy-ion collision experiments. The strength of the singularity and the shape of the critical region are parameterized using a standard parameter set. We impose stability and causality constraints and discuss the available ranges of critical point parameter choices, finding that they extend beyond earlier parametric QCD EoS proposals. We present thermodynamic observables, including baryon density, pressure, entropy density, energy density, baryon susceptibility and speed of sound, that cover a wide range in the QCD phase diagram relevant for experimental exploration.