Variations of the crossover and first-order phase transition curve in modeling the QCD equation of state

TL;DR

The paper tackles constructing a QCD equation of state that incorporates a critical point consistent with lattice QCD at small $\mu$ and perturbative QCD at high $T$, while embedding the critical behavior within a smooth background. It employs a singular scaling component aligned with the 3D Ising universality, mapped to QCD charges via conjugate variables, and merged with a noncritical background through a windowed coupling $P(\mu,T)=P_{BG}(\mu,T)+W(\mu,T)P_{*}(R,\theta)$. Two criteria (Conditions A and B) are explored to define the phase coexistence curve and a crossover line $\mu_x(T)$, yielding lines that intersect both $T$ and $\mu$ axes and are compatible with chemical freeze-out data. The background is calibrated to lattice results and matched to perturbative QCD, with results applicable to hydrodynamic simulations of heavy-ion collisions and neutron-star mergers; the framework is deliberately flexible, allowing variation of $T_c$, $\mu_c$, exponents, and background choices to study critical phenomena in QCD.

Abstract

Lattice QCD calculations have shown that the transition from hadrons to quarks and gluons is a rapid crossover at $T = 155-160$ MeV at vanishing chemical potential. Many model calculations show that the transition is first-order at sufficiently high baryon chemical potential. It is then natural to expect the existence of a critical point where the crossover and first-order phase transition lines meet. We show how to embed a phase boundary that terminates at the critical point in a smooth background equation of state, using several different but closely related criteria, so as to yield the critical exponents and critical amplitude ratios expected of a transition in the 3D Ising and liquid-gas universality class. The crossover curves can be tuned to pass through experimental freeze-out data from heavy ion collisions at RHIC and the LHC. The resulting equations of state can be used in hydrodynamic simulations of these collisions to probe the existence of a critical point and corresponding first-order phase transition.

Figures (16)

• Figure 1: Pressure versus temperature.
• Figure 2: Trace anomaly versus temperature.
• Figure 3: $\chi_2$ versus temperature.
• Figure 4: $\chi_4$ versus temperature.
• Figure 5: The phase coexistence boundary determined by the background density following Ref. Kapusta:2022pny. The dashed curve is the analytic extension for $T > T_c$.