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

TL;DR

This paper develops a flexible QCD equation of state model incorporating a critical point, enabling hydrodynamic simulations to explore the QCD phase diagram and compare with heavy ion collision data.

Contribution

It introduces a method to embed a phase boundary with a critical point into a smooth equation of state, matching expected universality class critical exponents.

Findings

The model reproduces the expected critical exponents and amplitude ratios.

Crossover curves can be aligned with experimental freeze-out data.

The equations of state are suitable for hydrodynamic simulations of heavy ion collisions.

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.