Phenomenological Modeling of the QCD Equation of State with a First Order Phase Transition

Abstract

QCD is expected to possess a first-order phase transition at large temperatures resultingfrom the breaking of chiral SU(2)_L × SU(2)_R flavor symmetry into SU(2)_V flavor symmetry. This transition is between a hadronic phase and a deconfined quark-gluon plasma (QGP) phase. Due to the finite quark masses, this transition becomes a smooth crossover for small baryon densities, resulting in the phase transition line terminating in a critical point at some finite T_c ≈ 150MeV and µ_c ≈ 500MeV. The technical complexities of QCD make computations of the equation of state for QCD matter challenging. In this work, we describe ways of expressing the QCD equation of state across a range of energy scales. These include perturbative QCD, hadron resonance gasses, and relativistic mean-field theory. From these, we construct a number of phenomenological equations of state with the aim of modeling the critical behavior of QCD. We compare these models highlighting their features and drawbacks. One method involves directly interpolating between low energy and high energy equations of state through the use of a switching function which parameterized the contribution of each. A number of such functions are presented. In another model, we embed a critical point into a smooth background equation of state through use of a multiplicative factor inspired by solutions to the general cubic. The last method is a modification of the Schofield parameterization of systems in the 3D-Ising universality class. We present two instances where we have used such models to good effect. First, we used a simplified crossover model to predict mass-radius relations for neutron stars. Second, a crossover model was used as part of the hydrodynamic phase of a recent simulation of heavy ion collisions, which were used to obtain transport coefficients of hadronic matter. We also provide a software framework for computing these equations of state and other relevant thermodynamic observables within each model.