Embedding a Critical Point in a Hadron to Quark-Gluon Crossover Equation of State

TL;DR

This paper presents a method to incorporate a critical point into a hadron to quark-gluon crossover equation of state, reproducing expected critical behavior and enabling better modeling of heavy ion collision data.

Contribution

It introduces a way to embed a critical point in a smooth equation of state, matching the universality class of the liquid-gas transition and 3D Ising model, with implications for heavy ion collision analysis.

Findings

Reproduces critical exponents and amplitude ratios consistent with universality class.

Derives automatic relations among critical exponents and amplitudes.

Provides parameters for hydrodynamic modeling of heavy ion collisions.

Abstract

It is shown how to embed a critical point in a smooth background equation of state so as to yield the critical exponents and critical amplitude ratios expected of a transition in the same universality class as the liquid-gas phase transition and the 3D Ising model. There are only two independent critical exponents; the relations $\alpha + 2\beta + \gamma = 2$ and $\beta (\delta - 1) = \gamma$ arise automatically, as does a new relation between the two critical amplitudes. The resulting equation of state has parameters which may be inferred by hydrodynamic modeling of heavy ion collisions in the Beam Energy Scan II at the Relativistic Heavy Ion Collider.