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

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.