# Embedding a critical point in a hadron to quark-gluon crossover equation of state

J. I. Kapusta, T. Welle, Christopher J Plumberg

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## Abstract

Lattice QCD simulations have shown unequivocally that the transition from hadrons to quarks and gluons is a crossover when the baryon chemical potential is zero or small. Many model calculations predict the existence of a critical point at a value of the chemical potential where current lattice simulations are unreliable. We show 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 three-dimensional Ising model. There are only two independent critical exponents; the relations α+2β+γ=2 and β(δ-1)=γ arise automatically, as does a relation between the two critical amplitudes. The resulting equation of state has parameters that may be inferred by hydrodynamic modeling of heavy-ion collisions in the Beam Energy Scan II at the BNL Relativistic Heavy Ion Collider or in experiments at other accelerators.

Original language English (US) 014909 Physical Review C 106 1 https://doi.org/10.1103/PhysRevC.106.014909 Published - Jul 2022

### Bibliographical note

Funding Information:
The work of J.I.K. and T.W. was supported by the U.S. DOE under Grant No. DE-FG02-87ER40328. The work of C.P. was supported by the U.S. DOE under Grant No. DE-SC0020633.