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We match three hadronic equations of state at low energy densities to aperturbatively computed equation of state of quarks and gluons at high energydensities. One of them includes all known hadrons treated as point particles,which approximates attractive interactions among hadrons. The other twoinclude, in addition, repulsive interactions in the form of excluded volumesoccupied by the hadrons. A switching function is employed to make the crossovertransition from one phase to another without introducing a thermodynamic phasetransition. A chi-square fit to accurate lattice calculations with temperature$100 < T < 1000$ MeV determines the parameters. These parameters quantify thebehavior of the QCD running gauge coupling and the hard core radius of protonsand neutrons, which turns out to be $0.62 \pm 0.04$ fm. The most physicallyreasonable models include the excluded volume effect. Not only do they includethe effects of attractive and repulsive interactions among hadrons, but theyalso achieve better agreement with lattice QCD calculations of the equation ofstate. The equations of state constructed in this paper do not result in aphase transition, at least not for the temperatures and baryon chemicalpotentials investigated. It remains to be seen how well these equations ofstate will represent experimental data on high energy heavy ion collisions whenimplemented in hydrodynamic simulations.

Matching Excluded Volume Hadron Resonance Gas Models and Perturbative QCD to Lattice Calculations