Do we know eventually p(e)?

TL;DR

This paper employs a quasi-particle model to derive an equation of state from lattice QCD data, useful for hydrodynamical simulations of matter created in ultra-relativistic heavy-ion collisions, highlighting uncertainties in the transition region.

Contribution

It introduces a method to construct a family of equations of state bridging high-energy and hadronic regions using lattice QCD data and the quasi-particle model, addressing uncertainties in the transition region.

Findings

Good agreement of pressure and energy density at high energies for pseudo-critical temperature 170 ± 15 MeV

Uncertainty in the transition region of the equation of state

Model tests and discussion of chiral extrapolation and Landau damping

Abstract

A quasi-particle model is employed to derive from available lattice QCD calculations an equation of state useable in hydrodynamical simulations of the expansion stage of strongly interacting matter created in ultra-relativistic heavy-ion collisions. Various lattice results give an astonishing agreement of the pressure as a function of energy density at large energy densities supposed the pseudo-critical temperature is in the range $170 \pm 15$ MeV, while in the transition region the equation of state is not yet well constrained. Therefore, one can construct a family of equations of state by bridging the uncertain region from the uniquely given high-energy density region part to a hadronic equation of state by suitable interpolation together with the extrapolation to non-zero baryon density by means of the quasi-particle model. We present a series of tests of the model, discuss the chiral extrapolation and the role of Landau damping. We also briefly sketch the path of cosmic matter in the early universe in the phase diagram.