Abstract
The Hadron-Resonance Gas (HRG) approach - used to model hadronic matter at small baryon potentials $\mu_B$ and finite temperature $T$ - is extended to finite and large chemical potentials by introducing interactions between baryons in line with relativistic mean-field theory defining an interacting HRG (IHRG). Using lattice data for $\mu_B=0$ as well as information on the nuclear equation of state at $T=0$ we constrain the attractive and repulsive interactions of the IHRG such that it reproduces the lattice equation of state at $\mu_B=0$ and the nuclear equation of state at $T=0$ and finite $\mu_B$. The formulated covariant approach is thermodynamically consistent and allows us to provide further information on the phase boundary between hadronic and partonic phases of strongly interacting matter by assuming constant thermodynamic potentials.
Highlights
The phase diagram of matter is one of the most important subjects in physics since it has important implications on chemistry and biology
Since lattice calculations so far suffer from the fermion-sign problem, no first-principles information on the phase boundary can be extracted from Lattice quantum-chromodynamics (lQCD) at large μB, whereas at low μB Taylor expansions of the thermodynamic potential provide an alternative solution as demonstrated in Refs. [9,10]
We find an excellent agreement between lQCD and the model NLDD1, which describes the whole equation of state within the error bars of the data, even at temperatures
Summary
The phase diagram of matter is one of the most important subjects in physics since it has important implications on chemistry and biology. A common model used in the first regime is the hadron-resonance gas (HRG) model that treats hadrons as a gas of noninteracting particles This model works at vanishing chemical potential but fails for the description of nuclear matter due to the lack of repulsive and attractive interactions. The latter are included in relativistic mean-field theories (RMFTs) whose interactions are based on meson-exchange potentials While these models can describe infinite nuclear matter with the right properties of the binding energy, they fail for the QCD equation of state at vanishing chemical potential μB. There is no consensus whether to include the σ and the κ in HRG models or not since calculations for the thermodynamic potential of an interacting pion gas in terms of experimental phase shifts show that the attractive pressure contribution from the scalar σ mesons gets exactly canceled by. A comparison between the HRG and lQCD data shows that the experimentally established hadrons are not sufficient to describe strangeness fluctuations [62], which indicates that a full description of QCD (above about temperatures of 150 MeV) in terms of hadronic degrees of freedom requires an even stronger interaction
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