1206.0901 (A. Tawfik et al.)
A. Tawfik, H. Magdy
The equation of state and squared speed of sound $c_s^2$ are studied in grand canonical ensemble of all hadron resonances having masses $\leq 2\,$GeV. The ensemble is divided into strange and non-strange hadron resonances. Furthermore, pionic, bosonic and femeionic sectors are considered, separately. It is found that $c_s^2$ calculated in the QCD matter below $T_c$ is obviously causal. There is no sign for superluminal phenomena. It is found that the lightest Goldstone bosons, the pions, represent the main contributors to $c_s^2$ at low temperatures. At this temperature scale, they determine the hadronic thermodynamics including the equation of state, almost entirely. The comparison of the barotropic dependence of the pressure calculated in the hadron resonance gas (HRG) with that of full lattice QCD at vanishing and finite chemical potential is excellent. Nevertheless, the comparison of $c_s^2$ at vanishing chemical potential is not that good. But, when switching on the chemical potential, HRG $c_s^2$ and that of full lattice QCD are in good agreement, especially when $c_s^2$ is calculated through the ratio $s/c_v$, where $s$ and $c_v$ being entropy and specific heat, respectively. Such a discrepancy in reproducing the equation of state, but not the speed of sound can be understood as the specific heat reflects several types of energy susceptibilities and fluctuations. Apparently, all these collective phenomena are not entirely implemented in HRG.
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http://arxiv.org/abs/1206.0901
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