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Investigation on the contribution of the particle mass to the interaction measure

Collective phenomena from RHIC and LHC experiments indicate a strongly coupled quark gluon plasma. Finite temperature lattice QCD calculations show the interaction measure, $Δ\equiv(ε-3p)/T^4$, is sizeable over a considerable range of temperatures above the deconfinement temperature, which may also indicate that the plasma is strongly interacting. For the ideal gas with massless particles, the interaction measure is zero. A nonzero value is probably due to either the interaction or the mass. In order to see the contribution of the particle mass to the interaction measure, in this paper we study a system without any interactions, i.e., an ideal gas with massive particles. After assembling the standard formulas of the quantum statistics with relativistic energy, we calculate the energy density, the pressure and the interaction measure. We find that their dependences on temperature reproduce the qualitative features of the lattice result. The interaction measure is nonzero for an ideal gas, which demonstrates that the particle mass contributes to the interaction measure. By our estimate, in the interaction measure obtained by the lattice calculation, quark mass contributes less than (40-50)%. There are sizeable residue interactions in the deconfined phase.