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Hot QCD equations of state and relativistic heavy ion collisions

We study two recently proposed equations of state (EOS) which are obtained from high temperature QCD, and show how they can be adapted to use them for making predictions for relativistic heavy ion collisions. The method involves extracting equilibrium distribution functions for quarks and gluons from the EOS, which in turn will allow a determination of the transport and other bulk properties of the quark gluon plasma. Simultaneously, the method also yields a quasi particle description of interacting quarks and gluons. The first EOS is perturbative in the QCD coupling constant and has contributions of $O(g^5)$. The second EOS is an improvement over the first, with contributions upto $ O(g^6 ln(\frac{1}{g}))$; it incorporates the nonperturbative hard thermal contributions. The interaction effects are shown to be captured entirely by the effective chemical potentials for the gluons and the quarks, in both the cases. The chemical potential is seen to be highly sensitive to the EOS. As an application, we determine the screening lengths which are, indeed the most important diagnostics for QGP. The screening lengths are seen to behave drastically differently depending on the EOS considered., and yield, therefore, a way to distinguish the two equations of state in heavy ion collisions.