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The QCD Plasma State

For an equilibrated system of quarks and gluons, the computer simulation on a lattice of finite temperature QCD provides to date the most reliable theoretical information. Using this tool we can determine the equation of state for strongly interacting matter through ab-initio calculations. As a result, we know that hadronic matter will undergo a deconfinement transition at a certain critical temperature Tc, closely accompanied by a second phase transition in which chiral symmetry is restored.
 
Figure: Results from numerical solutions of QCD on the lattice for the Wilson loop L, a measure of the parton free energy, as a function of temperature (in units of the critical temperature) and for the quark condensate . Also shown are the susceptibilities , a measure of the fluctuations.

 

The results of present lattice QCD calculations are illustrated in Figure [*] which shows the temperature dependence of the Wilson loop L and the quark condensate  along with the corresponding generalised susceptibilities . The quantity L is a measure of the free quark energy and thereby of the color mobility or color deconfinement. The sharp jump from very small values (low quark mobility) to large values occurs at the critical temperature corresponding to the deconfinement phase transition. At exactly the same position the quark condensate, a measure for the quark mass acquired by spontaneous breaking of the chiral symmetry in low temperature QCD, drops steeply. These calculations indicate that quarks and, hence, hadrons loose their mass (except for the small current quark masses) at a critical temperature Tc, a process called chiral symmetry restoration, and simultaneously acquire a finite free energy in the medium, resulting in a finite mobility corresponding to deconfinement. This interpretation is supported by a concurrent steep jump in the energy density (not illustrated). The susceptibilities shown as the red curves in Figure [*] are a measure of the fluctuations that characteristically are maximal in the vicinity of a phase transition. To put the critical temperature on an absolute energy scale requires calibration of the lattice results by tying them e.g. to a physical hadron mass. The best calibration to date fixes the critical temperature to 150 MeV. Including systematic errors, the temperature range for Tc inferred from lattice QCD is between 150 MeV and at most 200 MeV, as indicated in Figure [*] by the arrow. All lattice QCD results obtained so far are valid for a system of vanishing baryon number density (baryochemical potential $\mu_B$ = 0). To extend the knowledge of the hadron gas - quark-gluon plasma boundary into the domain of finite baryon number one needs to employ QCD inspired models (blue line in Figure [*]). Energy densities of about the required magnitude are indeed reached in the initial phase of central Pb+Pb collisions at the SPS together with baryon densities of up to 5 times nuclear matter density. However, the lattice calculations describe a stationary state whereas nuclear collisions are a typical example of a rapidly evolving system. Of equal importance as energy density are therefore lifetime and equilibration times in nuclear collisions. A very intense theoretical discussion is currently devoted to the question if thermal relaxation time scales are sufficiently small compared to the expansion time scale. However, the final answer concerning the creation of an equilibrated strongly interacting medium, of either partonic or a hadronic nature, can only be settled by experiment. To fully explore the high-density regime simulations of the collision show that beam energies of a few tens of GeV per nucleon are optimal. Maximum densities are reached when the colliding nuclei still barely stop each other. A study of the chiral and deconfinement phase transitions along the density axis is complementary to studies at high energy density i.e. high temperature and is equally important for a full understanding of the nature of these phase transitions. 


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