EFFECTIVE EQUATION OF STATE FOR A SPHERICALLY EXPANDING PION PLASMA

Following a relativistic heavy ion collision, the quark-gluon plasma p roduced eventually undergoes a chiral phase transition. We assume that during this phase transition one can describe the dynamics of the sys tem by the linear sigma model and that the expansion can be thought of as mostly radial. Because the sigma model is an effective field theor y there is an actual momentum cutoff (Landau pole) in the theory at ar ound 1 GeV. Thus it is necessary to find ways of obtaining a covariant ly conserved, renormalized energy-momentum tensor when there is a cuto ff present (which breaks covariance), in order to identify the effecti ve equation of state of this time evolving System. We show how to solv e this technical problem and then determine the energy density and pre ssure of the system as a function of the proper time. We consider diff erent initial conditions and search for instabilities which can lead t o the formation of disoriented chiral condensates. We find that the en ergy density and pressure both decrease quickly, as is appropriate for a rapidly cooling system, and that the energy is numerically conserve d. [S0556-2821(98)04501-9].