Ma. Lampert et C. Molinaparis, EFFECTIVE EQUATION OF STATE FOR A SPHERICALLY EXPANDING PION PLASMA, Physical review. D. Particles and fields, 57(1), 1998, pp. 83-92
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].