A Mean Field Theory of the Chiral Phase Transition

The recent discussions by Koci\'c and Kogut on the nature of the chiral phase transition are reviewed. The mean-field nature of the transition suggested by these authors is supported in random matrix theory by Verbaarschot and Jackson which reproduces many aspects of QCD lattice simulations. In this paper, we point out physical arguments that favor a mean-field transition, not only for zero density and high temperature, but also for finite density. We show, using the Gross-Neveu model in 3 spatial dimensions in mean-field approximation, how the phase transition is constructed. In order to reproduce the lowering of the $\rho=0$, $T=0$ vacuum evaluated in lattice calculations, we introduce {nucleons} rather than constituent quarks in negative energy states, down to a momentum cut-off of $\Lambda$. We also discuss Brown-Rho scaling of the hadron masses in relation to the QCD phase transition, and how this scaling affects the CERES and HELIOS-3 dilepton experiments.