A Mean Field Theory of the Chiral Phase Transition

Abstract

The recent discussions by Kocić 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.

23 pages, Latex, no figures

References in corpus (12)

• Thermal Equilibration and Expansion in Nucleus-Nucleus Collision at the AGS
• Enhancement of low-mass dileptons in heavy-ion collisions
• Chiral Restoration in Hot and/or Dense Matter
• Chiral Lagrangian Approach to Exchange Vector Currents in Nuclei
• Dilepton Production at SPS Energies
• Vacuum Contributions in a Chiral Effective Lagrangian for Nuclei
• From Chiral Mean Field to Walecka Mean Field and Kaon Condensation
• The chiral phase transition in a random matrix model with molecular correlations
• Chiral Effective Lagrangian Description of Bulk Nuclear Matter
• Phase Transitions at Finite Temperature and Dimensional Reduction for Fermions and Bosons
• Finite-Temperature Corrections in the Dilated Chiral Quark Model
• Cold Kaons from hot fireballs

Cited by in corpus (17)

• QCD at Finite Baryon Density: Nucleon Droplets and Color Superconductivity
• On the Phase Diagram of QCD
• Nucleon Resonance Transition Couplings to Vector Mesons
• Properties of Hadrons in the Nuclear Medium
• Dense Nuclear Matter: Landau Fermi-Liquid Theory and Chiral Lagrangian with Scaling
• Fluctuations In ``BR-Scaled'' Chiral Lagrangians
• First-order chiral phase transition may naturally lead to the ``quenched'' initial condition and strong soft-pion fields
• Dilatons in Hidden Local Symmetry for Hadrons in Dense Matter
• Scaling Of Chiral Lagrangians And Landau Fermi Liquid Theory For Dense Hadronic Matter
• Vector meson dominance and the rho meson
• Photon Rates for Heavy-Ion Collisions from Hidden Local Symmetry
• Strange Particles in Dense Matter and Kaon Condensates
• Subthreshold rho^0 photoproduction on 3He
• Unifying Nucleon and Quark Dynamics at Finite Baryon Number Density
• $\rho$-mass Modification in $H{e}^3$ - a Signal of Restoration of Chiral Symmetry or Test for Nuclear Matter Models ?
• Effective Field Theories, Landau-Migdal Fermi-Liquid Theory and Effective Chiral Lagrangians for Nuclear Matter
• $\rho$ - nucleus bound states in Walecka model