1. Phase Fluctuations near the Chiral Critical Point Joe Kapusta University of Minnesota Winter Workshop on Nuclear Dynamics Ocho Rios, Jamaica, January 2010

2. Phase Structure of QCD: Chiral Symmetry and Deconfinement If the up and down quark masses are zero and the strange quark mass is not, the transition may be first or second order at zero baryon chemical potential. If the up and down quark masses are small enough there may exist a phase transition for large enough chemical potential. This chiral phase transition would be in the same universality class as liquid-gas phase transitions and the 3D Ising model.

3. Phase Structure of QCD: Diverse Studies Suggest a Critical Point Nambu Jona-Lasinio model composite operator model random matrix model linear sigma model effective potential model hadronic bootstrap model lattice QCD

4. Goal: To understand the equation of state of QCD near the chiral critical point and its implications for high energy heavy ion collisions. Requirements: Incorporate critical exponents and amplitudes and to match on to lattice QCD at µ = 0 and to nuclear matter at T = 0. Model: Parameterize the Helmholtz free energy density as a function of temperature and baryon density to incorporate the above requirements.

5. lattice QCD nuclear matter

6. Coefficients are adjusted to: (i) free gas of 2.5 flavors of massless quarks (ii) lattice results near the crossover when µ=0 (iii) pressure = constant along critical curve.

7. Cold Dense Nuclear Matter Stiff Soft

8. Parameterize the Helmhotz free energy density to incorporate critical exponents and amplitudes and to match on to lattice QCD at µ = 0 and to nuclear matter at T = 0.

9. Parameterize the Helmhotz free energy density to incorporate critical exponents and amplitudes and to match on to lattice QCD at µ = 0 and to nuclear matter at T = 0.

10. Critical exponents and amplitudes

11. phase coexistence spinodal

15. Expansion away from equilibrium states using Landau theory 0 along coexistence curve The relative probability to be at a density other than the equilibrium one is

16. Volume = 400 fm 3

18. Future Work A more accurate parameterization of the equation of state for a wider range of T and µ. Incorporate these results into a dynamical simulation of high energy heavy ion collisions. What is the appropriate way to describe the transition in a small dynamically evolving system? Spinodal decomposition? Nucleation? What are the best experimental observables and can they be measured at RHIC, FAIR or somewhere else? Supported by the U.S. Department of Energy under Grant No. DE-FG02-87ER40328.