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Phase Fluctuations near the Chiral Critical Point. Joe Kapusta University of Minnesota. Winter Workshop on Nuclear Dynamics Ocho Rios, Jamaica, January 2010. Phase Structure of QCD: Chiral Symmetry and Deconfinement.
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Phase Fluctuations near the Chiral Critical Point Joe Kapusta University of Minnesota Winter Workshop on Nuclear Dynamics Ocho Rios, Jamaica, January 2010
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.
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
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.
lattice QCD nuclear matter
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.
Cold Dense Nuclear Matter Stiff Soft
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.
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.
phase coexistence spinodal
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
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.