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Hydrodynamical Evolution near the QCD Critical End Point

Hydrodynamical Evolution near the QCD Critical End Point. Duke University Chiho NONAKA. in Collaboration with. Masayuki Asakawa ( Kyoto University ). June 26, 2003@HIC03, McGill University, Montreal. RHIC. T. Critical end point. CFL. 2SC. m. GSI. Critical End Point in QCD ?.

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Hydrodynamical Evolution near the QCD Critical End Point

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  1. Hydrodynamical Evolution near the QCD Critical End Point Duke University Chiho NONAKA in Collaboration with Masayuki Asakawa (Kyoto University) June 26, 2003@HIC03, McGill University, Montreal

  2. RHIC T Critical end point CFL 2SC m GSI Critical End Point in QCD ? Suggestions • NJL model (Nf = 2) K. Yazaki and M.Asakawa., NPA 1989 • Lattice (with Reweighting) Z. Fodor and S. D. Katz (JHEP 0203 (2002) 014)

  3. Still we need to study • EOS • Focusing • Dynamics (Time Evolution) • Hadronic Observables : NOT directly reflect properties at E • Fluctuation, Collective Flow Phenomenological Consequence ? M. Stephanov, K. Rajagopal, and E.Shuryak, PRL81 (1998) 4816 critical end point Divergence of Fluctuation Correlation Length If expansion is adiabatic.

  4. T QGP Hadronic h r m EOS with CEP • How to Construct EOS with CEP? • Assumption Critical behavior dominates in a large region near end point • Near QCD end point singular part of EOS • Mapping • Matching with known QGP and Hadronic entropy density • Thermodynamical quantities 3d Ising Model QCD Same Universality Class

  5. h : external magnetic field QCD Mapping T h r m EOS of 3-d Ising Model • Parametric Representation of EOS Guida and Zinn-Justin NPB486(97)626

  6. T QGP Hadronic h r m Thermodynamical Quantities • Singular Part of EOS near Critical Point • Gibbs free energy • Entropy density • Matching • Entropy density • Thermodynamical quantities Baryon number density, pressure, energy density

  7. Equation of State CEP Baryon number density Entropy Density

  8. Comparison with Bag + Excluded Volume EOS • n /s trajectories in T- m plane B Bag Model + Excluded Volume Approximation (No End Point) With End Point = Usual Hydro Calculation Not Focused Focused

  9. r h faster (shorter) expansion Focusing Slowing out of Equilibrium • Berdnikov and Rajagopal’s Schematic Argument B. Berdnikov and K. Rajagopal, Phys. Rev. D61 (2000) 105017 slower (longer) expansion Correlation length longer than xeq xeq x along r = const. line • Effect of Focusing on x? E h Time evolution : Bjorken’s solution along nB/s t0 = 1 fm, T0 = 200 MeV

  10. x • Max. depends on n /s. eq B h • Trajectories pass through the region where • x is large. (focusing) r eq Correlation Length (I) • x eq Widom’s scaling low

  11. t • x is larger than x at Tf. • Differences among xs on n /s are small. • In 3-d, the difference between x and x becomes • large due to transverse expansion. eq B eq Correlation Length (II) • x : time evolution (1-d) Model C (Halperin RMP49(77)435)

  12. Consequences in Experiment (I) CERES: nucl-ex/0305002 • Fluctuations • CERES • 40,80,158 AGeV Pb+Au • collisions Mean PT Fluctuation No unusually large fluctuation CEP exists in near RHIC energy region ?

  13. ? EOS with CEP EOS with CEP gives the natural explanation to the behavior of T . Entropy density f J. Cleymans and K. Redlich, PRC, 1999 Consequences in Experiment (II) • Kinetic Freeze-out Temperature Low T comes from large flow. ? f Xu and Kaneta, nucl-ex/0104021(QM2001)

  14. Its Consequences • Slowing out of equilibrium • Large fluctuation • Freeze out temperature at RHIC • Fluctuation Focusing CEP and Its Consequences Future task • Realistic hydro calculation with CEP

  15. Back UP

  16. Hadronic Observables • Fluctuations • Mean transverse momentum fluctuation • Charge fluctuations • D-measure • Dynamical charge fluctuation • Balance function • Collective Flow • Effect of EOS Gazdzicki and Mrowczynski ZPC54(92)127 Korus and Mrowczynski, PRC64(01)054906 Asakawa, Heinz and Muller PRL85(00)2072 Jeon and Koch PRL85(00)2076 Pruneau et al, Phys.Rev. C66 (02) 044904 Bass, Danielewicz, Pratt, PRL85(2000)2689 Rischke et al. nucl-th/9504021

  17. Critical end point crossover 1st order Baryon Number Density Crossover : 1 st order :

  18. Focusing ! nB/S nB/S contours nB S

  19. Focusing and CEP

  20. T contours h r • Dominant terms • Critical behavior etc. m Focusing • What is the focusing criterion ? h r CEP From our model

  21. The critical point does not serve as a “focusing” point ! They found the Critical point in T- m plane. Sigma model Sigma model nB/S lines in T- m plane NJL model NJL model Focusing • Analyses from Linear sigma model & NJL model Scavenius et al. PRC64(2001)045202

  22. Hydrodynamical evolution Au+Au 150AGeV b=3 fm

  23. Relativistic Hydrodynamical Model Relativistic Hydrodynamical Equation Baryon Number Density Conservation Equation Lagrangian hydrodynamics Space-time evolution of volume element Effect of EoS Flux of fluid

  24. Sound velocity along n /s B /L /L TOTAL TOTAL • Clear difference between n /s=0.01 and 0.03 B Sound Velocity • Effect on Time Evolution • Collective flow EOS

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