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QCD Phase Diagram in Polyakov-NJL Model

Workshop on RHIC Physics and CSR Physics at Weihai. QCD Phase Diagram in Polyakov-NJL Model. Wei-jie Fu ITP, Chinese Academy of Science August 11, 2009. Outline. Introduction The PNJL Model Numerical Results Inhomogeneous Phases Summary. Introduction.

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QCD Phase Diagram in Polyakov-NJL Model

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  1. Workshop on RHIC Physics and CSR Physics at Weihai QCD Phase Diagram in Polyakov-NJL Model Wei-jie Fu ITP, Chinese Academy of Science August 11, 2009

  2. Outline • Introduction • The PNJL Model • Numerical Results • Inhomogeneous Phases • Summary

  3. Introduction • A semiquantitative QCD phase diagram • In term of temperature and density (chemical potential) • Experiments and observations: RHIC (temperature), Compact stars (density). The Frontiers of Nuclear Science, A Long Range Plan 2007

  4. QCD critical point • Phenomenological Models • Lattice Simulations 1. Reweighting 2. Imaginary chemical potential 3.Taylor expansion 4……. M. A. Stephanov, PoS, LAT2006, 024, 2006

  5. An example: Taylor Expansion C. R. Allton et al., PRD. 71, 054508, 2005

  6. Does the QCD critical point really exist? O. Philipsen, arXiv: 0808.0672, 2008

  7. The PNJL Model • The 2+1 flavor NJL model with a Polyakov-loop is given by where

  8. is the Polyakov-loop effective potential, which is as function of the Polyakov-loop • Two kinds of Polyakov-loop effective potential and

  9. The other is and The Polyakov-loop effective potential as function of the real part and the imaginary part of the Polyakov-loop at two values of the temperature:

  10. H. Hansen, et al., PRD. 75, 065004, 2007

  11. Phase Transition at Finite Temperature

  12. Phase Transition at Finite Temperature and Nonzero Chemical Potential

  13. Phase Diagram (Effects of Flavor-mixing and Quark Current Mass) Wei-jie Fu, Zhao Zhang, Yu-xin Liu., PRD. 77, 014006, 2008

  14. Mesonic Excitations at Finite Temperature Schematic representation of the effective interaction for the pseudoscalar modes in the RPA.

  15. The pseudoscalar polarization function is and the scalar polarization function is

  16. Goldberger-Treiman（GT）relation on the quark level at finite temperature: • Gell-Mann--Oakes--Renner （GOR）relation at finite temperature:

  17. Several critical temperatures Wei-jie Fu, Yu-xin Liu., PRD. 79, 074011, 2009

  18. The effect of color confinement screens the effect of temperature below the critical temperature

  19. Scattering Lengths

  20. Wei-jie Fu, Yu-xin Liu., PRD. 79, 074011, 2009

  21. P. Deb et al.,PRC 79,055208, 2009

  22. P. Deb et al., PRC 79,055208, 2009

  23. Inhomogeneous Phases D. Nickel,arXiv: 0906.5295, 2009

  24. Ginzburg-Landau Expansion

  25. D. Nickel,arXiv: 0902.1778, 2009

  26. Summary • The QCD phase diagram is calculated in the 2+1 flavor PNJL model. We have also investigated the dependence of the location of the QCD critical point on the strength of the ’t Hooft flavor-mixing interaction and the current mass of strange quarks. • Mesonic excitations is studied in the PNJL model. We find that the effect of color confinement screens the effect of temperature below the critical temperature. • Could the Polyakov dynamics affect the inhomogeneous phases, and how? Thank you !

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