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The hadronization line in stringy QGP

The hadronization line in stringy QGP. The hadronization line in stringy QGP. How can be E / N = 6 T ? Stringy corrections to QGP The zero pressure line High-T equation of state. T.S.Bíró , MTA KFKI RMKI Budapest, Hungary J. Cleymans, University of Cape Town, South Africa.

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The hadronization line in stringy QGP

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  1. The hadronization line in stringy QGP

  2. The hadronization line in stringy QGP • How can be E / N = 6 T ? • Stringy corrections to QGP • The zero pressure line • High-T equation of state T.S.Bíró, MTA KFKI RMKI Budapest, Hungary J. Cleymans, University of Cape Town, South Africa Graz – Zagreb – Budapest Triangle Meeting, Hévíz, Balaton, Jan. 23-25, 2008.

  3. How can be E / N = 6 T ? Statistical Model: hadronization point around µ = 0 (RHIC, LHC)

  4. How can be E / N = 6 T ? Massive hadrons (rho?)

  5. How can be E / N = 6 T ? Ideal gas of radiation

  6. How can be E / N = 6 T ? Bag Model for QGP

  7. How can be E / N = 6 T ? Stringy Massless QGP

  8. How can be E / N = 6 T ? This is more generally true! • correction depends on • constituents are massless • Boltzmann approximation is acceptable

  9. Stringy corrections to QGP color density free energy density fractional power chemical potential pressure energy density

  10. Stringy corrections to QGP Consistent solution for color density in equilibrium: It exists only beyond an endline in T - µ

  11. Stringy corrections to QGP One massless component, Boltzmann approximation: The solution is related to Lambert’s function

  12. Stringy corrections to QGP Endline: last possible solution Boltzmann approximation It is near to the zero pressure line for low chemical potential

  13. The zero pressure line Zero pressure in the Boltzmann approximation Endline and zero pressure line are relatively close! (T0  1.04 TE)

  14. E/N at the zero pressure line General relations

  15. High – T equation of state

  16. High-T behavior of lattice eos

  17. High-T behavior of lattice eos Fodor Katz Boltzmann approximation

  18. High-T behavior of lattice eos Fodor Katz Boltzmann approximation

  19. Where to stop with the Boltzmann approximation? Fermi integral  Boltzmann integral for negative or zero µ. The endline does not turn back!

  20. The zero pressure line Fermions (quarks only) at T = 0

  21. The endpoint at T=0 6µ 3µ

  22. The zero pressure line

  23. The zero pressure line QGP in Boltzmann approximation, numerical

  24. Summary • E / N = 6T only from stringy massless QGP • fractional power is 1/3 from high-T lattice eos • zero pressure line and endpoint of solution are close • at finite baryon density and zero temperature the hadronization line is at mu_B = 3 k_F

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