1. S C O T T PRATPRAT MICHIGANMICHIGAN S T T E UNIVRSITYUNIVRSITY T H BTBT PUZZLE PUZZLE Z A N D E X T E N D I N G HYRODYNAMICS HYRODYNAMICS

2. Extending Hydrodynamics and the HBT Puzzle Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University OUTLINE Remnants of the HBT Puzzle Extending Hydrodynamics Tsunamis

3. Extending Hydrodynamics and the HBT Puzzle Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University HBT Basics

4. Extending Hydrodynamics and the HBT Puzzle Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University Blast-Wave Models R v z =z/  V x =V  (r/R) Parameters: T, R, V , ,  Schnedermann, Sollfrank and Heinz Tomasik, Broniowski, Lisa and Retiere, …

5. Extending Hydrodynamics and the HBT Puzzle Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University NA49 vs. Therminator 3-dimensional details of blast-wave confirmed

6. Extending Hydrodynamics and the HBT Puzzle Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University Blast-Wave and the HBT Puzzle Parameters: T  110 MeV R  13 fm V   0.7c   10 fm/c   3 fm/c Similar Conclusions: Blast Waves (Lisa-Retiere, Tomasik) Therminator Buda-Lund Requires Kp spectra Rapid expansion sudden disintegration

7. Extending Hydrodynamics and the HBT Puzzle Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University HYDRO Overall sizes depend on EoS & breakup criteria

8. Extending Hydrodynamics and the HBT Puzzle Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University Cascade/Boltzmann More resonances -> softer -> bigger Strings -> softer -> bigger

9. Extending Hydrodynamics and the HBT Puzzle Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University HBT and the EoS: Dynamical Signature Leads to: R out /R side >> 1

10. Extending Hydrodynamics and the HBT Puzzle Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University HBT and EoS: Entropy Sizes and spectra give phase space density Phase space density gives Entropy

11. Extending Hydrodynamics and the HBT Puzzle Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University HBT and EoS: Entropy

12. Extending Hydrodynamics and the HBT Puzzle Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University Is Lattice Eq. of State excluded? Range Subrata Pal and S.P., PLB 2004

13. Extending Hydrodynamics and the HBT Puzzle Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University Total Entropy and the lattice EOS Final S consistent with lattice EOS (Crude) Entropy moved from pions to baryons

14. Extending Hydrodynamics and the HBT Puzzle Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University The HBT puzzle R side /R out  1 and  10 fm/c suggest rapid expansion - > hard EoS Entropy suggests softer EoS

15. Extending Hydrodynamics and the HBT Puzzle Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University Explanations to the HBT Puzzle Refraction (Cramer-Miller, 2005) - Requires extreme assumptions Surface Emission (Heiselberg, 2002) - What happened to energy in center? Initial transverse velocity (Sinyukov, 2007) - Cause ??? Super-Cooling (Csorgo&Csernai, hep-th/9312230) Needed: Explanation with consistent dynamical model

16. Extending Hydrodynamics and the HBT Puzzle Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University Extending Hydrodynamics 1.Longitudinal Acceleration 2.Later times (Chemistry) 3.Earlier times (Shear) 4.In between (Hadronization dynamics)

17. Extending Hydrodynamics and the HBT Puzzle Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University No Longitudinal Acceleration Bjorken

18. Extending Hydrodynamics and the HBT Puzzle Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University Analytic 1-D Solution (S.P. PRC 2007) Accelerationless models underestimate lifetime by  10% Bjorken

19. Extending Hydrodynamics and the HBT Puzzle Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University Later Times (Non-Equilibrium Chemistry Below T c ) Too many particles Pion, kaon, baryon fugacities > 1 Smaller P/  Less collective energy, more thermal

20. Extending Hydrodynamics and the HBT Puzzle Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University Early Times (Shear) In rest frame: Always true Perfect Hydro: Viscous Hydro:

21. Extending Hydrodynamics and the HBT Puzzle Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University Navier-Stokes Shear Bulk at early times Boosts early acceleration (D.Teaney,) Increases collective energy vs. thermal energy

22. Extending Hydrodynamics and the HBT Puzzle Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University Early times For  =s/4 , T zz becomes negative for  0.6 fm/c Eq.s of Motions for T ij Saturate Anisotropy saturates anisotropy relaxation time (Israel-Stewart)

23. Extending Hydrodynamics and the HBT Puzzle Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University Anisotropy at early times Classical Longitudinal Fields: CGC (Krasnitz, Nara &Venugopalan) : Collisionless Boltzmann:

24. Extending Hydrodynamics and the HBT Puzzle Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University Intermediate Times (Bulk Viscosity in Mixed Region) K.Paech and S.P., PRC 2006  P

25. Extending Hydrodynamics and the HBT Puzzle Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University Sigma Field out of Equilibrium Langevin "force"  can blow up at phase transition!

26. Extending Hydrodynamics and the HBT Puzzle Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University Example: Linear Sigma Model 1st order when g>3.55 K.Paech & A.Dumitru, PLB 623, 200 (2005)

27. Extending Hydrodynamics and the HBT Puzzle Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University Example: Linear Sigma Model For g=3.4, T xx -> 0 For big effects: Should solve Sigma Eq.s of Motion K.Paech & A.Dumitru, PLB 623, 200 (2005)

28. Extending Hydrodynamics and the HBT Puzzle Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University How might this affect dynamics? T xx r P

29. Extending Hydrodynamics and the HBT Puzzle Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University Tsunamis at RHIC See also nuclear doughnuts (Bauer and Bertsch, PRL '90)

30. Extending Hydrodynamics and the HBT Puzzle Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University Modeling Tsunamis at RHIC with Hydrodynamics  P  H L Increasing L or decreasing c 2 mixed -> stronger tsunami Resonance Gas

31. Extending Hydrodynamics and the HBT Puzzle Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University Hydrodynamic Evolution L=2 GeV/fm3, c 2 mixed =0.05  =1,3,5,7,9,11 fm/c

32. Extending Hydrodynamics and the HBT Puzzle Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University Changing EoS Large R side for L  2 GeV/fm 3 Bulk Viscosity in mixed phase strengthens tsunami

33. Extending Hydrodynamics and the HBT Puzzle Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University Navier-Stokes Dynamic T ij Dynamic Fields Summar y Slide #1 Boltzmann ?

34. Extending Hydrodynamics and the HBT Puzzle Scott Pratt Extending Hydrodynamics and the HBT Puzzle Michigan State University Summary #2 HBT is only hope to disentagle EoS Early-Time Shear Bulk Viscosity near Tc