1. Scott Pratt Michigan State University I SR E A L L Y PUZZLING?PUZZLING? S C O T T PRATTPRATT HBTHBT M I C H I G A N STATESTATE U N I V E R S I Y

2. Scott Pratt Michigan State University PUZZLES Why is the breakup density so high? Have we excluded the lattice EOS? How does it expand so fast and dissolve so suddenly? What do the measurements tell us? Theory Blast wave

3. Scott Pratt Michigan State University All the theory you need to know

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

5. Scott Pratt Michigan State University Blast-Wave Fits Lisa and Retiere, PRC 70:044907 (04) Broniowski et al., nucl-th/0212053

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

7. Scott Pratt Michigan State University Are the sizes too small? Adamova et al, PRL90 022301 (03) Breakup densities are high Hadronic cascades give similar sizes!!! Matter is expanding Density is falling Expansion becoming Hubble-like Chojnacki et al, PRC71 044902 (04)

8. Scott Pratt Michigan State University HYDRO Overall sizes depend on EOS & breakup criteria

9. Scott Pratt Michigan State University Cascade/Boltzmann More resonances -> softer -> bigger Strings -> softer -> bigger

10. Scott Pratt Michigan State University Is lattice Eq. of State excluded? Sizes and spectra give phase space density Phase space density gives Entropy Entropy: determined by initial  and EOS ~ conserved

11. Scott Pratt Michigan State University Is lattice Eq. of State excluded? increases with s 1/2 gives entropy for pions R inv and spectra for other species gives total S

12. Scott Pratt Michigan State University Is Lattice Eq. of State excluded? Range

13. Scott Pratt Michigan State University Total Entropy and the lattice EOS Final S consistent with lattice EOS CRUDE! Entropy moved from pions to baryons Chemical rates are important Greiner,Gong&Mueller, PLB316:226-230(93) Pratt&Haglin, PRC59:3304-3308(99) Rapp&Shuryak, PRL.86:2980-2983(01)

14. Scott Pratt Michigan State University How does it expand & dissolve so fast? Blast wave parameters: R=13 fm,  =10 fm/c, v=0.7c Surface grows 7 fm in 10 fm/c What about acceleration? Reducing R side or increasing  would help

15. Scott Pratt Michigan State University How does it expand & dissolve so fast? 1.Reduced Emissivity 2.Non-infinite longitudinal extent 3.Longitudinal acceleration 4.Shear Viscosity 5.Refraction of the mean field

16. Scott Pratt Michigan State University 1. Reduced Emissivity Sequential emission: Hubble-like expansion: Reasons for lower emissivity: phase change super-cooling Csorgo&Csernai, hep-th/9312230

17. Scott Pratt Michigan State University 2. Non-infinite longitudinal extent Assume boost invariance -> underestimate 

18. Scott Pratt Michigan State University 3. Longitudinal Acceleration Let surface (endcap) accelerate from y 0 to y f Ignore longitudinal a -> underestimate  3D codes are better Csorgo,Grassi,Hama,Kodama, PLB565, 107 (03) Hirano, nucl-th/040017

19. Scott Pratt Michigan State University 4. Shear Viscosity Shear viscosity increased transverse acceleration Teaney, nucl-th/0403053 Longitudinal classical fields -> hyper-viscous Note: Viscosity kills v 2 Cheng etal, PRC65:024901 (02)

20. Scott Pratt Michigan State University Refraction of the mean field ATTRACTIVE REPULSIVE Cramer et al.,Miller, PRL94, 102302 (05), Miller and Cramer, nucl-th/0507004 H.W.Barz, PRC59, 2214 (99); PRC53, 2536 (96)nucl-th/0507004 Kapusta and Li, www.arXiv.org:0505075 C.Y. Wong, hep-ph/0403025 M. Chu et al., PRC50, 3079 (94)

21. Scott Pratt Michigan State University Refraction of the mean field Stronger for low p t Stronger for R side

22. Scott Pratt Michigan State University How does it expand and dissolve so fast? All 5 corrections -> longer  or smaller R side Improved modeling required