1. Marcus Bleicher, ETD, Montreal 07/2007 Elliptic Flow and Fluctuations in Heavy Ion collisions Marcus Bleicher Institut für Theoretische Physik Goethe Universität - Frankfurt Germany

2. Marcus Bleicher, ETD, Montreal 07/2007 Thanks to the UrQMD group @ Frankfurt Sascha Vogel (Resonances and di-leptons) Katharina Schmidt (Di-leptons) Stephane Haussler (Event-by-Event Fluctuations) Hannah Petersen (Flow) Daniel Krieg (Recombination) Qingfeng Li (HBT) Xianglei Zhu (Charm)

3. Marcus Bleicher, ETD, Montreal 07/2007 Contents Introduction v1 and v2 v2 fluctuations Summary

4. Marcus Bleicher, ETD, Montreal 07/2007 Motivation At RHIC: look for signals of partonic matter. (large v2, hydro) At critRHIC/SPS: look for the mixed phase and the onset of deconfinement (flow stalls, large fluctuations, ideal hydro breaks down) E. Bratkovskaya, M.B. et al., PRC 2005

5. Marcus Bleicher, ETD, Montreal 07/2007 The tool: UrQMD v2.2 Non-equilibrium transport model Hadrons and resonances String excitation and fragmentation Cross sections are parameterized via AQM or calculated by detailed balance pQCD hard scattering at high energies Generates full space-time dynamics of hadrons and strings

6. Marcus Bleicher, ETD, Montreal 07/2007 Multiplicities Comparison to data over the whole energy range E. Bratkovskaya, M.B. et al., PRC 2005

7. Marcus Bleicher, ETD, Montreal 07/2007 Droplets:  > 10-100 (Mishustin) Taken from a talk by B. Lungwitz at CPOD 2007 UrQMD data from Lungwitz& Bleicher, arXiv:0707.1788

8. Marcus Bleicher, ETD, Montreal 07/2007 Maybe HBT can deliver… long life times in the mixed phase… Rischke, Gyulassy, Nucl.Phys.A608:479- 512,1996 ~ Energy density 10 fold increase in life time during the mixed phase

9. Marcus Bleicher, ETD, Montreal 07/2007 The HBT puzzle? Model calculations of R O /R S or (R O 2 -R S 2 ) 1/2 are usually larger than the experimental data Duration time (in the absence of flow): No indication of long life time in the data Li, Bleicher, Stoecker, arXiv:0706.2091. JPG in press

10. Marcus Bleicher, ETD, Montreal 07/2007 Flow is important! Many observables never fullfilled the promise  HBT, fluctuations, J/Psi,…  ideally one should be able to study them at all energies Transverse collective flow is intimately connected to pressure  Flow is sensitive to changes in the equation of state and therefore to phase transitions (H.Stöcker,W.Greiner Phys.Rep. 137 (1986) 277)

11. Marcus Bleicher, ETD, Montreal 07/2007 Introduction - directed flow Fourier expansion of the azimuthal distribution of the emitted particles : Directed flow  measures the total amount of transverse flow with Reaction plane (J.Y. Ollitrault, Phys. Rev. D, 46; A.M. Poskanzer, S.A. Voloshin, Phys. Rev. C, 58)

12. Marcus Bleicher, ETD, Montreal 07/2007 Excitation function 1-fluid hydro prediction for p x dir : softest point in the EoS leads to decreasing flow from D.Rischke, Y.Pürsün et al. (Heavy Ion Physics 1,309,1995)

13. Marcus Bleicher, ETD, Montreal 07/2007 Antiflow around midrapidity (L.Csernai, Phys.Lett. B 458, 1999) (J.Brachmann et al., Phys.Rev. C, 61, 2000) Prediction of antiflow if QGP is produced  softening of the EoS leads to flow in the „wrong“ direction

14. Marcus Bleicher, ETD, Montreal 07/2007 A problem with hydro Hydro is not a good tool to study the onset of deconfinement Agreement at top RHIC energies with ‘wrong’ EoS and ‘wrong’ initial c. (see talk by Dumitru)  try transport Heinz, Kolb,STAR

15. Marcus Bleicher, ETD, Montreal 07/2007 v 1 of protons @ 40 AGeV Comparison of rapidity spectra between model and data:  Largest flow at high rapidity values  Centrality dependence visible Data from C.Alt et al., Phys. Rev. C 68, 2003 Petersen et al, Phys.Rev.C74:064908,2006

16. Marcus Bleicher, ETD, Montreal 07/2007 v 1 of protons Slope around midrapidity characterizes shape of the rapidity distribution Extracted from normalized rapidity distribution via polynomial fit At low energies: potentials are important At high energies: data developes negative slope  ´wiggle´ QGP-signal? (L.P. Csernai, Phys.Lett. B 458,1999) Petersen et al, Phys.Rev.C74:064908,2006

17. Marcus Bleicher, ETD, Montreal 07/2007 Time evolution Pressure  Pressure gradients  Elliptic flow Petersen et al, Phys.Rev.C74:064908,2006

18. Marcus Bleicher, ETD, Montreal 07/2007 Time evolution at RHIC Elliptic flow builds up in the hadronic stage of the collision High-p t Low-p t Y. Lu et al, J.Phys.G32:1121-1130,2006

19. Marcus Bleicher, ETD, Montreal 07/2007 v 2 (y) of pions @ 40/160 AGeV Pb+Pb Petersen et al, Phys.Rev.C74:064908,2006

20. Marcus Bleicher, ETD, Montreal 07/2007 v 2 (y) of protons @40 AGeV  Collapse of elliptic flow? (H.Stöcker, Nucl.Phys. A 750, 2005)  Experimental situation unclear  Transport model calculation is compatible with the data Petersen et al, Phys.Rev.C74:064908,2006

21. Marcus Bleicher, ETD, Montreal 07/2007 Energy dependence Qualitative description OK Importance of potentials at low energies Lack of pressure shows up at lower SPS energies Petersen et al, Phys.Rev.C74:064908,2006

22. Marcus Bleicher, ETD, Montreal 07/2007 v2 fluctuations Tilted axis has to be taken into account with proper (participant) definition of eccentricity Broniowski et al

23. Marcus Bleicher, ETD, Montreal 07/2007 Additional fluctuations One would expect additional dynamical fluctuations, if the system is not a perfect liquid Degree of perfection is quantified by the Knudsen number Kn S. Vogel et al., nucl-th/0703031

24. Marcus Bleicher, ETD, Montreal 07/2007 Fluctuation analysis To strong fluctuations Cross section increase, decreases fluctuations S. Vogel et al., nucl-th/0703031

25. Marcus Bleicher, ETD, Montreal 07/2007 Extrapolation to small Knudsen numbers Experimental data requires tiny mean free path 1/Kn > 100-1000 Bhalerao, PLB2005 S. Vogel et al., nucl-th/0703031

26. Marcus Bleicher, ETD, Montreal 07/2007 Only ideal hydro can do it Calculation by Kodama et al., Fluctuating initial state from Nexus Where is viscosity?

27. Marcus Bleicher, ETD, Montreal 07/2007 Summary  Flow is the ideal tool to study the onset of deconfinement (critRHIC!)  However, ideal hydro fails below top RHIC energy  Unfortunately, hadron/string transport fails above SPS energies  At top RHIC energy: Elliptic flow fluctuations indicate very short mean free path  No sign of ANY turbulence or dynamical fluctuations