Roy Lacey ( for the PHENIX Collaboration ) Nuclear Chemistry Group Stony Brook University

1. PHENIX Measurements of 3D Emission Source Functions in Au+Au Collisions at Roy Lacey (for the PHENIX Collaboration) Nuclear Chemistry Group Stony Brook University

2. There are known knowns. These are things we know that we know. There are known unknowns. That is to say, there are things that we know we don't know. But there are also unknown unknowns. There are things we don't know we don't know Donald Rumsfeld

3. A Known Known: A Crossover transition to the strongly coupled thermalized QGP occurs at RHIC Courtesy S. Bass QGP and hydrodynamic expansion hadronic phase and freeze-out initial state pre-equilibrium hadronization We hold these truths to be self evident !

4. A Known unknown: Puzzle ? Are source Imaging measurements consistent with the crossover transition ? The Role of Femtoscopy QGP and hydrodynamic expansion hadronization The space-time extent can lend crucial insights A Cross over Strongly affects the Space-time Dynamics Experiment & theory indicate a crossover transition

5. Dave Brown WPCF - 2005 Set Rx=Ry=Rz=4fm, f/o=10 fm/c, T=175 MeV, f=0.56      Why source Imaging? Source Imaging gives access to important space-time information which is inaccessible via “traditional approach”

6. Discretize Integral Vary S(rj) to minimize Brown & Danielewicz PRC 57(98)2474 Direct Fit Source function (Distribution of pair separations) Correlation function Encodes FSI Source Imaging Methodology (1D) 1D Koonin Pratt Eqn. Inversion of this integral equation  Source Function Reliable measurement of the full 1D Source Function !

7. Expand R(q) and S(r) in Cartesian Harmonic basis (Danielewicz and Pratt nucl-th/0501003) Substitute (2) and (3) into (1) The 3D integral equation is reduced to a set of 1D relations for different l coefficients  moments Source Imaging Methodology (3D) 3D Koonin Pratt Eqn. Reliable measurement of the full Source Function in 3D !

8. Compare Proofing the Source Imaging Technique • Generate Events • Phasemaker • AMPT • Therminator • etc Correlation Function 3D C(q) Moments How well does it work ? Moment Fitting Calculated Source Function Imaging Extensive tests indicate that the method is robust

9. Test with simulated Gaussian source -- t =0 Very good simultaneous fit obtained as expected

10. Test with simulated Gaussian source -- t =0 Good reproduction of actual source function

11. Correlation Moments PHENIX Data Robust Experimental Source Functions obtained from moments Contributions from l > 6 is negligible

12. Model Comparison • Therminator: • A.Kisiel et al. Comput.Phys.Commun.174, 669 (2006) • Thermal model with Bjorken longitudinal expansion and transverse Flow • Spectra & yields constrain thermal properties • Transverse radius ρmax : controls • transverse extent • Breakup time in fluid element rest frame, • : controls longitudinal extent • Emission duration : controls tails in • long and out directions • a controls x-t correlations Source Function Comparison to Models Give robust life time estimates  Consistent with Crossover transition

13. QM

14. Summary/Conclusions • Souce Imaging provides important access to S(r) • Extensive study of imaging technique carried out • Used to extract the 3D pion emission source function, in • the PCMS frame • The source function has a much greater extent • in the out (x) and long (z), than in the side (y) direction. • Model comparison Timescales consistent with a crossover transition

15. Known Knowns • Dynamic recombination • 2. Partonic Thermalization! • 3. Strongly coupled QGP S.L. Huang QM08 15

16. Known Knowns x k ε scaling validated

17. Known Knowns P Baryons Mesons PHENIX preliminary KET scaling validated Quark Degrees of Freedom Evident

18. Known Knowns v2 for the φ follows that of other mesons Flow fully developed in the partonic phase

19. Known Knowns v2 for the heavy D meson follows that of other mesons A Phase with Quarks as dynamical degrees of freedom Dominates the flow

20. Test with simulated Gaussian source -- t =5 Simultaneous fit not very good

21. Test with simulated Gaussian source -- t =5 Source function from ellipsoid fit misses the mark

22. Test with simulated Gaussian source -- t =0 Very good simultaneous fit obtained as expected

23. Test with simulated Gaussian source -- t =0 Good reproduction of actual source function

24. Test with simulated Gaussian source -- t =5 Simultaneous with hump function – much better

25. Test with simulated Gaussian source -- t =5 Hump function and imaging compare well to actual source

26. 3D Analysis Basis of Analysis (Danielewicz and Pratt nucl-th/0501003 (v1) 2005) Expansion of R(q) and S(r) in Cartesian Harmonic basis 3D Koonin Pratt (3) Plug in (1) and (2) into (3) (1) (2)

27. Conjecture of heavy ion collision hadronic phase and freeze-out QGP and hydrodynamic expansion initial state pre-equilibrium hadronization Sharp 1st order QCD phase transition: (Pratt, Bertsch, Rischke, Gyulassy) Supercooled QGP (scQGP) (T. Csörgő, L.P. Csernai) 2nd order QCD phase transition: (T. Csörgő , S. Hegyi, T. Novák, W.A. Zajc) (Non Gaussian shape) Femtoscopy Prologue Courtesy S. Bass Femtoscopy Signatures: Cross-over transition: (Z. Fodor and S.D. Katz) (Rischke, Gyulassy) Femtoscopic signals are subtle and important for study of the QGP

28. Outline • Femtoscopic Prologue • Why source imaging ! • Source function extraction • Brief description of the technique • Proofing the technique • Imaging known sources • Results & Implications • What do we learn ?

29. hadronic phase and freeze-out hadronic phase and freeze-out QGP and hydrodynamic expansion QGP and hydrodynamic expansion initial state initial state pre-equilibrium pre-equilibrium hadronization hadronization A Known Known; Courtesy S. Bass Femtoscopy Signatures: Femtoscopic signals are subtle and important for study of the QGP

30. A Known Known: A Crossover transition to the strongly coupled thermalized QGP occurs at RHIC Courtesy S. Bass QGP and hydrodynamic expansion hadronic phase and freeze-out initial state pre-equilibrium hadronization

31. Demise of the RHIC HBT Puzzle Rishke et al Puzzle ? Experiment & theory indicate a crossover transition A Cross over Strongly affects the Space-time Dynamics Detailed measurements of the Space-time Dynamics are required

32. Demise of the RHIC HBT Puzzle Rishke et al Puzzle ? Experiment & theory indicate a crossover transition A Cross over Strongly affects the Space-time Dynamics Detailed measurements of the Space-time Dynamics are required