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

2. Roy Lacey, Stony Brook, Quark Matter 2008, Jaipur, India 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 Donald Rumsfeld

3. Roy Lacey, Stony Brook, Quark Matter 2008, Jaipur, India 3 initial state pre-equilibrium QGP and hydrodynamic expansion hadronization hadronic phase and freeze-out A Known Known: Courtesy S. Bass A Crossover transition to the strongly coupled thermalized QGP occurs at RHIC We hold these truths to be self evident !

4. Roy Lacey, Stony Brook, Quark Matter 2008, Jaipur, India 4 QGP and hydrodynamic expansion hadronization A Known unknown: The Role of Femtoscopy Are source Imaging measurements consistent with the crossover transition ? A Cross over Strongly affects the Space-time Dynamics Experiment & theory indicate a crossover transition The space-time extent can lend crucial insights Puzzle ?

5. Roy Lacey, Stony Brook, Quark Matter 2008, Jaipur, India 5 Set R x =R y =R z =4 fm,  f/o =10 fm/c, T=175 MeV, f=0.56 Dave Brown WPCF - 2005      Source Imaging gives access to important space-time information which is inaccessible via “traditional approach” Why source Imaging?

6. Roy Lacey, Stony Brook, Quark Matter 2008, Jaipur, India 6 Discretize Integral Source Imaging Methodology (1D) Source function (Distribution of pair separations) Encodes FSI Correlationfunction Inversion of this integral equation  Source Function 1D Koonin Pratt Eqn. Brown & Danielewicz PRC 57(98)2474 Direct Fit Vary S(r j ) to minimize Reliable measurement of the full 1D Source Function !

7. Roy Lacey, Stony Brook, Quark Matter 2008, Jaipur, India 7 Source Imaging Methodology (3D) 3D Koonin Pratt Eqn. Expand R(q) and S(r) in Cartesian Harmonic basis (Danielewicz and Pratt nucl-th/0501003) Reliable measurement of the full Source Function in 3D ! Substitute (2) and (3) into (1) The 3D integral equation is reduced to a set of 1D relations for different l coefficients  moments

8. Roy Lacey, Stony Brook, Quark Matter 2008, Jaipur, India 8 How well does it work ? Proofing the Source Imaging Technique Generate Events Phasemaker AMPT Therminator etc Correlation Function 3D C(q) Moments Moment Fitting Imaging Calculated Source Function Compare Extensive tests indicate that the method is robust

9. Roy Lacey, Stony Brook, Quark Matter 2008, Jaipur, India 9 Test with simulated Gaussian source -- t =0 Very good simultaneous fit obtained as expected

10. Roy Lacey, Stony Brook, Quark Matter 2008, Jaipur, India 10 Good reproduction of actual source function Test with simulated Gaussian source -- t =0

11. Roy Lacey, Stony Brook, Quark Matter 2008, Jaipur, India 11 Correlation Moments Robust Experimental Source Functions obtained from moments PHENIX Data Contributions from l > 6 is negligible

12. Roy Lacey, Stony Brook, Quark Matter 2008, Jaipur, India 12 Model Comparison Source Function Comparison to Models Give robust life time estimates  Consistent with Crossover transition 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 ρ max : 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

13. Roy Lacey, Stony Brook, Quark Matter 2008, Jaipur, India 13 QMQM

14. Roy Lacey, Stony Brook, Quark Matter 2008, Jaipur, India 14 Souce Imaging provides important access to S(r) Souce Imaging provides important access to S(r) Extensive study of imaging technique carried out 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 Model comparison Summary/Conclusions Timescales consistent with a crossover transition

15. Roy Lacey, Stony Brook, Quark Matter 2008, Jaipur, India 15 Known Knowns S.L. Huang QM08 15 1.Dynamic recombination 2. Partonic Thermalization! 3. Strongly coupled QGP

16. Roy Lacey, Stony Brook, Quark Matter 2008, Jaipur, India 16 ε scaling validated Known Knowns x k

17. Roy Lacey, Stony Brook, Quark Matter 2008, Jaipur, India 17 KE T scaling validated PHENIX preliminary P P Known Knowns Mesons Baryons Quark Degrees of Freedom Evident

18. Roy Lacey, Stony Brook, Quark Matter 2008, Jaipur, India 18 v 2 for the φ follows that of other mesons Flow fully developed in the partonic phase Known Knowns

19. Roy Lacey, Stony Brook, Quark Matter 2008, Jaipur, India 19 A Phase with Quarks as dynamical degrees of freedom Dominates the flow Known Knowns v2 for the heavy D meson follows that of other mesons

20. Roy Lacey, Stony Brook, Quark Matter 2008, Jaipur, India 20 Test with simulated Gaussian source -- t =5 Simultaneous fit not very good

21. Roy Lacey, Stony Brook, Quark Matter 2008, Jaipur, India 21 Source function from ellipsoid fit misses the mark Test with simulated Gaussian source -- t =5

22. Roy Lacey, Stony Brook, Quark Matter 2008, Jaipur, India 22 Test with simulated Gaussian source -- t =0 Very good simultaneous fit obtained as expected

23. Roy Lacey, Stony Brook, Quark Matter 2008, Jaipur, India 23 Good reproduction of actual source function Test with simulated Gaussian source -- t =0

24. Roy Lacey, Stony Brook, Quark Matter 2008, Jaipur, India 24 Test with simulated Gaussian source -- t =5 Simultaneous with hump function – much better

25. Roy Lacey, Stony Brook, Quark Matter 2008, Jaipur, India 25 Hump function and imaging compare well to actual source Test with simulated Gaussian source -- t =5

26. Roy Lacey, Stony Brook, Quark Matter 2008, Jaipur, India 26 3D Analysis (3) 3D Koonin Pratt Plug in (1) and (2) into (3) (1) (2) Expansion of R(q) and S(r) in Cartesian Harmonic basis Basis of Analysis (Danielewicz and Pratt nucl-th/0501003 (v1) 2005)

27. Roy Lacey, Stony Brook, Quark Matter 2008, Jaipur, India 27 initial state pre-equilibrium QGP and hydrodynamic expansion hadronization hadronic phase and freeze-out Conjecture of heavy ion collision Femtoscopy Prologue Courtesy S. Bass Femtoscopy Signatures: Cross-over transition: (Z. Fodor and S.D. Katz) (Rischke, Gyulassy) Sharp 1 st order QCD phase transition: (Pratt, Bertsch, Rischke, Gyulassy) 2 nd order QCD phase transition: (T. Csörgő, S. Hegyi, T. Novák, W.A. Zajc) (Non Gaussian shape) Supercooled QGP (scQGP) (T. Csörgő, L.P. Csernai) Femtoscopic signals are subtle and important for study of the QGP

28. Roy Lacey, Stony Brook, Quark Matter 2008, Jaipur, India 28 Outline I. Femtoscopic Prologue Why source imaging ! II. Source function extraction Brief description of the technique III. Proofing the technique Imaging known sources IV. Results & Implications What do we learn ?

29. Roy Lacey, Stony Brook, Quark Matter 2008, Jaipur, India 29 initial state pre-equilibrium QGP and hydrodynamic expansion hadronization hadronic phase and freeze-out A Known Known; Courtesy S. Bass Femtoscopy Signatures: Femtoscopic signals are subtle and important for study of the QGP initial state pre-equilibrium QGP and hydrodynamic expansion hadronization hadronic phase and freeze-out

30. Roy Lacey, Stony Brook, Quark Matter 2008, Jaipur, India 30 initial state pre-equilibrium QGP and hydrodynamic expansion hadronization hadronic phase and freeze-out A Known Known: Courtesy S. Bass A Crossover transition to the strongly coupled thermalized QGP occurs at RHIC

31. Roy Lacey, Stony Brook, Quark Matter 2008, Jaipur, India 31 Experiment & theory indicate a crossover transition Detailed measurements of the Space-time Dynamics are required Demise of the RHIC HBT Puzzle Puzzle ? A Cross over Strongly affects the Space-time Dynamics Rishke et al

32. Roy Lacey, Stony Brook, Quark Matter 2008, Jaipur, India 32 Experiment & theory indicate a crossover transition Detailed measurements of the Space-time Dynamics are required Demise of the RHIC HBT Puzzle Puzzle ? A Cross over Strongly affects the Space-time Dynamics Rishke et al