1. 1 Roy Lacey Nuclear Chemistry, SUNY, Stony Brook Proofing the Source Imaging Technique

2. Roy Lacey, Stony Brook WPCF 2007, Sonoma, California 2 Outline What is the Source Imaging Technique Pawel Done – Pawel Why do we need source imaging ? How do we proof and validate it ? Sample Results and Implications see Paul’s talk

3. Roy Lacey, Stony Brook WPCF 2007, Sonoma, California 3 initial state pre-equilibrium QGP and hydrodynamic expansion hadronization hadronic phase and freeze-out Conjecture of heavy ion collision Why we need source Imaging? Courtesy S. Bass Femtoscopy Signatures: Cross-over transition: Z. Fodor and S.D. Katz Strong 1st order QCD phase transition: (Pratt, Bertsch, Rischke, Gyulassy) Second 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

4. Roy Lacey, Stony Brook WPCF 2007, Sonoma, California 4 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 A Known Known: A Crossover transition to the strongly interacting QGP occurs at RHIC

5. Roy Lacey, Stony Brook WPCF 2007, Sonoma, California 5 ε scaling validated Known Knowns x k

6. Roy Lacey, Stony Brook WPCF 2007, Sonoma, California 6 KE T scaling validated PHENIX preliminary P P Known Knowns Mesons Baryons Quark Degrees of Freedom Evident

7. Roy Lacey, Stony Brook WPCF 2007, Sonoma, California 7 v 2 for the φ follows that of other mesons Flow fully developed in the partonic phase Known Knowns

8. Roy Lacey, Stony Brook WPCF 2007, Sonoma, California 8 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

9. Roy Lacey, Stony Brook WPCF 2007, Sonoma, California 9 Why we need source Imaging Validates cross over A Cross over Strongly affects the Space-time Dynamics

10. Roy Lacey, Stony Brook WPCF 2007, Sonoma, California 10 Set R x =R y =R z =4 fm,  f/o =10 fm/c, T=175 MeV, f=0.56 Boost + finite   tail, but only modest core increase, in L,O directions. Dave Brown WPCF - 2005      Why we need source Imaging

11. Roy Lacey, Stony Brook WPCF 2007, Sonoma, California 11 Life Time measurements As a probe for the transition Life Time measurements As a probe for the transition Source function (Distribution of pair separations) Encodes FSI Correlationfunction Inversion of this integral equation  Source Function 3D Koonin Pratt Eqn. New ! Expand R(q) and S(r) in Cartesian Harmonic basis (Danielewicz and Pratt nucl-th/0501003) Substitute (2) and (3) into (1) Reliable measurement of the full Source Function (finally) !

12. Roy Lacey, Stony Brook WPCF 2007, Sonoma, California 12 Proofing the Source Imaging Technique Generate Events Phasemaker AMPT Therminator etc Correlation Function 3D C(q) Moments Moment Fitting Source Imaging Calculated Source Function Compare

13. Roy Lacey, Stony Brook WPCF 2007, Sonoma, California 13 Test with simulated Gaussian source -- t =0 Very good simultaneous fit obtained as expected

14. Roy Lacey, Stony Brook WPCF 2007, Sonoma, California 14 Good reproduction of actual source function Test with simulated Gaussian source -- t =0

15. Roy Lacey, Stony Brook WPCF 2007, Sonoma, California 15 Test with simulated Gaussian source -- t =0 Very good simultaneous fit obtained as expected

16. Roy Lacey, Stony Brook WPCF 2007, Sonoma, California 16 Good reproduction of actual source function Test with simulated Gaussian source -- t =0

17. Roy Lacey, Stony Brook WPCF 2007, Sonoma, California 17 Test with simulated Gaussian source -- t =5 Simultaneous fit not very good

18. Roy Lacey, Stony Brook WPCF 2007, Sonoma, California 18 Source function from ellipsoid fit misses the mark Test with simulated Gaussian source -- t =5

19. Roy Lacey, Stony Brook WPCF 2007, Sonoma, California 19 Test with simulated Gaussian source -- t =5 Simultaneous with hump function – much better

20. Roy Lacey, Stony Brook WPCF 2007, Sonoma, California 20 Hump function and imaging compare well to actual source Test with simulated Gaussian source -- t =5

21. Roy Lacey, Stony Brook WPCF 2007, Sonoma, California 21 Sample Data Correlation Moments Source Function Comparison to Models Give robust life time estimates  Crossover transition

22. Roy Lacey, Stony Brook WPCF 2007, Sonoma, California 22 Extensive study of imaging technique Extensive study of imaging technique Technique is Robust

23. Roy Lacey, Stony Brook WPCF 2007, Sonoma, California 23 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)