1. 1 Roy Lacey & Paul Chung Nuclear Chemistry, SUNY, Stony Brook Evidence for a long-range pion emission source in Au+Au collisions at

2. Roy Lacey, SUNY Stony Brook 2 initial state pre-equilibrium QGP and hydrodynamic expansion hadronization hadronic phase and freeze-out Conjecture of collisions at RHIC : Motivation Courtesy S. Bass Increased System Entropy that survives hadronization Expectation: A strong first order phase transition leads to an emitting system characterized by a much larger space-time extent thanwould be expected from a system which remained in the hadronic phase A strong first order phase transition leads to an emitting system characterized by a much larger space-time extent than would be expected from a system which remained in the hadronic phase Guiding philosophy in first few years at RHIC =  Puzzle ?

3. Roy Lacey, SUNY Stony Brook 3 What do we know now ? Any Implications for HBT ?

4. Roy Lacey, SUNY Stony Brook 4 thermalization time (  0 ~ 0.2 – 1 fm/c)  Bj  ~ 5 – 15 GeV/fm 3 Extrapolation From E T Distributions What do we know ? Flow

5. Roy Lacey, SUNY Stony Brook 5 What do we know ? PHENIX Preliminary v 2 scales with eccentricity and across system size Strong Evidence for Thermalization and hydro scaling

6. Roy Lacey, SUNY Stony Brook 6 What do we know ? Scaling breaksPerfect fluid hydro Scaling holds up to ~ 1 GeV Mesons scale together Baryons scale together Strong hydro scaling with hint of quark degrees of freedom PHENIX preliminary data

7. Roy Lacey, SUNY Stony Brook 7 What do we know ? Scaling works Compatible with Valence Quark degrees of freedom Scaling holds over the whole range of KE T PHENIX preliminary data

8. Roy Lacey, SUNY Stony Brook 8 Oh yes - It is Comprehensive ! What do we know ?

9. Roy Lacey, SUNY Stony Brook 9 nucl-ex/0507004 What do we know ? T. Renk, J. Ruppert hep-ph/0509036 Strong centrality dependent modification of away-side jet in Au+Au Away-side peak consistent with mach-cone scenario nucl-th/0406018 Stoecker hep-ph/0411315 Casalderrey-Solana, et al other explanations ! Implication for viscosity and sound speed !

10. Roy Lacey, SUNY Stony Brook 10 View associated particles in frame with high pT direction as z-axis High pT particle Associated pt particles Simulated Result A Small digression A Small digression Yes ! We have results

11. Roy Lacey, SUNY Stony Brook 11 Sound Speed Estimate c s ~ 0.35 Soft EOS F. Karsch, hep-lat/0601013 What do we know ? Compatible with soft EOS Sound speed is not zero during an extended hadronization period. Space-time evolution more subtle ?

12. Roy Lacey, SUNY Stony Brook 12 Subtle signals require a paradigm shift Extract the full source function

13. Roy Lacey, SUNY Stony Brook 13 Extraction of Source functions Imaging & Fitting Moment Expansion

14. Roy Lacey, SUNY Stony Brook 14 Imaging Technique Technique Devised by: D. Brown, P. Danielewicz, PLB 398:252 (1997). PRC 57:2474 (1998). Inversion of Linear integral equation to obtain source function Source function (Distribution of pair separations) Encodes FSI Correlationfunction Inversion of this integral equation ==  Source Function Emitting source 1D Koonin Pratt Eqn. Well established inversion procedure

15. Roy Lacey, SUNY Stony Brook 15 Correlation Fits Parameters of the source function Minimize Chi-squared [Theoretical correlation function] convolute source function with kernel (P. Danielewicz) Measured correlation function

16. Roy Lacey, SUNY Stony Brook 16 Input source function recovered Procedure is Robust ! Quick Test with simulated source

17. Roy Lacey, SUNY Stony Brook 17 Experimental Results Gaussian Source functions do not provide good fits

18. Roy Lacey, SUNY Stony Brook 18 Evidence for long-range source at RHIC 1D Source imaging PHENIX Preliminary Source functions from spheroid or Gaussian + Exponential give good fit. not Source function tail is not due to: Kinematics Resonance contributions

19. Roy Lacey, SUNY Stony Brook 19 PHENIX Preliminary Centrality dependence also incompatible with resonance decay kinematics

20. Roy Lacey, SUNY Stony Brook 20 Pair fractions associated with long- and short-range structures T. Csorgo M. Csanad Core Halo assumption Expt  Contribution from decay insufficient to account for long- range component. Full fledge simulation indicate similar conclusion

21. Roy Lacey, SUNY Stony Brook 21 Experimental Results A hint of the shape of things to come

22. Roy Lacey, SUNY Stony Brook 22 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)

23. Roy Lacey, SUNY Stony Brook 23 Calculation of Correlation Moments: Fitting with truncated expansion series ! 6 independent moments (a)

24. Roy Lacey, SUNY Stony Brook 24 A look at the basis L=0 L=2

25. Roy Lacey, SUNY Stony Brook 25 Strategy Get values of Such that Fitwith moments as fitting parameters.

26. Roy Lacey, SUNY Stony Brook 26 Strategy With

27. Roy Lacey, SUNY Stony Brook 27 Simulation tests of the method Very clear proof of principle Procedure Generate moments for source. Carryout simultaneous Fit of all moments input output

28. Roy Lacey, SUNY Stony Brook 28 Results - moments Very good agreement as it should

29. Roy Lacey, SUNY Stony Brook 29 Results - moments Exquisite/Robust Results Sizeable signals observed for l = 2

30. Roy Lacey, SUNY Stony Brook 30 Results - moments l= 4 moments Exquisite/Robust Results

31. Roy Lacey, SUNY Stony Brook 31 Extensive study of two-pion source Extensive study of two-pion source images and moments in Au+Au collisions at RHIC images and moments in Au+Au collisions at RHIC First observation of a long-range source having an First observation of a long-range source having an extension in the out direction for pions extension in the out direction for pions Long-range source not due to kinematics or resonances kinematics or resonances Further Studies underway to quantify A variety of other source functions! Much more to come !

32. Roy Lacey, SUNY Stony Brook 32

33. Roy Lacey, SUNY Stony Brook 33 Source functions from spheroid and Gaussian + Exponential are in excellent agreement  need 3D info Comparison of Source Functions

34. Roy Lacey, SUNY Stony Brook 34 PHENIX Preliminary 3D Source imaging Deformed source in pair cm frame: Origin of deformation Kinematics ? or Time effect Instantaneous Freeze-out LCMS implies kinematics PCMS implies time effect

35. Roy Lacey, SUNY Stony Brook 35 PHENIX Preliminary 3D Source imaging Spherically symmetric source in pair cm. frame (PCMS) Isotropic emission in the pair frame

36. Roy Lacey, SUNY Stony Brook 36 Short and long-range components of the source Short-range  Long-range  T. Csorgo M. Csanad

37. Roy Lacey, SUNY Stony Brook 37 New 3D Analysis 1D analysis  angle averaged C(q) & S(r) info only no directional information Need 3D analysis to access directional information Correlation and source moment fitting and imaging

38. Roy Lacey, SUNY Stony Brook 38 3D Analysis How to calculate correlation function and Source function in any direction Source function/Correlation function obtained via moment summation

39. Roy Lacey, SUNY Stony Brook 39 Short and long-range components of the source T. Csorgo M. Csanad

40. Roy Lacey, SUNY Stony Brook 40 Extraction of Source Parameters Fit Function (Pratt et al.) This fit function allows extraction of both the short- and long-range components of the source image This fit function allows extraction of both the short- and long-range components of the source image Bessel Functions Radii Pair Fractions

41. Roy Lacey, SUNY Stony Brook 41 Outline 1. Motivation 2. Brief Review of Apparatus & analysis technique 3.1D Results Angle averaged correlation function Angle averaged source function 4.3D analysis Correlation moments Source moments 5.Conclusion/s

42. Roy Lacey, SUNY Stony Brook 42 Imaging Inversion procedure

43. Roy Lacey, SUNY Stony Brook 43 Fitting correlation functions Kinematics “Spheroid/Blimp” Ansatz Brown & Danielewicz PRC 64, 014902 (2001)

44. Roy Lacey, SUNY Stony Brook 44 Cuts Dphi (rad) Dz (cm)

45. Roy Lacey, SUNY Stony Brook 45 Cuts Dz (cm) Dphi (rad)

46. Roy Lacey, SUNY Stony Brook 46 Two source fit function This is the single particle distribution

47. Roy Lacey, SUNY Stony Brook 47 Two source fit function This is the two particle distribution

48. Roy Lacey, SUNY Stony Brook 48 Experimental Setup PHENIX Detector Several Subsystems exploited for the analysis Excellent Pid is achieved