1. November 29, 2010Zimanyi Winter School 2010, Budapest11 3D Pion & Kaon Source Imaging from 200 AGeV Au+Au collisions Paul Chung (STAR Collaboration) NPI ASCR Prague

2. November 29, 2010 Zimanyi Winter School 2010, Budapest 2 initial state pre-equilibrium QGP and hydrodynamic expansion hadronization hadronic phase and freeze-out Conjecture of collisions at RHIC : Motivation Which observables & phenomena connect to the de-confined stage?

3. PHENIX 1D Source Imaging Phys.Rev.Lett.98:132301,2007 November 29, 2010 Zimanyi Winter School 2010, Budapest 3 Phys.Rev.Lett.103:142301,2009

4. November 29, 2010 Zimanyi Winter School 2010, Budapest 44 Outline Run 4 Au+Au @ 200AGeV: 3D pion correlation functions Overview of 3D source shape analysis : Cartesian Spherical Harmonic decomposition & Imaging Technique Correlation moments for low kT (0.25<kT<0.35 GeV) pion pairs from peripheral collisions (50<cen<80%). 3D source function extraction: Moment Imaging & Fitting Therminator comparison for extracting pion source lifetime & pion emission duration 3D Kaon correlation functions from Run 4 & Run 7 central Au+Au collisions Kaon source extraction & Therminator comparison

5. November 29, 2010 Zimanyi Winter School 2010, Budapest 55 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. Extracted S(r) in pair CM frame Hence Model-independent i.e Kernel independent of freeze-out conditions No Shape assumption for S(r) 1D Imaging Formulation

6. November 29, 2010 Zimanyi Winter School 2010, Budapest 66 Imaging : Inversion procedure Freeze-out occurs after last scattering Hence only Coulomb & BE effect included in kernel Expansion in B-spline basis

7. November 29, 2010 Zimanyi Winter School 2010, Budapest 77 1D Imaging ST STAR PRELIMINARY

8. November 29, 2010 Zimanyi Winter School 2010, Budapest 88 (3) 3D Koonin Pratt Plug in (1) and (2) into (3) Invert (1) Invert (2) Expansion of R(q) and S(r) in Cartesian Harmonic basis [Danielewicz and Pratt nucl-th/0501003 (v1)] x=out-direction y=side-direction z=long-direction 3D Analysis Basics

9. November 29, 2010 Zimanyi Winter School 2010, Budapest 99 Monte Carlo Events: Phasemaker, Therminator CRAB3D C(q) Correlation Moments Source FITTING Source IMAGING Source Function Model calculation from space points SIMULATION PROCEDURE

10. November 29, 2010 Zimanyi Winter School 2010, Budapest 10 Fit Functions Ellipsoid Fit (3D Gaussian) : G = lambda exp[-{ (x/2r x ) 2 + (y/2r y ) 2 + (z/2r z ) 2 }] Hump Fit : H = exp[- F s { (x/2r xs ) 2 + (y/2r ys ) 2 + (z/2r zs ) 2 }] x exp[- F l { (x/2r xl ) 2 + (y/2r yl ) 2 + (z/2r zl ) 2 }] F s = 1/[1 + (r/r 0 ) 2 ] F l = 1 - F s

11. November 29, 2010 Zimanyi Winter School 2010, Budapest 11 Simulation – Therminator

12. November 29, 2010 Zimanyi Winter School 2010, Budapest 12 Comparison- C 0 moment vs 1D C(q) STAR PRELIM.STAR PRELIMINARY

13. L=2 & 4 moments November 29, 2010 Zimanyi Winter School 2010, Budapest 13 STAR PRELIMINARY

14. November 29, 2010 Zimanyi Winter School 2010, Budapest 14 L=6 moments STAR PRELIMINARY

15. November 29, 2010 Zimanyi Winter School 2010, Budapest 15 Imaging C 2 x2 & C 2 y2 STAR PRELIMINARY

16. November 29, 2010 Zimanyi Winter School 2010, Budapest 16 3D Imaging – S(r) & restored C(q) STAR PRELIMINARY

17. November 29, 2010 Zimanyi Winter School 2010, Budapest 17 Ellipsoid vs Hump Fit : l=0 & 2 mom. STAR PRELIMINARY

18. November 29, 2010 Zimanyi Winter School 2010, Budapest 18 Ellipsoid vs Hump Fit : l=4 moments STAR PRELIMINARY

19. November 29, 2010 Zimanyi Winter School 2010, Budapest 19 Ellipsoid vs Hump Fit : l=6 moments STAR PRELIMINARY

20. November 29, 2010 Zimanyi Winter School 2010, Budapest 20 Image vs Ellipsoid & Hump S(r) STAR PRELIMINARY

21. November 29, 2010 Zimanyi Winter School 2010, Budapest 21 3D C(q) : Ellipsoid vs Hump Fit STAR PRELIMINARY

22. November 29, 2010 Zimanyi Winter School 2010, Budapest 22 Therminator BW: Source lifetime & Pion emission duration extraction Therminator (Kisiel et al PRC 73, 064902 2006) : Production of particles from thermalized and expanding system with Boost invariance & cylindrical symmetry BW mode: Freeze-out hypersurface defined by constant laboratory time independent of transverse radius

23. November 29, 2010 Zimanyi Winter School 2010, Budapest 23 STAR vs PHENIX comparison STAR PRELIMINARY

24. Source extraction – central collisions PRL100, 232301 (2008) (PHENIX) Transverse dimension = 8.9fm Source lifetime = 8.5fm/c Emission duration = 2fm/c Source parameters larger for central collisions than for peripheral collisions Full centrality dependence extraction underway November 29, 2010 Zimanyi Winter School 2010, Budapest 24

25. Extracted Pion Source Images from semi-central & peripheral collisions November 29, 2010 Zimanyi Winter School 2010, Budapest 25

26. November 29, 2010 Zimanyi Winter School 2010, Budapest 26 Run 7 & Run 4 KK : C 0 vs 1D C(q inv ) STAR PRELIMINARY

27. November 29, 2010 Zimanyi Winter School 2010, Budapest 27 Run 7 + Run 4 KK : C 0 vs 1D C(q inv ) STAR PRELIMINARY

28. Run 7 + Run 4 KK : l=2 & l=4 moments November 29, 2010 Zimanyi Winter School 2010, Budapest 28 STAR PRELIMINARY

29. KK: Ellipsoid Fit November 29, 2010 Zimanyi Winter School 2010, Budapest 29 STAR PRELIMINARY

30. THERMINATOR Model comparison November 29, 2010 Zimanyi Winter School 2010, Budapest 30

31. November 29, 2010 Zimanyi Winter School 2010, Budapest 31 Conclusion Correlation moments for low kT pion pairs from Run4 peripheral Au+Au collisions well described by the Hump Fit function. For low kT pion pairs from peripheral collisions, inferred pion source lifetime ~ 3.5 fm/c & pion emission duration ~ 1.5 fm/c < central collisions. Extracted Kaon source function essentially Gaussian – No significant non-Gaussian tail observed. Kaon source dimension & lifetime comparable to pion source; Kaon emission instantaneous (Therminator)