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3D Pion & Kaon Source Imaging from Run4 and Run7 200 AGeV Au+Au collisions

Paul Chung (STAR Collaboration) NPI ASCR Prague. 3D Pion & Kaon Source Imaging from Run4 and Run7 200 AGeV Au+Au collisions. 1. PHENIX 1D Source Imaging. Phys.Rev.Lett.98:132301,2007. Phys.Rev.Lett.103:142301,2009. Outline. Run 4 Au+Au @ 200AGeV: 3D pion correlation functions

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3D Pion & Kaon Source Imaging from Run4 and Run7 200 AGeV Au+Au collisions

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  1. WPCF 2010, Kiev Paul Chung (STAR Collaboration) NPI ASCR Prague 3D Pion & Kaon Source Imaging from Run4 and Run7 200 AGeV Au+Au collisions 1

  2. WPCF 2010, Kiev PHENIX 1D Source Imaging Phys.Rev.Lett.98:132301,2007 Phys.Rev.Lett.103:142301,2009

  3. WPCF 2010, Kiev 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 3

  4. WPCF 2010, Kiev Emitting source 1D Imaging Formulation Technique Devised by: D. Brown, P. Danielewicz, PLB 398:252 (1997).PRC 57:2474 (1998). Inversion of Linear integral equation to obtain source function 1D Koonin Pratt Eqn. Encodes FSI Source function (Distribution of pair separations) Correlation function No Shape assumption for S(r) Inversion of this integral equation == Source Function Extracted S(r) in pair CM frame Hence Model-independent i.e Kernel independent of freeze-out conditions 4

  5. WPCF 2010, Kiev Imaging : Inversion procedure Expansion in B-spline basis Freeze-out occurs after last scattering Hence only Coulomb & BE effect included in kernel 5

  6. WPCF 2010, Kiev 1D Imaging STAR PRELIMINARY STAR PRELIMINARY ST 6

  7. WPCF 2010, Kiev 3D Analysis Basics [Danielewicz and Pratt nucl-th/0501003 (v1)] Expansion of R(q) and S(r) in Cartesian Harmonic basis x=out-direction y=side-direction z=long-direction 3D Koonin Pratt (3) Plug in (1) and (2) into (3) Invert (1) Invert (2) 7

  8. WPCF 2010, Kiev SIMULATION PROCEDURE Monte Carlo Events: Phasemaker, Therminator CRAB 3D C(q) Model calculation from space points Source Function Source FITTING Correlation Moments Source IMAGING 8

  9. WPCF 2010, Kiev Fit Functions • Ellipsoid Fit (3D Gaussian) : • G = lambda exp[-{ (x/2rx)2 + (y/2ry)2 + (z/2rz)2 }] • Hump Fit : • H = exp[- Fs { (x/2rxs)2 + (y/2rys)2 + (z/2rzs)2 }] x • exp[- Fl { (x/2rxl)2 + (y/2ryl)2 + (z/2rzl)2 }] • Fs = 1/[1 + (r/r0)2 ] • Fl = 1 - Fs

  10. WPCF 2010, Kiev Simulation – Therminator 10

  11. WPCF 2010, Kiev Comparison- C0 moment vs 1D C(q) STAR PRELIMINARY STAR PRELIM.

  12. WPCF 2010, Kiev L=2 & 4 moments STAR PRELIMINARY STAR PRELIMINARY

  13. WPCF 2010, Kiev L=6 moments STAR PRELIMINARY

  14. WPCF 2010, Kiev Imaging C2x2 & C2y2 STAR PRELIMINARY STAR PRELIMINARY 14

  15. WPCF 2010, Kiev 3D Imaging – S(r) & restored C(q) STAR PRELIMINARY STAR PRELIMINARY

  16. WPCF 2010, Kiev Ellipsoid vs Hump Fit : l=0 & 2 mom. STAR PRELIMINARY

  17. WPCF 2010, Kiev Ellipsoid vs Hump Fit : l=4 moments STAR PRELIMINARY STAR PRELIMINARY

  18. WPCF 2010, Kiev Ellipsoid vs Hump Fit : l=6 moments STAR PRELIMINARY

  19. WPCF 2010, Kiev Image vs Ellipsoid & Hump S(r) STAR PRELIMINARY STAR PRELIMINARY

  20. WPCF 2010, Kiev 3D C(q) : Ellipsoid vs Hump Fit STAR PRELIMINARY STAR PRELIMINARY

  21. WPCF 2010, Kiev 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

  22. WPCF 2010, Kiev STAR vs PHENIX comparison STAR PRELIMINARY STAR PRELIMINARY

  23. WPCF 2010, Kiev 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

  24. WPCF 2010, Kiev Run 7 & Run 4 KK : C0 vs 1D C(qinv) STAR PRELIMINARY STAR PRELIMINARY

  25. WPCF 2010, Kiev Run 7 + Run 4 KK : C0 vs 1D C(qinv) STAR PRELIMINARY

  26. WPCF 2010, Kiev Run 7 + Run 4 KK : l=2 & l=4 moments STAR PRELIMINARY STAR PRELIMINARY

  27. WPCF 2010, Kiev KK: Ellipsoid Fit STAR PRELIMINARY STAR PRELIMINARY

  28. WPCF 2010, Kiev THERMINATOR Model comparison

  29. WPCF 2010, Kiev 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 fm/c < central collisions. Extracted Kaon source function essentially Gaussian – No significant non-Gaussian tail observed. Kaon source dimension & lifetime smaller than for pion source; Kaon emission instantaneous (Therminator) 29

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