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Paul Chung ( for the PHENIX Collaboration ) Nuclear Chemistry, SUNY, Stony Brook

Evidence for a long-range pion emission source in Au+Au collisions at. Paul Chung ( for the PHENIX Collaboration ) Nuclear Chemistry, SUNY, Stony Brook. Outline Motivation Brief Review of Apparatus & analysis technique 1D Results Angle averaged correlation function

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Paul Chung ( for the PHENIX Collaboration ) Nuclear Chemistry, SUNY, Stony Brook

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  1. Evidence for a long-range pion emission source in Au+Au collisions at Paul Chung (for the PHENIX Collaboration) Nuclear Chemistry, SUNY, Stony Brook

  2. Outline • Motivation • Brief Review of Apparatus & analysis technique • 1D Results • Angle averaged correlation function • Angle averaged source function • 3D analysis • Correlation moments • Source moments • Conclusion/s

  3. hadronic phase and freeze-out QGP and hydrodynamic expansion initial state pre-equilibrium hadronization Motivation Conjecture of collisions at RHIC : Courtesy S. Bass Which observables & phenomena connect to the de-confined stage?

  4. Motivation One Scenario: Increased System Entropy that survives hadronization QGP and hydrodynamic expansion Expectation: A de-confined phase 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

  5. Experimental Setup PHENIX Detector Several Subsystems exploited for the analysis Excellent Pid is achieved

  6. Analysis Summary • Image analysis in PHENIX Follows three basic steps. • Track selection • Evaluation of the • Correlation Functions (with pair-cuts etc. • Analysis of correlation functions: • Imaging • Direct fits 1D & 3D analysis

  7. Cuts Dphi (rad) Dz (cm)

  8. Cuts Dphi (rad) Dz (cm)

  9. Emitting source 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 1D Koonin Pratt Eqn. Encodes FSI Source function (Distribution of pair separations) Correlation function Inversion of this integral equation == Source Function

  10. Imaging Inversion procedure

  11. Correlation Fits [Theoretical correlation function] convolute source function with kernel (P. Danielewicz) Measured correlation function Minimize Chi-squared Parameters of the source function

  12. Quick Test with simulated source Input source function recovered Procedure is Robust !

  13. Fitting correlation functions Kinematics “Spheroid/Blimp” Ansatz Brown & Danielewicz PRC 64, 014902 (2001)

  14. 1D Source imaging PHENIX Preliminary Evidence for long-range source at RHIC

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

  16. Comparison of Source Functions Source functions from spheroid and Gaussian + Exponential are in excellent agreement

  17. PHENIX Preliminary Centrality dependence incompatible with resonance decay

  18. Short and long-range components of the source T. Csorgo M. Csanad Short-range  Long-range 

  19. Short and long-range components of the source T. Csorgo M. Csanad

  20. Pair fractions associated with long- and short-range structures Core Halo assumption T. Csorgo M. Csanad Expt  Contribution from decay insufficient to account for long-range component.

  21. 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

  22. 3D Analysis Basis of Analysis (Danielewicz and Pratt nucl-th/0501003 (v1) 2005) Expansion of R(q) and S(r) in Cartesian Harmonic basis 3D Koonin Pratt (3) Plug in (1) and (2) into (3) (1) (2)

  23. 3D Analysis How to calculate correlation function and Source function in any direction Source function/Correlation function obtained via moment summation

  24. PHENIX Preliminary 3D Source imaging Origin of deformation Kinematics ? or Time effect • Instantaneous • Freeze-out • LCMS implies kinematics • PCMS implies time effect Deformed source in pair cm frame:

  25. PHENIX Preliminary 3D Source imaging • Isotropic emission in the • pair frame Spherically symmetric source in pair cm. frame (PCMS)

  26. Extensive study of two-pion source • images and moments in Au+Au collisions at RHIC • First observation of a long-range source having an • extension in the out direction for pions • First explicit determination of a spherical proton source Further Studies underway to quantify extent of long-range source!

  27. Two source fit function This is the single particle distribution

  28. input Simulation tests of the method • Procedure • Generate moments for • source. • Carryout simultaneous • Fit of all moments output Very clear proof of principle

  29. Two source fit function This is the two particle distribution

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