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

P. Chung, SUNY Stony Brook 2 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

P. Chung, SUNY Stony Brook 3 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? Courtesy S. Bass

P. Chung, SUNY Stony Brook 4 QGP and hydrodynamic expansion One Scenario : Motivation Expectation: A de-confined phase 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 Increased System Entropy that survives hadronization

P. Chung, SUNY Stony Brook 5 Experimental Setup PHENIX Detector Several Subsystems exploited for the analysis Excellent Pid is achieved

P. Chung, SUNY Stony Brook 6 Analysis Summary Image analysis in PHENIX Follows three basic steps. I. Track selection II. Evaluation of the Correlation Functions (with pair-cuts etc. III.Analysis of correlation functions: Imaging Direct fits 1D & 3D analysis

P. Chung, SUNY Stony Brook 7 Cuts Dphi (rad) Dz (cm)

P. Chung, SUNY Stony Brook 8 Cuts Dz (cm) Dphi (rad)

P. Chung, SUNY Stony Brook 9 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.

P. Chung, SUNY Stony Brook 10 Imaging Inversion procedure

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

P. Chung, SUNY Stony Brook 12 Input source function recovered Procedure is Robust ! Quick Test with simulated source

P. Chung, SUNY Stony Brook 13 Fitting correlation functions Kinematics “Spheroid/Blimp” Ansatz Brown & Danielewicz PRC 64, (2001)

P. Chung, SUNY Stony Brook 14 Evidence for long-range source at RHIC 1D Source imaging PHENIX Preliminary

P. Chung, SUNY Stony Brook 15 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

P. Chung, SUNY Stony Brook 16 Source functions from spheroid and Gaussian + Exponential are in excellent agreement Comparison of Source Functions

P. Chung, SUNY Stony Brook 17 PHENIX Preliminary Centrality dependence incompatible with resonance decay

P. Chung, SUNY Stony Brook 18 Short and long-range components of the source Short-range  Long-range  T. Csorgo M. Csanad

P. Chung, SUNY Stony Brook 19 Short and long-range components of the source T. Csorgo M. Csanad

P. Chung, 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.

P. Chung, SUNY Stony Brook 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

P. Chung, 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/ (v1) 2005)

P. Chung, SUNY Stony Brook 23 3D Analysis How to calculate correlation function and Source function in any direction Source function/Correlation function obtained via moment summation

P. Chung, SUNY Stony Brook 24 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

P. Chung, SUNY Stony Brook 25 PHENIX Preliminary 3D Source imaging Spherically symmetric source in pair cm. frame (PCMS) Isotropic emission in the pair frame

P. Chung, SUNY Stony Brook 26 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 First explicit determination of a spherical proton source First explicit determination of a spherical proton source Further Studies underway to quantify extent of long-range source!

P. Chung, SUNY Stony Brook 27

P. Chung, SUNY Stony Brook 28 Two source fit function This is the single particle distribution

P. Chung, SUNY Stony Brook 29 Simulation tests of the method Very clear proof of principle Procedure Generate moments for source. Carryout simultaneous Fit of all moments input output

P. Chung, SUNY Stony Brook 30 Two source fit function This is the two particle distribution