Are elliptic flow v2 measurements consistent with the formation of the Quark Gluon Plasma at RHIC

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

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Motivation
Conjecture of collisions at RHIC
Courtesy S. Bass
Which observables phenomena connect to the
de-confined stage?
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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 than would be expected from a
system which remained in the hadronic phase
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Experimental Setup
PHENIX Detector Several Subsystems exploited for
the analysis
Excellent Pid is achieved
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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
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Cuts
Dphi (rad)
Dz (cm)
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Cuts
Dphi (rad)
Dz (cm)
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Imaging Technique
Technique Devised by D. Brown, P.
Danielewicz, PLB 398252 (1997). PRC 572474
(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
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Imaging
Inversion procedure
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Correlation Fits
Theoretical correlation function convolute
source function with kernel (P. Danielewicz)
Measured correlation function
Minimize Chi-squared
Parameters of the source function
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Quick Test with simulated source
Input source function recovered Procedure is
Robust !
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Fitting correlation functions
Kinematics Spheroid/Blimp Ansatz
Brown Danielewicz PRC 64, 014902 (2001)
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1D Source imaging
PHENIX Preliminary
Evidence for long-range source at RHIC
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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
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Comparison of Source Functions
Source functions from spheroid and Gaussian
Exponential are in excellent agreement
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Centrality dependence incompatible with resonance
decay
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Short and long-range components of the source
T. Csorgo M. Csanad
Short-range ?
Long-range ?
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Short and long-range components of the source
T. Csorgo M. Csanad
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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.
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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
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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)
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3D Analysis
How to calculate correlation function and Source
function in any direction
Source function/Correlation function obtained via
moment summation
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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
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3D Source imaging

• Isotropic emission in the
• pair frame

Spherically symmetric source in pair cm. frame
(PCMS)
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• Extensive study of two-pion source
• images and moments in AuAu 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!
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Two source fit function
This is the single particle distribution
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input
Simulation tests of the method

• Procedure
• Generate moments for
• source.
• Carryout simultaneous
• Fit of all moments

output
Very clear proof of principle
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Two source fit function
This is the two particle distribution