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

1
Two-pion Emission Source Images A probe for
short- and long-range emission sources at RHIC
Roy A. Lacey Nuclear Chemistry, SUNY, Stony Brook
Acknowledgements P. Danielewicz S. Pratt D. Brown
2
Motivation
Conjecture of collisions at RHIC
Courtesy S. Bass
Which observables phenomena connect to the
de-confined stage?
3
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
4
Well known Hydrodynamic Expansion
eBjorken 5 - 15 GeV/fm3
Strong Radial Flow
PHENIX (nucl-ex/0410012)
Two-particle interferometry studies provides an
important probe
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.)
• Imaging of
• Correlation functions
• Fits to correlation function

7
Analysis Technique
Correlation Function
Direct Fits to the Correlation Functions
Imaging
Source Function
8
Imaging Technique
Technique Devised by D. Brown, P.
Danielewicz, PLB 398252 (1997). PRC 572474
(1998).
Inversion of Linear integral equation to obtain
source function
Encodes FSI
Source function (Distribution of pair separations)
Correlation function
Inversion of this integral equation ? Source
Function
9
Imaging
Inversion procedure
10
Quick Test
Simulated Source image (exponential Gaussian)

• Source faithfully recovered

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 - 1
Input source function recovered Procedure is
Robust !
13
Fitting correlation functions
Kinematics Spheroid/Blimp Ansatz
Brown Danielewicz PRC 64, 014902 (2001)
spheroid/Blimp parameters
14
Sensitivity Tests
Fix RT R and vary a Source parameters
Recovered
15
Sensitivity Tests
Fix a and vary R Source parameters Recovered
16
Results
Results

• Non Gaussian tail observed in source function

17
Results

• Non Gaussian tail observed in source function

18
Results

• Non Gaussian tail NOT observed at the AGS

19
Results

• Spheroid source function yield excellent fits
  to data

20
Comparison of Source Functions
Source functions from Imaging and Correlation fit
are in excellent agreement
21
Comparison of Source Functions
Comparison of source functions show clear
evidence for long-range source
22
Comparison of Source Functions
Tail even more Prominent at Lower kT
Source functions from Imaging and Correlation fit
are in excellent agreement
23
Comparison of Source Functions
Prominent tail not observed at relatively large
kT
24
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
25
Results
Systematic Error Band (AuAu)

• Familiar mT dependence

26
Results
Systematic Error Band (AuAu)

• Long-range source is substantially larger

27
Results

• Short-range sources show characteristic
  centrality dependence

28
Results

• long- and short-range sources show similar
  centrality dependence

29

• First Extensive study of two-pion source
• images in dAu and AuAu collisions at RHIC
• Results indicate initial hints of an important
  long-range
• source with characteristic mT and Npart
  dependence !

Further Studies/Checks Required to pin down
details of long-range source!
30
(No Transcript)
31

• Outline
• Motivation
• Brief Review of Correlation analysis methods
• Brief Review of Imaging
• Advantages
• Data Analysis Results
• Correlation functions
• Source functions
• Source parameters dependence (centrality, mT,
  etc)
• Conclusion/s

32
Imaging Technique
Operational Procedure
Technique Devised by D. A. Brown, P.
Danielewicz, Phys. Lett. B 398252-258 (1997).
Phys. Rev. C 572474-2483 (1998).
Inversion of Linear integral equation to obtain
source function
Encodes FSI
Source function (Distribution of pair separations)
Correlation function
An Earlier Application of the Method to data
obtained at lower energies P. Chung et. al
(E895) Phys.Rev.Lett.91162301, 2003
Inversion of this integral equation ? Source
Function
Fit Source function to obtain Source parameters
33
Two-particle Interferometry

• HBT Approach
• Assumes negligible final-State Interactions
  (FSI)
• Coulomb corrected correlation function
• Assumes Gaussian emitting source function
• Measured correlation function is the Fourier
  Transform of the two-particle source function
• Applicable to pions only

• Imaging Approach
• Extraction of Complete Source function
• No shape assumption for source
• No direct Coulomb correction of correlation
  function
• Method applicable to all particle pair
  combinations

34
Results

• Non-Gaussian tails for dAu and AuAu

35
Quick Test - 2
Same correlation function with larger
statistical error bars
Input source function recovered with larger
error Statistics
important !