1 paul chung ( for the phenix collaboration ) nuclear chemistry, suny, stony brook evidence for a...
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1
Paul Chung (for the PHENIX Collaboration)
Nuclear Chemistry, SUNY, Stony Brook
Evidence for a long-range pion emission source inEvidence for a long-range pion emission source inAu+Au collisions atAu+Au collisions at 200 NNs GeV
2P. Chung, SUNY Stony Brook
Outline
1. Motivation2. 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
3P. Chung, SUNY Stony Brook
initial state
pre-equilibrium
QGP andhydrodynamic expansion
hadronization
hadronic phaseand freeze-out
Conjecture of collisions at RHIC :
MotivationMotivation
Which observables & phenomena connect Which observables & phenomena connect to the de-confined stage?to the de-confined stage?
Courtesy S. BassCourtesy S. Bass
4P. Chung, SUNY Stony Brook
QGP andhydrodynamic expansion
One Scenario:
MotivationMotivation
Expectation:Expectation:A de-confined phase leads to an emitting system A de-confined phase leads to an emitting system
characterized by a much larger space-time extent thancharacterized by a much larger space-time extent than would be expected from a system which remained in the would be expected from a system which remained in the
hadronic phase hadronic phase
Increased System Entropy Increased System Entropy that survives that survives hadronizationhadronization
5P. Chung, SUNY Stony Brook
Experimental SetupExperimental Setup
PHENIX Detector
Several Subsystems exploited for the
analysis
Excellent Pid is achievedExcellent Pid is achieved
~ 120 ps /K 2 GeV/c
~ 450 ps /K 1 GeV/c
TOF
EMC
6P. Chung, SUNY Stony Brook
Analysis SummaryAnalysis 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
( )( )
( )cor
mix
N qC q
N q
( )( )
( )cor
mix
N qC q
N q
1D & 3D 1D & 3D analysisanalysis
7P. Chung, SUNY Stony Brook
CutsCuts
Dphi (rad) Dz (cm)
8P. Chung, SUNY Stony Brook
CutsCuts
Dz (cm)
Dphi (rad)
9P. Chung, SUNY Stony Brook
Imaging TechniqueImaging 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
20( ) 1 ) (,4 ( )C K q r S rq drr
Source Source functionfunction
(Distribution of pair separations)
Encodes FSI
CorrelationCorrelationfunctionfunction
Inversion of this integral equation== Source Function
Emitting source
1D Koonin Pratt Eqn.
10P. Chung, SUNY Stony Brook
Imaging Imaging
Inversion procedure
2( ) 4 ( , ) ( )C q drr K q r S r ( ) ( )j j
j
S r S B r ( )
( , ) ( )
Thi ij j
j
ij j
C q K S
K dr K q r B r
2
22
( )
( )
Expti ij j
j
Expti
C q K S
C q
11P. Chung, SUNY Stony Brook
Correlation FitsCorrelation Fits
Parameters of the source functionParameters of the source function
Minimize Chi-squared
[Theoretical correlation function]convolute source function convolute source function with kernel with kernel (P. Danielewicz)(P. Danielewicz) Measured correlation function
12P. Chung, SUNY Stony Brook
Input source function recoveredInput source function recoveredProcedure is Robust !Procedure is Robust !
Quick Test with simulated sourceQuick Test with simulated source
13P. Chung, SUNY Stony Brook
Fitting correlation functionsFitting correlation functions
KinematicsKinematics““Spheroid/Blimp” AnsatzSpheroid/Blimp” Ansatz
2
3 2
2
( ) exp 8 4 2
1b= 1- , a,
a
T T
TT
r bS r erfi
b R a R
rR
R
2
3 2
2
( ) exp 8 4 2
1b= 1- , a,
a
T T
TT
r bS r erfi
b R a R
rR
R
Brown & Danielewicz PRC 64, 014902 (2001)Brown & Danielewicz PRC 64, 014902 (2001)
14P. Chung, SUNY Stony Brook
Evidence for long-range source at RHICEvidence for long-range source at RHIC
1D Source imaging1D Source imaging
PHENIX Preliminary
200 GeVnnAu Au s
15P. Chung, SUNY Stony Brook
Extraction of Source ParametersExtraction of Source Parameters
Fit Function Fit Function (Pratt et al.)(Pratt et al.)
2
2 22
exp
4
exp
3exp
3 0 1exp 2
2
exp exp
( ) +( , )2
( ) 2 ( )( , ) 4
=2 ,
gaus
rrRRgaus
gaus
gaus
eS r e
N RR
K z K zN R
z z
Rz
R R
This fit function allows extraction of both This fit function allows extraction of both the short- and long-range the short- and long-range
components of the source imagecomponents of the source image
This fit function allows extraction of both This fit function allows extraction of both the short- and long-range the short- and long-range
components of the source imagecomponents of the source image
Bessel Functions
RadiiPair Fractions
16P. Chung, SUNY Stony Brook
Source functions from spheroid and Gaussian + Exponential are in Source functions from spheroid and Gaussian + Exponential are in excellent agreement excellent agreement
Comparison of Source FunctionsComparison of Source FunctionsComparison of Source FunctionsComparison of Source Functions
17P. Chung, SUNY Stony Brook
PHENIX Preliminary
Centrality dependence incompatible with resonance decay
18P. Chung, SUNY Stony Brook
Short and long-range components of the sourceShort and long-range components of the sourceShort and long-range components of the sourceShort and long-range components of the source
2
3 2
2
( ) exp 8 4 2
1b= 1- , a,
a
L T
T T
TT
R a R
r bS r erfi
b R a R
rR
R
2
3 2
2
( ) exp 8 4 2
1b= 1- , a,
a
L T
T T
TT
R a R
r bS r erfi
b R a R
rR
R
Short-range
Long-range
01.2 4 3.0ls T l T T
s
RR R R R a R R
R
T. CsorgoM. Csanad
1.0l
s
19P. Chung, SUNY Stony Brook
Short and long-range components of the sourceShort and long-range components of the sourceShort and long-range components of the sourceShort and long-range components of the source
T. CsorgoM. Csanad
20P. Chung, SUNY Stony Brook
Pair fractions associated with long- and short-range structuresPair fractions associated with long- and short-range structuresPair fractions associated with long- and short-range structuresPair fractions associated with long- and short-range structures
T. CsorgoM. Csanad
2s
l
l
s s
=
= 2
2 0.12 2 0.3
0.5
c HBT
c
c
f
f f
f f
f
Core Halo assumption
1.0l
s
Expt
Contribution from decay insufficient to account for long-range component.
21P. Chung, SUNY Stony Brook
New 3D AnalysisNew 3D Analysis
1D analysis angle averaged C(q) & S(r) info only• no directional information
Need 3D analysis to access directional informationNeed 3D analysis to access directional information
Correlation and source moment fitting and imagingCorrelation and source moment fitting and imagingCorrelation and source moment fitting and imagingCorrelation and source moment fitting and imaging
22P. Chung, SUNY Stony Brook
3D Analysis3D Analysis
1 11
1 11
.... ........
.... ........
( ) ( ) (1)
( ) ( ) (2)
l ll
l ll
l lq
l
l lr
l
R q R q
S r S r
3( ) ( ) 1 4 ( , ) ( )R q C q dr K q r S r
(3)3D Koonin3D KooninPrattPratt
Plug in (1) and (2) into (3)1 1
2.... ....
( ) 4 ( , ) ( ) (4)l l
l llR q drr K q r S r
1 1
2.... ....
( ) 4 ( , ) ( ) (4)l l
l llR q drr K q r S r
1 1
1 1
.... ....
.... ....
2 1 !!( ) ( ) ( ) (4)
! 42 1 !!
( ) ( ) ( ) (5)! 4
l l
l l
ql lq
l lrr
dlR q R q
ll d
S r S rl
1 1
1 1
.... ....
.... ....
2 1 !!( ) ( ) ( ) (4)
! 42 1 !!
( ) ( ) ( ) (5)! 4
l l
l l
ql lq
l lrr
dlR q R q
ll d
S r S rl
(1)
(2)
Expansion of R(q) and S(r) in Cartesian Harmonic basisExpansion of R(q) and S(r) in Cartesian Harmonic basis
Basis of AnalysisBasis of Analysis
(Danielewicz and Pratt nucl-th/0501003 (v1) 2005)(Danielewicz and Pratt nucl-th/0501003 (v1) 2005)
23P. Chung, SUNY Stony Brook
3D Analysis3D Analysis
How to calculate correlation function and Source function in any direction
0 1 2
0 1 2
0 1 2
0 1 2
( ) ( ) ( ) ( ) ...
( ) ( ) ( ) ( ) ...
( ) ( ) ( ) ( ) ...
( ) ( ) ( ) ( ) ...
x x xx
x x xx
y y yy
y y yy
C q C q C q C q
S r S r S r S r
C q C q C q C q
S r S r S r S r
0 1 2
0 1 2
0 1 2
0 1 2
( ) ( ) ( ) ( ) ...
( ) ( ) ( ) ( ) ...
( ) ( ) ( ) ( ) ...
( ) ( ) ( ) ( ) ...
x x xx
x x xx
y y yy
y y yy
C q C q C q C q
S r S r S r S r
C q C q C q C q
S r S r S r S r
Source function/Correlation function obtained via moment Source function/Correlation function obtained via moment summationsummation
24P. Chung, SUNY Stony Brook
PHENIX Preliminary
3D Source imaging3D Source imaging
Deformed source in pair cm frame:Deformed source in pair cm frame:
200 GeVnnAu Au s
x out
y side
z long
Origin of deformationKinematics ?
orTime effectTime effect
Instantaneous Freeze-out
• LCMS implies kinematics• PCMS implies time effect
25P. Chung, SUNY Stony Brook
PHENIX Preliminary
pp3D Source imaging3D Source imaging
Spherically symmetric source in pair cm. frame (PCMS)Spherically symmetric source in pair cm. frame (PCMS)
200 GeVnnAu Au s
x out
y side
z long
Isotropic emission in thepair frame
•
26P. Chung, SUNY Stony Brook
• Extensive study of two-pion source Extensive study of two-pion source images and moments in Au+Au collisions at RHICimages 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 pionsextension in the out direction for pions
• First explicit determination of a spherical proton sourceFirst explicit determination of a spherical proton source
Further Studies underway to quantify extent of long-range source!
27P. Chung, SUNY Stony Brook
28P. Chung, SUNY Stony Brook
Two source fit functionTwo source fit function
1 s
2 2 2
3 2 2 2
2 2 2
3 2 2 2
( ) =
1exp
22
1exp
22
s l l
s
s s ss s so s ls l o
l
l l ll l lo s ls l o
S r G G
x y z
R R RR R R
x y z
R R RR R R
1 s
2 2 2
3 2 2 2
2 2 2
3 2 2 2
( ) =
1exp
22
1exp
22
s l l
s
s s ss s so s ls l o
l
l l ll l lo s ls l o
S r G G
x y z
R R RR R R
x y z
R R RR R R
This is the single particle distribution
29P. Chung, SUNY Stony Brook
Simulation tests of the methodSimulation tests of the method
Very clear proof of principleVery clear proof of principle
ProcedureProcedure• Generate moments forsource.
• Carryout simultaneous Fit of all moments
input
output
30P. Chung, SUNY Stony Brook
Two source fit functionTwo source fit function
31 2 2 2
2 2 2 2
3 2 2 2
2 2 2 2
3 2 2 2
3 2 2 2 2 2 2
2
2 2
( ) = d
1exp
42
1exp
42
2
2
1exp
2
q
s
s s ss s so s ls l o
l
l l ll l lo s ls l o
s l
s l s l s ls s l l o o
s lo o
S r r S r r S r
x y z
R R RR R R
x y z
R R RR R R
R R R R R R
x y
R R
2 2
2 2 2 2s l s ls s l l
z
R R R R
31 2 2 2
2 2 2 2
3 2 2 2
2 2 2 2
3 2 2 2
3 2 2 2 2 2 2
2
2 2
( ) = d
1exp
42
1exp
42
2
2
1exp
2
q
s
s s ss s so s ls l o
l
l l ll l lo s ls l o
s l
s l s l s ls s l l o o
s lo o
S r r S r r S r
x y z
R R RR R R
x y z
R R RR R R
R R R R R R
x y
R R
2 2
2 2 2 2s l s ls s l l
z
R R R R
This is the two particle distribution