paul chung ( for the phenix collaboration ) nuclear chemistry, suny, stony brook

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


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


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


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


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


CutsCuts

Dphi (rad) Dz (cm)


CutsCuts

Dz (cm)

Dphi (rad)


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.


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


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


Input source function recoveredInput source function recoveredProcedure is Robust !Procedure is Robust !

Quick Test with simulated sourceQuick Test with simulated source


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)


Evidence for long-range source at RHICEvidence for long-range source at RHIC

1D Source imaging1D Source imaging

PHENIX Preliminary

200 GeVnnAu Au s


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


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


PHENIX Preliminary

Centrality dependence incompatible with resonance decay


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


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


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.


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


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)


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


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


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

•


• 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!


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


l


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


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


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


l


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


l


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

paul chung ( for the phenix collaboration ) nuclear chemistry, suny, stony brook

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