Roy Lacey & Paul Chung Nuclear Chemistry, SUNY, Stony Brook

1

Roy Lacey & Paul Chung 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

2Roy Lacey, SUNY Stony Brook

initial state

pre-equilibrium

QGP andhydrodynamic expansion

hadronization

hadronic phaseand freeze-out

Conjecture of collisions at RHIC :MotivationMotivation

Courtesy S. BassCourtesy S. Bass

Increased System Entropy Increased System Entropy that survives that survives hadronizationhadronization

Expectation:Expectation:A strong first order phase transition leads to an emitting A strong first order phase transition leads to an emitting system characterized by a much larger space-time extent system characterized by a much larger space-time extent thanthan would be expected from a system which remained in would be expected from a system which remained in

the hadronic phase the hadronic phase

Guiding philosophy in first few years at RHIC =Guiding philosophy in first few years at RHIC = Puzzle ? Puzzle ?


What do we know now

What do we know now

??

Any Implicatio

ns for

Any Implicatio

ns for

HBT ?HBT ?


thermalization time (0 ~ 0.2 – 1 fm/c)

Bj~ 5 – 15 GeV/fm3

dy

dE

RT

Bj0

2

11

Extrapolation From EExtrapolation From ETT

DistributionsDistributions

What do we know ?What do we know ?

s/

P ²

FlowFlow



PHENIX Preliminary

PHENIX Preliminary

v2 scales with eccentricityand across system size

Strong Evidence for Thermalization Strong Evidence for Thermalization and hydro scalingand hydro scaling



Scaling breaks

Perfect fluid hydro Scaling holds up to ~ 1 GeV

Mesons scale together

Baryons scale together

Strong hydro scaling with hint of quark degrees of freedom

PHENIX preliminary data



Scaling works

Compatible with Valence Quark degrees of freedom

Scaling holds over the whole range of KET

PHENIX preliminary data


Oh yes - It is Comprehensive !



nucl-ex/0507004

What do we know ?What do we know ?What do we know ?What do we know ?

T. Renk, J. Ruppert hep-ph/0509036

Strong centrality dependent modification Strong centrality dependent modification of away-side jet in Au+Auof away-side jet in Au+Au

Away-side peak consistentAway-side peak consistentwith mach-cone scenariowith mach-cone scenario

nucl-th/0406018 Stoeckerhep-ph/0411315 Casalderrey-Solana, et al

other explanationsother explanations ! !

Implication for viscosityand sound speed !


View associated particles in frame View associated particles in frame with high pT direction as z-axiswith high pT direction as z-axis

12

High pT particleHigh pT particle

Associated pt

Associated pt

particles

particles

1312 13

Simulated ResultSimulated Result

A Small digressionA Small digression

Yes ! We have resultsYes ! We have results


Sound Speed Estimate

cs ~ 0.35 Soft EOS F. Karsch, hep-lat/0601013


Compatible with soft EOSCompatible with soft EOSSound speed is not zero during an extended hadronization period.Sound speed is not zero during an extended hadronization period.Space-time evolution more subtle ?Space-time evolution more subtle ?


Subtle sig

nals

Subtle sig

nals

require a paradigm

require a paradigm

shiftshift

Extract the full source functionExtract the full source function


Extraction of Source functionsExtraction of Source functions

Imaging & Fitting Moment Expansion


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.

Well established inversion procedureWell established inversion procedure


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


Experimental ResultsExperimental Results

Gaussian Source

Gaussian Source

functions d

o not provide

functions d

o not provide

good fits

good fits


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

1D Source imaging1D Source imaging

PHENIX Preliminary

200 GeVnnAu Au s

Source functions from Source functions from spheroid or spheroid or Gaussian + Exponential Gaussian + Exponential give good fit.give good fit.

Source function tail is notnot due to:• Kinematics• Resonance contributions


PHENIX Preliminary

Centrality dependence also incompatible with resonance decay

kinematics

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


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.

Full fledge simulation indicate similar conclusionFull fledge simulation indicate similar conclusion


Experimental ResultsExperimental Results

A hint of the shape of

A hint of the shape of

things to come

things to come


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)


Calculation of Correlation Moments:Calculation of Correlation Moments:

1 1

1

.... ........

0 0 2 2 2 2

2 2 4 4 4 4

4 4 2 2 2 2 2 2 2 2

2 2 2

( , ) ( ) ( )

to order 4

( , ) ( ) ( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( ) ( )

( ) ( ) 6 ( ) ( ) 6 ( ) ( )

6 ( )

l l

l

l l

x x y y

z z x x y y

z z x y x y x z x z

y z y z

C q C q

up

C q C q C q C q

C q C q C q

C q C q C q

C q

2

0 2 2 4 4 4

6

ii=1

( )

C , , , , ,

( , ) f ( )

x y x y z i

Th i

C C C C C C

C q C

Fitting with truncated expansion series !Fitting with truncated expansion series !

6 independent moments

(a)


A look at the basisA look at the basis

L=0

L=2

xxA yyA zzA

xx yy zzA A A S

S


StrategyStrategy

Get values of 0 2 2 4 4 4C , , , , ,x y x y zC C C C C

Such that ( , ) ( , )Th ExpC q C q

Fit ( , ) to ( , ) Th ExpC q C q with moments as fitting parameters.

2

exp22

22

2

2

6

ijj=1

( ) ( ) for each q.

( )

Minimize 0 i=1,..,6

1 2 0

B i=1,....,6

Exp

Th

i

ThTh

i

j i

C C

C

CC C

C

C D


StrategyStrategy

With

2

2

1

1 ;

1 ; C

for each q

ij i j i i

i Exp i Exp Exp

j ij j

B f f f f

D C f C

C B D


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


Results - momentsResults - moments

0 ( )invC C q

Very good agreement as it should



Exquisite/Robust ResultsExquisite/Robust Results

Sizeable signals observed

for l = 2



l= 4 momentsl= 4 moments

Exquisite/Robust ResultsExquisite/Robust Results


• 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

Long-range source not due to Long-range source not due to kinematics or resonanceskinematics or resonances

Further Studies underway to quantify A variety of other source functions!

Much more to come !Much more to come !



Source functions from spheroid and Gaussian + Exponential are in Source functions from spheroid and Gaussian + Exponential are in excellent agreement excellent agreement need 3D info need 3D info

Comparison of Source FunctionsComparison of Source FunctionsComparison of Source FunctionsComparison of Source Functions


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

•


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


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

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


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


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


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


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


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)


CutsCuts

Dphi (rad) Dz (cm)


CutsCuts

Dz (cm)

Dphi (rad)


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


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


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

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Roy Lacey & Paul Chung Nuclear Chemistry, SUNY, Stony Brook

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