1 roy lacey ( for the phenix collaboration ) nuclear chemistry group stony brook university phenix...

1

Roy Lacey (for the PHENIX Collaboration)Nuclear Chemistry Group

Stony Brook University

PHENIX Measurements of 3D Emission Source Functionsin Au+Au Collisions at NNs 200 GeV

2Roy Lacey, Stony Brook, Quark Matter 2008, Jaipur, India

There are known knowns. These are things we know that we know.

There are known unknowns. That is to say, there are things that we know we don't know.

But there are also unknown unknowns. There are things we don't know we don't know

Donald Rumsfeld


initial state

pre-equilibrium

QGP andhydrodynamic expansion

hadronization

hadronic phaseand freeze-out

A Known Known:A Known Known:

Courtesy S. BassCourtesy S. Bass

A Crossover transition to the A Crossover transition to the strongly coupled thermalized strongly coupled thermalized

QGP occurs at RHICQGP occurs at RHIC

2

1

) (pv

) (pv

T2

q2,

Tq4,

We hold these truths to be self evident !We hold these truths to be self evident !



hadronization

A Known A Known unknown:unknown:

The Role of FemtoscopyThe Role of Femtoscopy

Are source Imaging measurements Are source Imaging measurements consistent with the crossover consistent with the crossover

transition ?transition ?

A Cross over Strongly affects A Cross over Strongly affects the Space-time Dynamicsthe Space-time Dynamics

Experiment & theory indicate a crossover transitionExperiment & theory indicate a crossover transition

The space-time extent can The space-time extent can lend crucial insightslend crucial insights

Puzzle ?


Set Rx=Ry=Rz=4 fm, f/o=10 fm/c, T=175 MeV, f=0.56

Dave Brown Dave Brown WPCF - 2005WPCF - 2005

Source Imaging gives access to important space-time information Source Imaging gives access to important space-time information which is inaccessible via “traditional approach”which is inaccessible via “traditional approach”

Why source Imaging?Why source Imaging?


04 ( , ) ( )j i j j ij jj

R rK q r S r K S

Discretize IntegralDiscretize IntegralSource Imaging Methodology (1D)Source Imaging Methodology (1D)Source Imaging Methodology (1D)Source Imaging Methodology (1D)

20 ( )( ) ( ) 1 4 (1( , ) )R SKq C q drr q r r

Source functionSource function(Distribution of pair

separations)

Encodes FSIEncodes FSICorrelationCorrelation

functionfunction

Inversion of this integral equationInversion of this integral equation Source FunctionSource Function

1D Koonin Pratt Eqn.1D Koonin Pratt Eqn.

)/)(/(

/)(

2111

212

pp

ppq

ddNddN

dddNC

Brown &

Daniel

ewicz

PRC 57(98)2474

Direct Fit

Direct Fit

Vary S(rj) to minimize

Reliable measurement of the fullReliable measurement of the full1D Source Function ! 1D Source Function !


Source Imaging Methodology (3D)Source Imaging Methodology (3D)Source Imaging Methodology (3D)Source Imaging Methodology (3D)

20 (( ) ( ) 1 ) 1) (,4 ( )K q S rR q C q dr rr

3D Koonin Pratt Eqn.3D Koonin Pratt Eqn.

1 11

1 11

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

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

( ) ( ) (2)

( ) ( ) (3)

l ll

l ll

l lq

l

l lr

l

R q R q

S r S r

Expand R(q) and S(r) in Expand R(q) and S(r) in Cartesian Harmonic basisCartesian Harmonic basis

(Danielewicz and Pratt nucl-th/0501003)(Danielewicz and Pratt nucl-th/0501003)

1 1

2.... ....

( ) 4 ( , ) ( ) (4)l l

l llR q drr K q r S r

1 1

2.... ....

( ) 4 ( , ) ( ) (4)l l


1 1.... ....

2 1 !!( ) ( ) ( ) (4)

! 4l l

ql lq

dlR q R q

l

1 1.... ....

2 1 !!( ) ( ) ( ) (4)

! 4l l

ql lq

dlR q R q

l

)/)(/(

/)(

2111

212

pp

ppq

ddNddN

dddNC

Reliable measurement of the full Source Function in 3D ! Reliable measurement of the full Source Function in 3D !

Substitute (2) and (3) into (1)Substitute (2) and (3) into (1)

The 3D integral equation is reduced to a set of 1D relations for different l coefficients moments


How well does it work ?How well does it work ?

Proofing the Source Imaging TechniqueProofing the Source Imaging Technique

Generate Events• Phasemaker• AMPT• Therminator• etc

Correlation Function 3D C(q)

Moments

Moment Fitting

Imaging

Calculated Source Function

Compare

Extensive tests indicate that the method is robustExtensive tests indicate that the method is robust


Test with simulated Gaussian source -- t =0Test with simulated Gaussian source -- t =0

Very good simultaneous fit obtained as expectedVery good simultaneous fit obtained as expected


Good reproduction of actual source functionGood reproduction of actual source function



Correlation MomentsCorrelation Moments

1 1

1

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

( ) ( ) l l

l

l lr

l

S r S r

Robust Experimental Source Functions obtained from Robust Experimental Source Functions obtained from momentsmoments

PHENIX DataPHENIX DataPHENIX DataPHENIX Data

1 1.... ....

( ) ( ) ( ) 4l l

ql lq

dR q R q

1 1

1

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

( ) ( ) l l

l

l lq

l

R q R q

Contributions froml > 6 is negligible


Model ComparisonModel ComparisonModel ComparisonModel Comparison

Source Function Comparison to Models Give robust life time Source Function Comparison to Models Give robust life time estimates estimates Consistent with Crossover transition Consistent with Crossover transition

Therminator:A.Kisiel et al. Comput.Phys.Commun.174, 669 (2006)

Thermal model with Bjorken longitudinal expansion and transverse Flow

• Spectra & yields constrain thermal properties • Transverse radius ρmax : controls transverse extent• Breakup time in fluid element rest frame, : controls longitudinal extent• Emission duration : controls tails in long and out directions • a controls x-t correlations

LCM

~ 9

~ 2

~ 12

Outside-in burning

fm

fm

t fm

LCM

~ 9

~ 2

~ 12

Outside-in burning

fm

fm

t fm


QMQMQMQM


• Souce Imaging provides important access to S(r) Souce Imaging provides important access to S(r) • Extensive study of imaging technique carried outExtensive study of imaging technique carried out

• Used to extract the 3D pion emission source function, in the PCMS frame

• The source function has a much greater extent in the out (x) and long (z), than in the side (y) direction.

• Model comparisonModel comparison

Summary/ConclusionsSummary/Conclusions

LCM

~ 9

~ 2

~ 12

Outside-in burning

fm

fm

t fm

LCM

~ 9

~ 2

~ 12

Outside-in burning

fm

fm

t fm

Timescales consistent with a crossover transitionTimescales consistent with a crossover transition


Known KnownsKnown KnownsKnown KnownsKnown Knowns

S.L. Huang QM08 15

4,q T4,M

2 22,M T 2,q T

4,q T4,B

2 22,B T 2,q T

v (p )v (2p ) 1 1( )

v (2p ) 4 2 v (p )

v (p )v (3p ) 1 1( )

v (3p ) 3 3 v (p )

T

T

a

a

2

1

) (pv

) (pv

T2

q2,

Tq4,

1.8a

1. Dynamic recombination2. Partonic Thermalization!3. Strongly coupled QGP


ε scaling validated


pT (GeV/c)0 1 2 3 4 5

v 2(C

en

t, p

T)/

v 2(C

en

t)

0

1

2

3

4

5

00-05 05-10 10-20 20-30 30-4030-40 (PHENIX)

STAR DATA

J. Adams et al, Phys. Rev. C72, 014904 (2005)

x k


KET scaling validated

PHENIX preliminary

21

2Therm colKE KE KE m u

PP


Mesons

Baryons

Quark Degrees of Freedom EvidentQuark Degrees of Freedom Evident


vv22 for the for the φφ follows that of other mesons follows that of other mesons

Flow fully developed in the partonic phaseFlow fully developed in the partonic phase



A Phase with Quarks as dynamical degrees of freedom A Phase with Quarks as dynamical degrees of freedom Dominates the flow Dominates the flow

Known KnownsKnown Knowns

v2 for the heavy D meson follows v2 for the heavy D meson follows that of other mesonsthat of other mesons quark

ThadronT

quarkT

quarkhadronT

hadron

nKEKE

KEnvKEv

)()( 22



Simultaneous fit not very goodSimultaneous fit not very good


Source function from ellipsoid fit misses the markSource function from ellipsoid fit misses the mark




Very good simultaneous fit obtained as expectedVery good simultaneous fit obtained as expected


Good reproduction of actual source functionGood reproduction of actual source function




Simultaneous with hump function – much betterSimultaneous with hump function – much better


Hump function and imaging compare well to actual sourceHump function and imaging compare well to actual source



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


1 1

2.... ....

( ) 4 ( , ) ( ) (4)l l


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)


initial state

pre-equilibrium


hadronization


Conjecture of heavy ion collision

Femtoscopy PrologueFemtoscopy Prologue


Femtoscopy Signatures:Femtoscopy Signatures:

Cross-over transition: (Z. Fodor and S.D. Katz)(Rischke, Gyulassy)

Sharp 1st order QCD phase transition: (Pratt, Bertsch, Rischke, Gyulassy)

1out

side

R

R

2nd order QCD phase transition:(T. Csörgő , S. Hegyi, T. Novák, W.A. Zajc)

(Non Gaussian shape)

Supercooled QGP (scQGP) (T. Csörgő, L.P. Csernai)

~out sideR R

Femtoscopic signals are subtle and important for study of the QGPFemtoscopic signals are subtle and important for study of the QGP

expTOR

2

2expTS

2expTO2

222TO

2TO

2TS

2TS

2L

2L2

RR

RqRqRqexp1C


OutlineOutline

I. Femtoscopic Prologue Why source imaging !

II. Source function extraction Brief description of the technique

III. Proofing the technique Imaging known sources

IV. Results & Implications What do we learn ?


initial state

pre-equilibrium


hadronization


A Known Known;A Known Known;


Femtoscopy Signatures:Femtoscopy Signatures:

Femtoscopic signals are subtle and important for study of the QGPFemtoscopic signals are subtle and important for study of the QGP

initial state

pre-equilibrium


hadronization



initial state

pre-equilibrium


hadronization


A Known Known:A Known Known:


A Crossover transition to the A Crossover transition to the strongly coupled thermalized strongly coupled thermalized

QGP occurs at RHICQGP occurs at RHIC

2

1

) (pv

) (pv

T2

q2,

Tq4,


Experiment & theory indicate Experiment & theory indicate a crossover transitiona crossover transition

Detailed measurements of the Space-time Dynamics are requiredDetailed measurements of the Space-time Dynamics are required

Demise of the RHIC HBT Demise of the RHIC HBT PuzzlePuzzle

Puzzle ?


Rishke et al

1 roy lacey ( for the phenix collaboration ) nuclear chemistry group stony brook university phenix...

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