Roy Lacey ( for the PHENIX Collaboration ) Nuclear Chemistry Group Stony Brook University
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Transcript of Roy Lacey ( for the PHENIX Collaboration ) Nuclear Chemistry Group Stony Brook University
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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
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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 !
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QGP andhydrodynamic expansion
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 ?
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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?
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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 !
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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
l llR q drr K q r S r
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
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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
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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
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Good reproduction of actual source functionGood reproduction of actual source function
Test with simulated Gaussian source -- t =0Test with simulated Gaussian source -- t =0
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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
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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
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QMQMQMQM
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• 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
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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
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ε scaling validated
Known KnownsKnown KnownsKnown KnownsKnown Knowns
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
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KET scaling validated
PHENIX preliminary
21
2Therm colKE KE KE m u
PP
Known KnownsKnown KnownsKnown KnownsKnown Knowns
Mesons
Baryons
Quark Degrees of Freedom EvidentQuark Degrees of Freedom Evident
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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
Known KnownsKnown KnownsKnown KnownsKnown Knowns
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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
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Test with simulated Gaussian source -- t =5Test with simulated Gaussian source -- t =5
Simultaneous fit not very goodSimultaneous fit not very good
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Source function from ellipsoid fit misses the markSource function from ellipsoid fit misses the mark
Test with simulated Gaussian source -- t =5Test with simulated Gaussian source -- t =5
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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
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Good reproduction of actual source functionGood reproduction of actual source function
Test with simulated Gaussian source -- t =0Test with simulated Gaussian source -- t =0
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Test with simulated Gaussian source -- t =5Test with simulated Gaussian source -- t =5
Simultaneous with hump function – much betterSimultaneous with hump function – much better
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Hump function and imaging compare well to actual sourceHump function and imaging compare well to actual source
Test with simulated Gaussian source -- t =5Test with simulated Gaussian source -- t =5
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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)
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initial state
pre-equilibrium
QGP andhydrodynamic expansion
hadronization
hadronic phaseand freeze-out
Conjecture of heavy ion collision
Femtoscopy PrologueFemtoscopy Prologue
Courtesy S. BassCourtesy S. Bass
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
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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 ?
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initial state
pre-equilibrium
QGP andhydrodynamic expansion
hadronization
hadronic phaseand freeze-out
A Known Known;A Known Known;
Courtesy S. BassCourtesy S. Bass
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
QGP andhydrodynamic expansion
hadronization
hadronic phaseand freeze-out
30Roy Lacey, Stony Brook, Quark Matter 2008, Jaipur, India
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,
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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 ?
A Cross over Strongly affects A Cross over Strongly affects the Space-time Dynamicsthe Space-time Dynamics
Rishke et al
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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 ?
A Cross over Strongly affects A Cross over Strongly affects the Space-time Dynamicsthe Space-time Dynamics
Rishke et al