November 29, 2010Zimanyi Winter School 2010, Budapest11 3D Pion & Kaon Source Imaging from 200 AGeV Au+Au collisions Paul Chung (STAR Collaboration) NPI

November 29, 2010Zimanyi Winter School 2010,

Budapest 11

3D Pion & Kaon Source Imaging from 200 AGeV Au+Au collisions

Paul Chung (STAR Collaboration)

NPI ASCR Prague

November 29, 2010

Zimanyi Winter School 2010, Budapest 2

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?

PHENIX 1D Source Imaging Phys.Rev.Lett.98:132301,2007


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Phys.Rev.Lett.103:142301,2009


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Outline

Run 4 Au+Au @ 200AGeV: 3D pion correlation functions Overview of 3D source shape analysis : Cartesian

Spherical Harmonic decomposition & Imaging Technique Correlation moments for low kT (0.25<kT<0.35 GeV)

pion pairs from peripheral collisions (50<cen<80%). 3D source function extraction: Moment Imaging & Fitting Therminator comparison for extracting pion source

lifetime & pion emission duration 3D Kaon correlation functions from Run 4 & Run 7

central Au+Au collisions Kaon source extraction & Therminator comparison


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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.

Extracted S(r) in pair CM frameHence Model-independent i.e Kernel independent of freeze-out conditions

No Shape assumption for S(r)

1D Imaging Formulation 1D Imaging Formulation


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Imaging : Inversion procedureImaging : Inversion procedure

2( ) 4 ( , ) ( )C q drr K q r S r

( ) ( )j jj

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

Freeze-out occurs after last scattering Hence only Coulomb & BE effect included in kernel

Expansion in B-spline basis


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1D Imaging1D Imaging

ST

STAR PRELIMINARY STAR PRELIMINARY


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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

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

Invert (1)

Invert (2)

Expansion of R(q) and S(r) in Cartesian Harmonic basisExpansion of R(q) and S(r) in Cartesian Harmonic basis[Danielewicz and Pratt nucl-th/0501003 (v1)][Danielewicz and Pratt nucl-th/0501003 (v1)]

x=out-direction

y=side-direction

z=long-direction

3D Analysis Basics


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Monte Carlo Events:Phasemaker, Therminator

CRAB 3D C(q)

Correlation Moments

Source FITTING

Source IMAGING

SourceFunction

Model calculation from space points

SIMULATION PROCEDURE


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Fit Functions

Ellipsoid Fit (3D Gaussian) :

G = lambda exp[-{ (x/2rx)2 + (y/2ry)2 + (z/2rz)2 }]

Hump Fit :

H = exp[- Fs { (x/2rxs)2 + (y/2rys)2 + (z/2rzs)2 }] x

exp[- Fl { (x/2rxl)2 + (y/2ryl)2 + (z/2rzl)2 }]

Fs = 1/[1 + (r/r0)2 ]

Fl = 1 - Fs


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Simulation – Therminator


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Comparison- C0 moment vs 1D C(q)

STAR PRELIM.STAR PRELIMINARY

L=2 & 4 moments


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L=6 moments

STAR PRELIMINARY


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Imaging C2x2 & C2

y2



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3D Imaging – S(r) & restored C(q)

STAR PRELIMINARY

STAR PRELIMINARY


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Ellipsoid vs Hump Fit : l=0 & 2 mom.

STAR PRELIMINARY


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Ellipsoid vs Hump Fit : l=4 moments

STAR PRELIMINARYSTAR PRELIMINARY


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Ellipsoid vs Hump Fit : l=6 moments

STAR PRELIMINARY


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Image vs Ellipsoid & Hump S(r)



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3D C(q) : Ellipsoid vs Hump Fit



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Therminator BW: Source lifetime & Pion emission duration extractionTherminator (Kisiel et al PRC

73, 064902 2006) : Production of particles from thermalized and expanding system with

Boost invariance & cylindrical symmetry

BW mode: Freeze-out hypersurface defined by constant laboratory time independent of transverse radius


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STAR vs PHENIX comparison


Source extraction – central collisions PRL100, 232301 (2008) (PHENIX) Transverse dimension = 8.9fm

Source lifetime = 8.5fm/c

Emission duration = 2fm/c

Source parameters larger for central collisions than for peripheral collisions

Full centrality dependence extraction underway


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Extracted Pion Source Images from semi-central & peripheral collisions


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Run 7 & Run 4 KK : C0 vs 1D C(qinv)



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Run 7 + Run 4 KK : C0 vs 1D C(qinv)

STAR PRELIMINARY

Run 7 + Run 4 KK : l=2 & l=4 moments


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KK: Ellipsoid Fit


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STAR PRELIMINARYSTAR PRELIMINARY

THERMINATOR Model comparison


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Conclusion

Correlation moments for low kT pion pairs from Run4 peripheral Au+Au collisions well described by the Hump Fit function.

For low kT pion pairs from peripheral collisions, inferred pion source lifetime ~ 3.5 fm/c & pion emission duration ~ 1.5 fm/c < central collisions.

Extracted Kaon source function essentially Gaussian – No significant non-Gaussian tail observed.

Kaon source dimension & lifetime comparable to pion source; Kaon emission instantaneous (Therminator)

Documents

November 29, 2010Zimanyi Winter School 2010, Budapest11 3D Pion & Kaon Source Imaging from 200 AGeV Au+Au collisions Paul Chung (STAR Collaboration) NPI