QM06, Shanghai, China, Nov 19 2006

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Evidence of non-Gaussian tail in Pion Emission Source @ SPS:Sensitivity to source formation

& emission duration Paul Chung

SUNY Stony Brook

NA49 Collaboration

QM06, Shanghai, China, Nov 19 2006

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PHENIX nucl-ex/0605032

1D Pion-Pion Correl Func Au+Au sqrt(s)=200AGeV

Imaging source function vs 3D HBT source function

Discrepancy for r>20fm Corresponds to q<10MeV

30% more pions in tail above 3D HBT Gaussian source

20% in <r> compared to 3D HBT

Long range structure in pion source @ RHIC

QM06, Shanghai, China, Nov 19 2006

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Outline

Probing origin of observed long range pion structure: scan energy range available at SPS

NA49 @ SPS : 20, 40, 80, 160 AGeV Pb+Pb collisions Overview of 3D source function shape analysis :

Cartesian Spherical Harmonic decomposition & Imaging Technique

low pT (0<pT<70MeV) pion moments in 40 & 160GeV central (cen<7%) Pb+Pb evnts

3D source function extraction: Moment Imaging & Fitting @40&160GeV

Source formation & emission duration link to source function shape

QM06, Shanghai, China, Nov 19 2006

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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)

QM06, Shanghai, China, Nov 19 2006

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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)

X=out-direction

Y=side-direction

Z=long-direction

QM06, Shanghai, China, Nov 19 2006

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Correlation moments: 40AGeV

Choice of low pT pairs exclude effect of Lorentz γ boost

QM06, Shanghai, China, Nov 19 2006

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Correlation moments: 160AGeV

QM06, Shanghai, China, Nov 19 2006

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Imaging C0 : 40 AGeV & 160 AGeV

Difference at q < 10 MeV => Difference at r > 20 fm

QM06, Shanghai, China, Nov 19 2006

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Imaging Cx2 : 40 AGeV & 160 AGeV

Negative Moment in q => Positive Moment in r

QM06, Shanghai, China, Nov 19 2006

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Imaging Cy2 : 40 AGeV & 160 AGeV

Positive Moment in q => Negative Moment in r

QM06, Shanghai, China, Nov 19 2006

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Fitting functions: Ellipsoid & 2-Src model Ellipsoid : S(x,y,z) = λ G(x,y,z)

λ , Rx , Ry , Rz

2-Src model : S1 = λs gs + λl gl λs , Rxs , Rys , Rzs , λl , Rxl , Ryl , Rzl

S(x,y,z) = λs2 Gs + λl

2 Gl + 2 λs λl Gsl

QM06, Shanghai, China, Nov 19 2006

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40AGeV – Ellipsoid & 2-Src Fit

Pair Fraction (2-Src Fit) = 0.292 => 12% increase

Ellipsoid shape represents data poorly

QM06, Shanghai, China, Nov 19 2006

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160AGeV – Ellipsoid & 2-Src Fit

Pair Fraction (2-Src Fit) = 0.28 => 40% increase

Ellipsoid shape describes data poorly

QM06, Shanghai, China, Nov 19 2006

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3D Image & Fit S(r): 40 & 160 AGeV

Source Image & 2-Src Fit in good agreementProminent non-Gaussian tails in z-direction @ both energiesNon-Gaussian tail in x-direction @ 160GeV

rms Rx/Ry = 1.3±0.1 rms Rx/Ry = 1.2±0.1

rms Rz=11fm rms Rz=12fm

QM06, Shanghai, China, Nov 19 2006

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Interpretation of large space-time extents x-direction: Rx/Ry > 1 => Finite non-zero pion emission duration => Measure of pion source emission lifetime

z-direction: rms pair separation = 12fm @ 160AGeV, 11fm @ 40AGeV Lorentz-contracted nuclear diameter = 1.5fm @ 160AGeV, 3fm @ 40AGeV => rms pair separation due to created pion source = 10.5fm @ 160AGeV, 8fm @ 40AGeV => rms spatial extent of source emission points due to nuclear passage (vel=c) => Measure of formation time of emission points = 10 fm/c @ 160AGeV , 8fm/c @ 40AGeV

QM06, Shanghai, China, Nov 19 2006

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Conclusions

Low pT (0<pT<70MeV/c) pion moments in central 40 & 160 GeV Pb+Pb events : gradual evolution of deformations with beam energy (1) x-moment changes sign from 40 to 160 GeV (2) z-extension increases from 40 to 160GeV

Prominent non-Gaussian tails in source image along z @ 40 & 160GeV and along x @ 160GeV

Non-Gaussian tails in source images well described by a 2-Src fit model at 40 & 160 GeV

Interpretation of extracted space-time extents @ 160geV: (1) Rx/Ry > 1 due to finite non-zero emission duration (2) tail in z related to source formation duration time ~ 10fm/c

3D HBT technique gives Rx/Ry =1 at low pT due to Gaussian shape assumption inability to describe non-Gaussian tail of source function.