3d pion emission sources from au+au collisions @ rhic: probe of source breakup times

SQM07, Levoca, Slovakia, June 27 2006

1

3D Pion Emission Sources from Au+Au collisions @ RHIC: probe of source breakup times

Paul Chung

SUNY Stony Brook

PHENIX Collaboration


2

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


3

Outline

Probing origin of observed 1D long range pion structure: 3D shape analysis of emission source function

Overview of 3D source function shape analysis : Cartesian Spherical Harmonic decomposition & Imaging Technique

low pT (0.2<pT<0.36 GeV) pion moments in central (cen<20%) Au+Au events @ 200 AGeV

3D source function extraction: Moment Imaging & Fitting

Therminator event generator - Source breakup times extraction from 3D source function shape


4

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)


5

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

Freezeout occurs after last scatteringHence only Coulomb & BE effect included in kernel

Expansion in B-spline basis


6

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


7

Moments restoredfrom Imaging Moments decrease

with increasing order for x, y and z :

truncate at l=6 Restored moments

in good agreement with data moments :

Imaging under control


8

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

λ , Rx , Ry , Rz

2-Gaussian : S(x,y,z) = λ Gs . Gl

Gs - 3D Gaussian Rxs , Rys , Rzs

Gl - 3D Gaussian Rxl , Ryl , Rzl

fs = 1/( 1 + (r/r0)2 )

fl = (r/r0)2 /( 1 + (r/r0)2 )


9

Ellipsoid & 2-Gaussian Fits

2-Gaussian shape provides better representation of data


10

2-Gaussian Fit:

All independent moments well reproduced by 2-Gaussian fit


11

3D C(q) & S(r)

X-Y assymetry reflects non-zeroEmission duration

Long-range Exponential-likeTail in z direction:Signature of Blast-Wave dynamicsS.Pratt PRD 33, 5, 1314 (1986)


12

Therminator model Event Generator Kisiel, Broniowski, Florkiowski

Comput.Phys.Commun.174, 669 (2006) Thermal model with Bjorken longitudinal expansion Transverse Flow vt constant Includes all known resonance decays Emission from infinitely long cylinder transverse

radius ρmax=8.92 fm – controls sideward extent Single proper breakup time in fluid element rest

frame, tau=8.55 fm/c – controls longitudinal extent


13

Therminator model comparison


14

Conclusions

First 3D pion source imaging analysis at RHIC: pion moments in central 200 AGeV Au+Au events indicate:

Prominent non-Gaussian tails in source image in longitudinal and outward directions

3D source function well described by 2-Gaussian function in good agreement with source image

3D source image in agreement with Therminator Blast- Wave calculations with transverse radius=8.92 fm, tau=8.55 fm/c, spread(tau)=2 fm/c

Exponential tail in long direction: (1) verifies details of 3D dynamics (2) critical signature of blast-wave dynamics for longitudinal flow first proposed by Scott Pratt PRD 33, 5, 1314-1327 (1986)

3d pion emission sources from au+au collisions @ rhic: probe of source breakup times

Documents