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
SQM07, Levoca, Slovakia, June 27 2006
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
SQM07, Levoca, Slovakia, June 27 2006
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
SQM07, Levoca, Slovakia, June 27 2006
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)
SQM07, Levoca, Slovakia, June 27 2006
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
SQM07, Levoca, Slovakia, June 27 2006
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
SQM07, Levoca, Slovakia, June 27 2006
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
SQM07, Levoca, Slovakia, June 27 2006
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 )
SQM07, Levoca, Slovakia, June 27 2006
9
Ellipsoid & 2-Gaussian Fits
2-Gaussian shape provides better representation of data
SQM07, Levoca, Slovakia, June 27 2006
10
2-Gaussian Fit:
All independent moments well reproduced by 2-Gaussian fit
SQM07, Levoca, Slovakia, June 27 2006
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)
SQM07, Levoca, Slovakia, June 27 2006
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
SQM07, Levoca, Slovakia, June 27 2006
13
Therminator model comparison
SQM07, Levoca, Slovakia, June 27 2006
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)