WPCF07, Sonoma, California, August 2 2007
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Observation of Extended Pion Sources in Relativistic Heavy Ion Collisions: extraction of source breakup time & emission duration
Paul Chung
SUNY Stony Brook
NA49 Collaboration
WPCF07, Sonoma, California, August 2 2007
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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
WPCF07, Sonoma, California, August 2 2007
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Outline
Probing origin of observed long range pion structure: scan energy range available at SPS
NA49 @ SPS : 30, 80, 158 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 158 AGeV central (cen<7%) Pb+Pb evnts
3D source function extraction: Moment Imaging & Fitting
Therminator model comparison - Source breakup time & emission duration extraction from 3D source function shape @ SPS & RHIC
WPCF07, Sonoma, California, August 2 2007
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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)
WPCF07, Sonoma, California, August 2 2007
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158 AGeV -Angle-averaged C(q) & S(r)
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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
WPCF07, Sonoma, California, August 2 2007
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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 - spherically symmetric Gaussian R0
Gl - 3D Gaussian Rxl , Ryl , Rzl
fs = 1/( 1 + (r/r0)2 )
fl = (r/r0)2 /( 1 + (r/r0)2 )
WPCF07, Sonoma, California, August 2 2007
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158AGeV – Ellipsoid & 2-Gaussian Fit
Pair Fraction (2-Gaus Fit) = 0.28 => 40% increase
Ellipsoid shape describes data poorly
WPCF07, Sonoma, California, August 2 2007
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Ellipsoid & 2-Gaus. fit for all moments
WPCF07, Sonoma, California, August 2 2007
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158 AGeV - 3D C(q) & S(r)
Non-Gaussian tails in xx-y assymetric indicates non-zero relative emissiontime in LCMS
Long-range exponential-likeTail in longitudinal direction
Signature of blast-wave dynamicsS.Pratt PRD 33, 5, 1314 (1986)
WPCF07, Sonoma, California, August 2 2007
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30 & 80 AGeV – 3D S(r)
Less prominent tails in z @ 30 and 80 AGeV3D source essentially Gaussian
WPCF07, Sonoma, California, August 2 2007
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Therminator model Event Generator A.Kisiel et al. 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 : controls sideward extent Proper breakup time in fluid element rest frame,
tau : controls longitudinal extent Modified by Kisiel to implement emission duration
Δtau : controls tails in long and out directions
WPCF07, Sonoma, California, August 2 2007
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Therminator model comparison
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Conclusions
First 3D source imaging analysis at SPS: Low pT (0<pT<70MeV/c) pion moments in central sqrt_s=17.3AGeV Pb+Pb events indicate:
Prominent non-Gaussian tails in source image in longitudinal and outward directions @ sqrt_s=17.3AGeV
Less prominent tails at lower beam energies 3D source function well described by 2-Gaussian function in good
agreement with source image 3D source image at sqrt_s=17.3AGeV in agreement with Therminator
Blast-Wave calculations with tau=7.3fm/c, Δtau=3.7fm/c 3D source image at sqrt_s=200AGeV gives tau=8.5fm/c, Δtau=2fm/c
Exponential tail in long direction:
(1) verification of details of 3D dynamics (2) critical signature of blast-wave dynamics for longitudinal flow Scott Pratt PRD 33, 5, 1314-1327 (1986)
