Transcript Pion Source Imaging update: Systematic error determination

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
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Long range structure in pion source @ RHIC
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PHENIX nucl-ex/0605032
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1D Pion-Pion Correl Func
Au+Au sqrt(s)=200AGeV
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Imaging source function vs 3D
HBT source function
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Discrepancy for r>20fm
Corresponds to q<10MeV
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30% more pions in tail above
3D HBT Gaussian source
20% in <r> compared to 3D
HBT
SQM07, Levoca, Slovakia, June 27 2006
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Outline
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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
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Technique Devised by:
D. Brown, P. Danielewicz,
PLB 398:252 (1997).
PRC 57:2474 (1998).
Emitting source
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No Shape assumption for S(r)
Inversion of Linear integral
equation to obtain source function
1D Koonin Pratt Eqn.
C (q )  1  4  drr 2 K 0 (q, r )S (r )
Encodes FSI
Correlation
function
Source
function
(Distribution of pair
separations)
Inversion of this integral equation
== Source Function
Extracted S(r) in pair CM frame
Hence Model-independent i.e Kernel independent of freeze-out conditions
SQM07, Levoca, Slovakia, June 27 2006
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Imaging
Inversion procedure
C (q )  4  drr 2 K (q, r )S (r )
S ( r )   S j  B j (r )
Expansion in B-spline basis
j
CiTh (q)   Kij  S j
j
Kij   dr  K (q, r ) B j (r )
 Expt
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 Ci (q)   Kij  S j 
j

2  
 2Ci (q) Expt
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Freezeout occurs after last scattering
Hence only Coulomb & BE effect included in kernel
SQM07, Levoca, Slovakia, June 27 2006
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3D Analysis
Basis of Analysis
(Danielewicz and Pratt nucl-th/0501003 (v1) 2005)
Expansion of R(q) and S(r) in Cartesian Harmonic basis
R(q )  
l
S (r )  
l

 
1 ....

 
Rl 1 ....l  q  l
1
Sl 1 ....l  r  l
1
1 .... l
Y=side-direction
Z=long-direction
(2)
R(q )  C (q )  1  4  dr 3 K ( q , r )S ( r ) (3)
Plug in (1) and (2) into (3)
(2)
.... l
( r )
X=out-direction
(1)
l
3D Koonin
Pratt
(1)
.... l
( q )
l
R1 ....l
Rl 1 ....l (q)  4  drr 2 Kl (q, r ) Sl
2l  1!!

(q ) 
1

d q
l
.... l
SQM07, Levoca, Slovakia, June 27 2006
(r )
(4)
(q ) R(q ) (4)
l!
4
2l  1!! d r l

l
S1 ....l (r ) 
 .... ( r ) S (r )

1
l
l!
4
1
.... l
(5)
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Moments restored
from Imaging
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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
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Fitting functions: Ellipsoid & 2-Gaussian
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Ellipsoid : S(x,y,z) = λ G(x,y,z)
λ , Rx , Ry , R z
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 )
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Ellipsoid & 2-Gaussian Fits
2-Gaussian shape provides better representation of data
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2-Gaussian Fit:
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All independent
moments well
reproduced by
2-Gaussian fit
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3D C(q) & S(r)
X-Y assymetry reflects non-zero
Emission duration
Long-range Exponential-like
Tail in z direction:
Signature of Blast-Wave dynamics
S.Pratt PRD 33, 5, 1314 (1986)
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Therminator model Event Generator
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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
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Therminator model comparison
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Conclusions
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First 3D pion source imaging analysis at RHIC: pion moments in
central 200 AGeV Au+Au events indicate:
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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 BlastWave 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)
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