Transcript Slide 1

Two pion correlations at SPS energies
Dariusz Antończyk
Institut fuer Kernphysik Frankfurt
11-14.09.2008
Workshop on Particle Correlations and Femtoscopy 2008
Krakow, Poland
Outline
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Overview of SPS runs
Experimental setups
Two particle analysis approach
Energy dependence of HBT radii
Reaction plane dependency analysis of HBT radii
Discussion and Comments
11-14.08.2008
Dariusz Antończyk
WPCF 2008 Krakow, Poland
Historic overview of SPS runs
• First beam more then 20 years ago
• In 1986, 16O accelerated to 60 AGeV
• Many experiments, covering broad spectrum of physics
topics, including HBT.
• Recently, HBT analysis performed by CERES/NA45, NA49, NA57.
NA49/SHINE
114In
158A GeV
207Pb
20A GeV
30A GeV
NA45/CERES
40A GeV
NA57
80A GeV
158A GeV
12O
1990
11-14.08.2008
1992
1994
1996
1998
2000
Dariusz Antończyk
2002
2004
2006
/ 32S
60/200A GeV
2008
WPCF 2008 Krakow, Poland
Experimental Setups
Detector
System
Energy
s AGeV
Acceptance y
Particle ID
NA45/CERES
Pb+Au
8.7, 12.3, 17.2
1.5-2.5
via dE/dx (TPC)
NA45/CERES
Pb+Au
12.3, 17.2
1.5-2.5
via dE/dx (TPC)
NA49
Pb+Pb
6.3, 7.6, 8.7, 12.5,
17.3
1.0-6.0
h-h-
NA57
Pb+Pb
8.8
2.4-3.2
h- h-
CERES – Nucl. Phys. A714 (2003) 124
Re-analysis of CERES HBT results for total available statistic and improved
momentum, centrality and reaction plane resolution.
NA49 – PRC 77, 064908 (2008)
NA57 – J. Phys. G: 34 (2007) 403-429
11-14.08.2008
Dariusz Antończyk
WPCF 2008 Krakow, Poland
Two particle analysis approach (1)
Correlation function
Analysis frame
n(p1,p2 )
real event pairs
C2(p1,p2 ) 

n(p1 )n(p 2 ) mixed event pairs
Bertsch-Pratt (qlong-qside-qout ) coordinate system in LCMS
mean transverse
pair momentum


1 
1
k   p1,  p 2,   P
2
2
11-14.08.2008
Dariusz Antończyk
WPCF 2008 Krakow, Poland
Two particle analysis approach (2)
• Standard Gaussian fit used by all experiments



2
G(q)  exp   Ri , j qi q j 
 i, j

with i,j = out, side, long
• Fitting algorithm
• CERES and NA57 maximum likelihood assuming Poison distribution
• NA49 minimization of 2
• No common method for removing Coulomb impact on HBT radii
11-14.08.2008
Dariusz Antończyk
WPCF 2008 Krakow, Poland
Projection of correlation functions
CERES 158 AGeV
w/o Coulomb
w. Coulomb
11-14.08.2008
Dariusz Antończyk
WPCF 2008 Krakow, Poland
HBT radii vs. k┴
Centrality:
CERES 0-5 %
NA49
0-7.5%
Analysis of 80 GeV by
S.Schichmann (IKF)
11-14.08.2008
Dariusz Antończyk
WPCF 2008 Krakow, Poland
HBT radii vs. k┴
Centrality:
CERES 0-5 %
NA49
0-7.5%
11-14.08.2008
Dariusz Antończyk
WPCF 2008 Krakow, Poland
HBT radii
@
40AGev
Centrality:
CERES 0-5 %
5-10 %
NA49
0-7.5 %
NA57
0-11 %
J. Phys. G: 34 (2007) 403-429
11-14.08.2008
Dariusz Antończyk
WPCF 2008 Krakow, Poland
Beam energy systematics
PRL 90 (2003) 022301
Freeze-out volume
2
Vf  2 3 2 RlongRside
has a minimum at a beam energy of 10-40 AGeV
Nσ, particle multiplicity times mean hadronhadron cross-section, has a similar beam energy
dependence
Vf / Nσ = λ f = 1 fm
independent of beam energy
Freeze-out when mean free path  1 fm
11-14.08.2008
Dariusz Antończyk
WPCF 2008 Krakow, Poland
Mean free path
• Extended with recent
• data from RHIC
• data by NA49, NA35
Including heavy and light systems
Agreement with fy1fm for all
energies and systems
1
Universal pion freeze-out
condition
Compilation by S.Schuchmann (IKF)
11-14.08.2008
Dariusz Antończyk
WPCF 2008 Krakow, Poland
HBT vs. Reaction Plane
• Reaction plane orientation from
second Fourier harmonic
RP
 Y2 
1
 arctan 
2
 X2 
X 2   p t  cos2i 
i
Y2   p t  sin2i 
i
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Dariusz Antończyk
recentering (Step 1)
dividing by width of
X, Y distribution,
respectively (Step 2)
WPCF 2008 Krakow, Poland
Resolution of the reaction
plane angle
Obtained reaction plane resolution  31-38 (centrality dependence)
Ollitrault, arXiv:nucl-ex/9711003 (Met. 1)
Poskanzer , Voloshin, Phys. Rev. C58(1998)1671 (Met. 2)
11-14.08.2008
Dariusz Antończyk
WPCF 2008 Krakow, Poland
HBT vs. RP - analysis strategy
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HBT radii vs. reaction plane orientation probe spatial anisotropy at
freeze-out U.A.Wiedemann, PRC 57 (1998) 266
3-dimensional correlation functions calculated separately in 8 bins
of pair - RP
Assuming pure geometric effect
one should expect such
dependence of HBT radii
RP resolution influence on HBT
vs. RP results corrected based
on MC study
Rside
Rout
Rlong
Reaction plane determined via elliptic flow,
range between -/2 and /2
11-14.08.2008
Dariusz Antończyk
WPCF 2008 Krakow, Poland
HBT vs. RP – CERES 158 AGev Data
uncorrected for RP resolution
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11-14.08.2008
Dariusz Antończyk
Centrality 15-25%
HBT vs. RP parameterized by
WPCF 2008 Krakow, Poland
Azimuthal pion source eccentricity
vs. event centrality
From geometrical expectation
• Rout,22 suggest out-of-plane
elongation
• Rside,22 and Rlong,22 unexpected
• Rout-side,22 consistent with Rout,22
11-14.08.2008
Dariusz Antończyk
WPCF 2008 Krakow, Poland
Excitation function of source
anisotropy
• Common centrality
• 15-25%
• Source eccentricity
•  ≈ R2side,2 / R2side,0
• At SPS  = 0.043±0.023
11-14.08.2008
Dariusz Antończyk
WPCF 2008 Krakow, Poland
Discussion and Comments
• Good agreement between new and old CERES results
as well NA49 for 158 and 80 AGeV, analysis for 40
AGeV in progress
• azimuthal anisotropy of Rout as expected, however
• no significant azimuthal anisotropy of the source
observed by Rside radii. Possible softening by bayronmeson mixed state.
• Possible source of Rlong oscillation - initial collision
condition
• More azimuthal anisotropy studies are need (RHIC low
energy runs)
11-14.08.2008
Dariusz Antończyk
WPCF 2008 Krakow, Poland
More from SPS
• Hydro calculation for SPS – works well for flow and pt-spectra
but fails to reproduce HBT radii, see presentation form
D.Miśkowiec (WPCF 2007)
• 3D source imaging technique applied to SPS/NA49 data
arXiv:0807.4892
11-14.08.2008
Dariusz Antończyk
WPCF 2008 Krakow, Poland
Backup
11-14.08.2008
Dariusz Antończyk
WPCF 2008 Krakow, Poland
CERES/NA45 Setup
System
Pb+Au @ 17.2,
s  12.3, 8.8 GeV
Target
13/8 gold disks (diameter 600 m, thickness 25 m)
SiDC1+2 Vertex reconstruction
RICH1+2 Electron ID
TPC
Charge particle ID
Acceptance
2.03 <  < 2.65
Momentum resolution p/p = 2%  1%·p/GeV
Energy loss resolution (dE/dx)/(dE/dx)=10%
Radial drift field (1/r), azimuthal deflection
11-14.08.2008
Dariusz Antończyk
WPCF 2008 Krakow, Poland
Data set - Pb+Au @ 158 AGeV
Available statistics
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30 M events with centrality 7%
2 M events with centrality 20 %
500 k minimum bias events
Track cuts
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good fit quality from tracking
high number of fitted hits (long track)
matching between TPC and SD < 2 
partial PID via dE/dx vs. momentum
11-14.08.2008
Dariusz Antończyk
WPCF 2008 Krakow, Poland
Data set – Pair cuts
Sailor
Cowboy
Different minimum opening cuts
needed for the two topologies:
Sailor
11-14.08.2008
Dariusz Antończyk
Cowboy
WPCF 2008 Krakow, Poland
Coulomb interaction
Schrödinger equation describing
particle in the Coulomb field is
 
 
 
 
 2
  
 V r2  r1  coul k , r  E p coul k , r

 2

wave function squared
 coul
 
 
 
k,r
2
  2

2 i rk  
r  k  

 2
e
 F1  i ; 1; ik  r 


e 1
k



m 
q
Coulomb correlation function:
square of the non-relativistic
wave function averaged over
finite Gaussian source.
11-14.08.2008
Dariusz Antończyk
WPCF 2008 Krakow, Poland
Previous HBT radii results
analysis by Heinz Tilsner and Harald Appelshäuser
Nucl. Phys. A714 (2003) 124
11-14.08.2008
Dariusz Antończyk
WPCF 2008 Krakow, Poland
Effect of the Coulomb correction
attenuated by λ
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full strength
Dariusz Antończyk
WPCF 2008 Krakow, Poland
Effect of the Coulomb correction
attenuated by λ
11-14.08.2008
full strength
Dariusz Antończyk
WPCF 2008 Krakow, Poland
Correction for momentum resolution
• example: highest p bin
(the largest correction)
• determined by Monte Carlo
• lines: various attempts to
parameterized effect
• correction applied to the radii
obtained from the fit
11-14.08.2008
Dariusz Antończyk
WPCF 2008 Krakow, Poland
Extracting source parameters
System size, transverse flow velocity
R side  R geom
1  m  f2 Tf
Chapman, Phys. Rev C52(1995) 2694
/GEOM  0-2.5 %
System lifetime
R long   f
m
K 2   T 

Tf
f

m K  m 
1
Tf 
Sinyukov, Z. Phys. C39(1998) 69,
Herrmann, Bertsh, Phys. Rev. C51(1995)328
/GEOM  15-25 %
/GEOM ~ 17.5 %
11-14.08.2008
assuming Tf=0.12 GeV
Dariusz Antończyk
WPCF 2008 Krakow, Poland
Pair acceptance
- – standard HBT analysis
midrapidity = 2.91
11-14.08.2008
Dariusz Antończyk
WPCF 2008 Krakow, Poland
Centrality dependence of f , RG
and f2/Tf
1.3 < Y<2.8
11-14.08.2008
fix Tf=0.12 GeV
Dariusz Antończyk
WPCF 2008 Krakow, Poland
Fitting the HBT correlation
functions
• Standard Gaussian fit used
• Maximum likelihood assuming Poison distribution
• Coulomb included in the fit, calculated for a similar source
size and attenuated by 



 


C(q,k)  N  1  λ(k)  (1  G(q))  Fcoul(q)-1
where
• N is a normalization and (k) is a correlation strength



2
• G(q)  exp   Ri , j qi q j  with i,j = out, side, long
 i, j

• Fcoul(q) is a Coulomb correlation function
11-14.08.2008
Dariusz Antończyk
WPCF 2008 Krakow, Poland
HBT radii vs. k┴ for 158 AGeV
Comparison to
CERES previous results
centrality 0-5%
Nucl. Phys. A714 (2003) 124
Comparison to
NA49 preliminary results
centrality 0-7.5%
PRC 77, 064908 (2008)
11-14.08.2008
Dariusz Antończyk
WPCF 2008 Krakow, Poland