two pion correlations at sps energies
DESCRIPTION
Two pion correlations at SPS energies. Dariusz Anto ń czyk Institut fuer Kernphysik Frankfurt. 11-14 .09.2008. Workshop on Particle Correlations and Femtoscopy 2008 Krakow, Poland. Outline. Overview of SPS runs Experimental setups - PowerPoint PPT PresentationTRANSCRIPT
Two pion correlations at SPS energies
Dariusz AntoDariusz AntońńczykczykInstitut fuer Kernphysik FrankfurtInstitut fuer Kernphysik Frankfurt
11-14.09.2008 Workshop on Particle Correlations and Femtoscopy 2008 Krakow, Poland
11-14.08.2008 Dariusz Antończyk WPCF 2008 Krakow, Poland
OutlineOutline
• Overview of SPS runsOverview of SPS runs• Experimental setups Experimental setups • Two particle analysis approachTwo particle analysis approach• Energy dependence of HBT radii Energy dependence of HBT radii • Reaction plane dependency analysis of HBT Reaction plane dependency analysis of HBT
radiiradii• Discussion and CommentsDiscussion and Comments
11-14.08.2008 Dariusz Antończyk WPCF 2008 Krakow, Poland
Historic overview of SPS Historic overview of SPS runs runs
• First beam more then 20 years agoFirst beam more then 20 years ago• In 1986, In 1986, 16O accelerated to 60 AGeVO accelerated to 60 AGeV
• Many experiments, covering broad spectrum of physics Many experiments, covering broad spectrum of physics topics, including HBT.topics, including HBT.• Recently, HBT analysis performed by CERES/NA45, NA49, NA57.Recently, HBT analysis performed by CERES/NA45, NA49, NA57.
1996 1998 2000 2002 2004 2006 2008199419921990
60/200A GeV
158A GeV
80A GeV
40A GeV
30A GeV
20A GeV
158A GeV114In207Pb
12O / 32S
NA45/CERES
NA49/SHINE
NA57
11-14.08.2008 Dariusz Antończyk WPCF 2008 Krakow, Poland
Experimental SetupsExperimental Setups
DetectorDetector SysteSystemm
Energy Energy AGeVAGeV
Acceptance Acceptance yy
Particle IDParticle ID
NA45/NA45/CERESCERES
Pb+Au 8.7, 12.3, 17.2 1.5-2.5 via dE/dx (TPC)
NA45/NA45/CERESCERES
Pb+Au 12.3, 17.2 1.5-2.5 via dE/dx (TPC)
NA49NA49 Pb+Pb 6.3, 7.6, 8.7, 12.5, 17.3
1.0-6.0 h-h-
NA57NA57 Pb+Pb 8.8 2.4-3.2 h-h-
s
Re-analysis of CERES HBT results for total available statistic and improved Re-analysis of CERES HBT results for total available statistic and improved momentum, centrality and reaction plane resolution. momentum, centrality and reaction plane resolution.
NA49 – PRC 77, 064908 (2008)NA49 – PRC 77, 064908 (2008)
NA57 – J. Phys. G: 34 (2007) 403-429NA57 – J. Phys. G: 34 (2007) 403-429
CERES – Nucl. Phys. A714 (2003) 124CERES – Nucl. Phys. A714 (2003) 124
11-14.08.2008 Dariusz Antończyk WPCF 2008 Krakow, Poland
Two particle analysis approach Two particle analysis approach (1)(1)
t pairsmixed even
pairsreal event
))n(pn(p
),pn(p),p(pC
21
21212
Correlation function
Analysis frame Bertsch-Pratt (qlong-qside-qout ) coordinate system in LCMS
mean transverse
pair momentum Pppk ,,
2
1
2
121
11-14.08.2008 Dariusz Antończyk WPCF 2008 Krakow, Poland
• Standard Gaussian fit used by all experiments
• Fitting algorithm• CERES and NA57 maximum likelihood assuming Poison
distribution
• NA49 minimization of 2
• No common method for removing Coulomb impact on HBT radii
Two particle analysis Two particle analysis approach (2)approach (2)
with i,j = out, side, long
ji
jiji qqR)qG(,
2,exp
11-14.08.2008 Dariusz Antończyk WPCF 2008 Krakow, Poland
Projection of correlation Projection of correlation functions CERES 158 AGeVfunctions CERES 158 AGeV
w. Coulomb
w/o Coulomb
11-14.08.2008 Dariusz Antończyk WPCF 2008 Krakow, Poland
HBT radii vs. kHBT radii vs. k┴┴
Centrality: CERES 0-5 % NA49 0-7.5%
Analysis of 80 GeV byAnalysis of 80 GeV byS.Schichmann (IKF)S.Schichmann (IKF)
11-14.08.2008 Dariusz Antończyk WPCF 2008 Krakow, Poland
HBT radii vs. kHBT radii vs. k┴┴
Centrality: CERES 0-5 % NA49 0-7.5%
11-14.08.2008 Dariusz Antończyk WPCF 2008 Krakow, Poland
HBT radii HBT radii @ @
40AGev40AGev
Centrality: CERES 0-5 % 5-10 % NA49 0-7.5 % NA57 0-11 %
J. Phys. G: 34 (2007) 403-429J. Phys. G: 34 (2007) 403-429
11-14.08.2008 Dariusz Antończyk WPCF 2008 Krakow, Poland
Beam energy systematics Beam energy systematics
PRL 90 (2003) 022301
Freeze-out volume
has a minimum at a beam energy of 10-40 AGeV
Nσ, particle multiplicity times mean hadron-hadron cross-section, has a similar beam energy
dependence
Vf / Nσ = λ f = 1 fmindependent of beam energy
Freeze-out when mean free path 1 fm
2232 sidelongf RRV
11-14.08.2008 Dariusz Antończyk WPCF 2008 Krakow, Poland
Mean free pathMean free path
• Extended with Extended with recentrecent• data from RHICdata from RHIC• data by NA49, NA35data by NA49, NA35
Including heavy and light systems Including heavy and light systems
Compilation by S.Schuchmann (IKF)Compilation by S.Schuchmann (IKF)
Agreement with Agreement with ffyy1fm for all 1fm for all energies and systemsenergies and systems
Universal pion freeze-out Universal pion freeze-out
conditioncondition
1
11-14.08.2008 Dariusz Antończyk WPCF 2008 Krakow, Poland
HBT vs. Reaction Plane HBT vs. Reaction Plane
• Reaction plane orientation from second Fourier harmonic
2
2
2
1
XY
arctanRP
i
it cospX 22
i
it sinpY 22
• recentering (Step 1)• dividing by width of
X, Y distribution, respectively (Step 2)
11-14.08.2008 Dariusz Antończyk WPCF 2008 Krakow, Poland
Resolution of the reaction Resolution of the reaction plane angleplane 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 strategyHBT vs. RP - analysis strategy
• 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 - RPRside
Rout
Rlong
Reaction plane determined via elliptic flow,
range between -/2 and /2
• 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
11-14.08.2008 Dariusz Antończyk WPCF 2008 Krakow, Poland
HBT vs. RP – CERES 158 AGev DataHBT vs. RP – CERES 158 AGev Datauncorrected for RP resolutionuncorrected for RP resolution
• Centrality 15-25%• HBT vs. RP parameterized
by
11-14.08.2008 Dariusz Antończyk WPCF 2008 Krakow, Poland
Azimuthal pion source Azimuthal pion source eccentricity vs. event eccentricity vs. event
centralitycentrality
From geometrical From geometrical expectationexpectation
• RRout,2out,222 suggest out-of-plane suggest out-of-plane
elongationelongation• RRside,2side,2
22 and R and Rlong,2long,222 unexpected unexpected
• RRout-side,2out-side,222 consistent with R consistent with Rout,2out,2
22
11-14.08.2008 Dariusz Antończyk WPCF 2008 Krakow, Poland
Excitation function of source Excitation function of source anisotropyanisotropy
• Common centralityCommon centrality• 15-25%15-25%
• Source eccentricitySource eccentricity ≈≈ RR22
side,2 side,2 / R/ R22side,0side,0
• At SPS At SPS = = 0.0430.043±0.023±0.023
11-14.08.2008 Dariusz Antończyk WPCF 2008 Krakow, Poland
Discussion and CommentsDiscussion and Comments
• Good agreement between new and old CERES results Good agreement between new and old CERES results as well NA49 for 158 and 80 AGeV, analysis for 40 as well NA49 for 158 and 80 AGeV, analysis for 40 AGeV in progressAGeV in progress
• azimuthal anisotropy of Razimuthal anisotropy of Routout as expected, however as expected, however
• no significant azimuthal anisotropy of the source no significant azimuthal anisotropy of the source observedobserved by R by Rsideside radii radii. Possible softening by bayron-. Possible softening by bayron-
meson mixed state. meson mixed state. • Possible source of RPossible source of Rlong long oscillation - initial collision oscillation - initial collision
conditioncondition• More azimuthal anisotropy studies are need (RHIC low More azimuthal anisotropy studies are need (RHIC low
energy runs)energy runs)
11-14.08.2008 Dariusz Antończyk WPCF 2008 Krakow, Poland
More from SPSMore from SPS
• Hydro calculation for SPS – works well for flow and pt-spectra Hydro calculation for SPS – works well for flow and pt-spectra but fails to reproduce HBT radii, see presentation form but fails to reproduce HBT radii, see presentation form D.Miśkowiec (WPCF 2007)D.Miśkowiec (WPCF 2007)
• 3D source imaging technique applied to SPS/NA49 data 3D source imaging technique applied to SPS/NA49 data arXiv:0807.4892arXiv:0807.4892
11-14.08.2008 Dariusz Antończyk WPCF 2008 Krakow, Poland
BackupBackup
11-14.08.2008 Dariusz Antończyk WPCF 2008 Krakow, Poland
s
CERES/NA45 SetupCERES/NA45 Setup
System Pb+Au @ 17.2, 12.3, 8.8 GeVTarget 13/8 gold disks (diameter 600 m, thickness 25 m)
SiDC1+2 Vertex reconstructionRICH1+2 Electron IDTPC Charge particle ID
Acceptance 2.03 < < 2.65Momentum resolution p/p = 2% 1%·p/GeVEnergy 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 AGeVData set - Pb+Au @ 158 AGeV
• 30 M events with centrality 7%• 2 M events with centrality 20 %• 500 k minimum bias events
Track cuts
Available statistics
• 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 cutsData set – Pair cuts
Different minimum opening cuts needed for the two topologies:
Sailor Cowboy
Sailor Cowboy
11-14.08.2008 Dariusz Antończyk WPCF 2008 Krakow, Poland
Coulomb interactionCoulomb interaction
Schrödinger equation describing particle in the Coulomb field is
wave function squared
Coulomb correlation function: square of the non-relativistic
wave function averaged over finite Gaussian source.
rkErkrrV coulpcoul
,,
2 12
2
q
m
k
krrikiFe
erk kri
coul
2
12
2
;1;1
2,
11-14.08.2008 Dariusz Antończyk WPCF 2008 Krakow, Poland
Previous HBT radii resultsPrevious HBT radii resultsanalysis 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 Effect of the Coulomb correctioncorrection
attenuated by λ full strength
11-14.08.2008 Dariusz Antończyk WPCF 2008 Krakow, Poland
Effect of the Coulomb Effect of the Coulomb correctioncorrection
attenuated by λ full strength
11-14.08.2008 Dariusz Antończyk WPCF 2008 Krakow, Poland
Correction for momentum Correction for momentum resolutionresolution
• 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 parametersExtracting source parameters
ffgeomside TmRR 21
/GEOM 0-2.5 %
/GEOM 15-25 %/GEOM ~ 17.5 %
System size, transverse flow velocity
f
ffflong
TmK
TmK
mT
R1
2
System lifetime
Chapman, Phys. Rev C52(1995) 2694
Sinyukov, Z. Phys. C39(1998) 69,Herrmann, Bertsh, Phys. Rev.
C51(1995)328
assuming Tassuming Tff=0.12 GeV=0.12 GeV
11-14.08.2008 Dariusz Antończyk WPCF 2008 Krakow, Poland
Pair acceptance Pair acceptance
- – standard HBT analysis
midrapidity = 2.91
11-14.08.2008 Dariusz Antończyk WPCF 2008 Krakow, Poland
Centrality dependence of Centrality dependence of f f , R, RGG and and ff
22/T/Tff
1.3 < Y<2.8 fix TTff=0.12 GeV=0.12 GeV
11-14.08.2008 Dariusz Antończyk WPCF 2008 Krakow, Poland
Fitting the HBT correlation Fitting the HBT correlation functionsfunctions
111 )-q(F))qG(()kλ(N)k,qC( coul
where
• N is a normalization and (k) is a correlation strength
• with i,j = out, side, long
• Fcoul(q) is a Coulomb correlation function
• Standard Gaussian fit used• Maximum likelihood assuming Poison distribution• Coulomb included in the fit, calculated for a
similar source size and attenuated by
ji
jiji qqR)qG(,
2,exp
11-14.08.2008 Dariusz Antończyk WPCF 2008 Krakow, Poland
HBT radii vs. kHBT radii vs. k┴ ┴ for 158 AGeVfor 158 AGeV
Comparison to CERES previous results
centrality 0-5%
Nucl. Phys. A714 (2003) 124
Comparison toNA49 preliminary results
centrality 0-7.5%
PRC 77, 064908 (2008)