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Two pion correlations at SPS energies Dariusz Antończyk Institut fuer Kernphysik Frankfurt Workshop on Particle Correlations and Femtoscopy 2008 Krakow, Poland

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Dariusz Antończyk WPCF 2008 Krakow, Poland Outline Overview of SPS runsOverview of SPS runs Experimental setupsExperimental setups Two particle analysis approachTwo particle analysis approach Energy dependence of HBT radiiEnergy dependence of HBT radii Reaction plane dependency analysis of HBT radiiReaction plane dependency analysis of HBT radii Discussion and CommentsDiscussion and Comments

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Dariusz Antończyk WPCF 2008 Krakow, Poland Historic overview of SPS runs First beam more then 20 years agoFirst beam more then 20 years ago In 1986, O accelerated to 60 AGeVIn 1986, 16 O accelerated to 60 AGeV Many experiments, covering broad spectrum of physics topics, including HBT.Many experiments, covering broad spectrum of physics topics, including HBT. Recently, HBT analysis performed by CERES/NA45, NA49, NA57.Recently, HBT analysis performed by CERES/NA45, NA49, NA /200A GeV 158A GeV 80A GeV 40A GeV 30A GeV 20A GeV 158A GeV 114 In 207 Pb 12 O / 32 S NA45/CERES NA49/SHINE NA57

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Dariusz Antończyk WPCF 2008 Krakow, Poland Experimental Setups DetectorSystem Energy AGeV Acceptance y Particle ID NA45/CERESPb+Au8.7, 12.3, via dE/dx (TPC) NA45/CERESPb+Au12.3, via dE/dx (TPC) NA49Pb+Pb6.3, 7.6, 8.7, 12.5, h-h-h-h- NA57Pb+Pb h-h-h-h- Re-analysis of CERES HBT results for total available statistic and improved momentum, centrality and reaction plane resolution. NA49 – PRC 77, (2008) NA57 – J. Phys. G: 34 (2007) CERES – Nucl. Phys. A714 (2003) 124

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Dariusz Antończyk WPCF 2008 Krakow, Poland Two particle analysis approach (1) Correlation function Analysis frame Bertsch-Pratt (q long -q side -q out ) coordinate system in LCMS mean transverse pair momentum

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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 approach (2) with i,j = out, side, long

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Dariusz Antończyk WPCF 2008 Krakow, Poland Projection of correlation functions CERES 158 AGeV w. Coulomb w/o Coulomb

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Dariusz Antończyk WPCF 2008 Krakow, Poland HBT radii vs. k HBT radii vs. k Centrality: CERES 0-5 % NA % Analysis of 80 GeV by S.Schichmann (IKF)

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Dariusz Antończyk WPCF 2008 Krakow, Poland HBT radii vs. k HBT radii vs. k Centrality: CERES 0-5 % NA %

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Dariusz Antończyk WPCF 2008 Krakow, Poland HBT 40AGev Centrality: CERES 0-5 % 5-10 % NA % NA % J. Phys. G: 34 (2007)

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Dariusz Antończyk WPCF 2008 Krakow, Poland Beam energy systematics PRL 90 (2003) Freeze-out volume has a minimum at a beam energy of AGeV Nσ, particle multiplicity times mean hadron- hadron cross-section, has a similar beam energy dependence V f / Nσ = λ f = 1 fm independent of beam energy Freeze-out when mean free path 1 fm

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Dariusz Antończyk WPCF 2008 Krakow, Poland Mean free path Extended with recentExtended with recent data from RHICdata from RHIC data by NA49, NA35data by NA49, NA35 Including heavy and light systems Compilation by S.Schuchmann (IKF) Agreement with f y 1fm for all energies and systems Universal pion freeze-out condition 1

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Dariusz Antończyk WPCF 2008 Krakow, Poland HBT vs. Reaction Plane Reaction plane orientation from second Fourier harmonic recentering (Step 1) dividing by width of X, Y distribution, respectively (Step 2)

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Dariusz Antończyk WPCF 2008 Krakow, Poland Resolution of the reaction plane angle Obtained reaction plane resolution (centrality dependence) Ollitrault, arXiv:nucl-ex/ (Met. 1) Poskanzer, Voloshin, Phys. Rev. C58(1998)1671 (Met. 2)

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Dariusz Antończyk WPCF 2008 Krakow, Poland HBT vs. RP - analysis strategy HBT radii vs. reaction plane orientation probe spatial anisotropy at freeze-out U.A.Wiedemann, PRC 57 (1998) dimensional correlation functions calculated separately in 8 bins of pair - RP R side R out R long 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

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Dariusz Antończyk WPCF 2008 Krakow, Poland HBT vs. RP – CERES 158 AGev Data uncorrected for RP resolution Centrality 15-25% HBT vs. RP parameterized by

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Dariusz Antończyk WPCF 2008 Krakow, Poland Azimuthal pion source eccentricity vs. event centrality From geometrical expectation R out,2 2 suggest out-of-planeR out,2 2 suggest out-of-plane elongation elongation R side,2 2 and R long,2 2 unexpectedR side,2 2 and R long,2 2 unexpected R out-side,2 2 consistent with R out,2 2R out-side,2 2 consistent with R out,2 2

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Dariusz Antończyk WPCF 2008 Krakow, Poland Excitation function of source anisotropy Common centralityCommon centrality 15-25%15-25% Source eccentricitySource eccentricity R 2 side,2 / R 2 side,0 R 2 side,2 / R 2 side,0 At SPS = 0.043±0.023At SPS = 0.043±0.023

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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 progressGood agreement between new and old CERES results as well NA49 for 158 and 80 AGeV, analysis for 40 AGeV in progress azimuthal anisotropy of R out as expected, howeverazimuthal anisotropy of R out as expected, however no significant azimuthal anisotropy of the source observed by R side radii. Possible softening by bayron- meson mixed state.no significant azimuthal anisotropy of the source observed by R side radii. Possible softening by bayron- meson mixed state. Possible source of R long oscillation - initial collision conditionPossible source of R long oscillation - initial collision condition More azimuthal anisotropy studies are need (RHIC low energy runs)More azimuthal anisotropy studies are need (RHIC low energy runs)

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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)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: D source imaging technique applied to SPS/NA49 data arXiv:

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Dariusz Antończyk WPCF 2008 Krakow, Poland Backup

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Dariusz Antończyk WPCF 2008 Krakow, Poland CERES/NA45 Setup System 17.2, 12.3, 8.8 GeV T arget 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

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Dariusz Antończyk WPCF 2008 Krakow, Poland Data set 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

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Dariusz Antończyk WPCF 2008 Krakow, Poland Data set – Pair cuts Different minimum opening cuts needed for the two topologies: Sailor Cowboy

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Dariusz Antończyk WPCF 2008 Krakow, Poland Coulomb 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.

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Dariusz Antończyk WPCF 2008 Krakow, Poland Previous HBT radii results Previous HBT radii results analysis by Heinz Tilsner and Harald Appelshäuser Nucl. Phys. A714 (2003) 124

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Dariusz Antończyk WPCF 2008 Krakow, Poland Effect of the Coulomb correction attenuated by λ full strength

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Dariusz Antończyk WPCF 2008 Krakow, Poland Effect of the Coulomb correction attenuated by λ full strength

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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

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Dariusz Antończyk WPCF 2008 Krakow, Poland Extracting source parameters / GEOM % / GEOM % / GEOM ~ 17.5 % System size, transverse flow velocity System lifetime Chapman, Phys. Rev C52(1995) 2694 Sinyukov, Z. Phys. C39(1998) 69, Herrmann, Bertsh, Phys. Rev. C51(1995)328 assuming T f =0.12 GeV

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Dariusz Antończyk WPCF 2008 Krakow, Poland Pair acceptance - – standard HBT analysis midrapidity = 2.91

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Dariusz Antończyk WPCF 2008 Krakow, Poland Centrality dependence of f, R G and f 2 /T f T f =0.12 GeV 1.3 < Y <2.8 fix T f =0.12 GeV

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Dariusz Antończyk WPCF 2008 Krakow, Poland Fitting the HBT correlation functions where N is a normalization and (k) is a correlation strength with i,j = out, side, long F coul (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

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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, (2008)

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