Three-dimensional Kaon Source Extraction from STAR Experiment at RHIC

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Michal Šumbera NPI ASCR Prague (for the STAR Collaboration). Three-dimensional Kaon Source Extraction from STAR Experiment at RHIC . 1. Outline. Why and how to extract the source shape? 1D source extraction: previous and recent results Kaon data analysis details
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M.Š. EPS-HEP 2011, GrenobleMichal ŠumberaNPI ASCR Prague(for the STAR Collaboration)Three-dimensional Kaon Source Extraction from STAR Experiment at RHIC 1OutlineWhy and how to extract the source shape?1D source extraction: previous and recent results Kaon data analysis details3D source shape analysis: Cartesian surface – spherical harmonic decomposition technique3D source function extraction: correlation moments fitting Comparison to thermal blast wave modelConclusionsM.Š. EPS-HEP 2011, Grenoble2M.Š. EPS-HEP 2011, GrenobleSource imagingTechnique devised byD. Brown and P. DanielewiczPLB398:252, 1997PRC57:2474, 1998Inversion of linear integral equation to obtain source function1DKoonin-Pratt equationEncodes FSISource function(Distribution of pair separations in pair rest frame)Emitting sourceCorrelationfunction
  • Kernel is independent
  • of freeze-out conditions
  • Model-independent analysis of emission shape
  • (goes beyond Gaussian shape assumption)
  • 3M.Š. EPS-HEP 2011, GrenobleInversion procedureFreeze-out occurs after last scattering.  Only Coulomb & quantum statistics effects included the kernel.Expansion into B-spline basis4M.Š. EPS-HEP 2011, GrenoblePrevious 1D source imaging results PHENIX, PRL 98:132301,2007PHENIX, PRL 103:142301,2009Observed long non-gaussian tails attributed to non-zero particle emision duration and contribution of long-lived resonances M.Š. EPS-HEP 2011, GrenobleKaon data analysis20% most central Au+Au @ √sNN=200 GeVRun 4: 4.6 Mevts, Run 7: 16 MevtsParticle ID selection via TPC dE/dx: NSigmaKaon<2.0 && NSigmaPion>3.0 && NSigmaElectron>2.0TPCdE/dx vs rigidity: before after PID cuts |y| < 0.5 & 0.2 < pT < 0.4 GeV/cM.Š. EPS-HEP 2011, GrenobleSTAR kaon 1D source shape result 34M+83M=117M K+K+ & K-K- pairsSTAR data arewell described by Gaussian,contrary toPHENIX no non-gaussiantails are observed.May be due to a differentkT-range:STAR bin is4x narrower.PHENIX, PRL 103:142301,2009STAR preliminarySTAR preliminaryM.Š. EPS-HEP 2011, Grenoble3D source shape analysisDanielewicz and Pratt, Phys.Lett. B618:60, 2005Expansion of R(q) and S(r) in Cartesian Harmonic basisai = x, y or zx = out-directiony = side-directionz = long-direction (3)3D Koonin-Pratt:Plug (1) and (2) into (3)Invert (1)Invert (2)M.Š. EPS-HEP 2011, GrenobleC0(qinv) vsC(qinv): comparisonK+K+ & K-K-l=0 momentC0(qinv)C(qinv)STAR preliminaryM.Š. EPS-HEP 2011, GrenobleExtracting 3D source function
  • Fit to the 3D correlation function with a trial functional form for S(r).
  • Trial function: 4-parameter ellipsoid (3D Gaussian)
  • Since the 3D correlation function has been decomposed into its independent moments, this is equivalent to a simultaneous fit of 6 independent moments with the trial functional form.
  • M.Š. EPS-HEP 2011, GrenobleIndependent correlation moments Rlα1…αl, 0≤l≤4Extracted 3D Gaussianfit parameters:λ = 0.48 ± 0.01rx = (4.8 ± 0.1) fmry = (4.3 ± 0.1) fmrz = (4.7 ± 0.1) fmSTAR preliminaryM.Š. EPS-HEP 2011, GrenobleKaon correlation function profilesC(qx)  C(qx,0,0)C(qy)  C(0,qy,0)C(qz)  C(0,0,qz)STAR preliminaryM.Š. EPS-HEP 2011, GrenobleKaon vs. pion 3D source shapeP. Chung, STAR, arXiv:1012.5674 [nucl-ex] PRL 98:13230PRL 98:13230STAR preliminarySTAR preliminaryPion and kaon 3D source shapes are very different: Is this due to the different dynamics? Very good agreement on 3D pion source shape between PHENIX and STARM.Š. EPS-HEP 2011, GrenobleComparison to thermal BW model Therminator(A. Kisielet al., Phys. Rev. C 73:064902 2006) basic ingredients: Longitudinal boost invariance. Blast-wave expansion with transverse velocity profile semi-linear in transverse radius ρ: vr(ρ)=(ρ/ρmax)/(ρ/ρmax+vt).Value of vt =0.445 comesfrom the BW fits to particle spectra from Au+Au @ 200GeV: STAR, PRC 79:034909, 2009.Thermal emission takes place at proper time t, from a cylinder of infinite longitudinal size and finite transverse dimension ρmax.Freeze-out occurs at t = t0 +aρ. Particles which are emitted at (z, ρ) have LAB emission time t2 = (t0 +aρ)2+z2.Emission duration is included via Δt.STAR preliminaryM.Š. EPS-HEP 2011, GrenobleConclusions
  • First model-independent extraction of kaon 3D source shape.
  • Source function of mid-rapidity, low-momentum kaons from 20% most central Au+Au collisions at √sNN=200 GeV is Gaussian – no significant non-Gaussian tail is observed.
  • Comparison with Therminator model indicates kaon emission from a fireball with transverse dimension and lifetime which are consistent with values from two-pioninterferometry.
  • In contrast to pions, kaons are emitted instantaneously in the source element rest frame from a freeze-out hypersurface with no r−t correlation.
  • Kaons and pions may be subject to different dynamics owing to their emission over different timescales.
  • M.Š. EPS-HEP 2011, GrenobleBackup slidesM.Š. EPS-HEP 2011, GrenobleKaon vs. pion 3D source shapeP. Chung, STAR, arXiv:1012.5674 [nucl-ex] PRL 98:13230PRL 98:13230STAR preliminarySTAR preliminaryPion and kaon 3D source shapes are very different: Is this due to the different dynamics? Very good agreement on 3D pion source shape between PHENIX and STARM.Š. EPS-HEP 2011, GrenobleCartesian harmonics basis
  • Based on the products of unit vector components, nα1 nα2 ,…, nαℓ .Unlike the spherical harmonics they are real.
  • Due to the normalization identity n2x + n2y + n2z = 1, at a given ℓ ≥ 2, the different component products are not linearly independent as functions of spherical angle.
  • At a given ℓ, the products are spanned by spherical harmonics of rank ℓ′ ≤ ℓ, with ℓ′ of the same evenness as ℓ.
  • M.Š. EPS-HEP 2011, GrenobleEllipsoid fitSTAR preliminarySTAR preliminaryM.Š. EPS-HEP 2011, GrenobleMomentum resolution correction1D C(q) Corrected vsC(q) UnSmeared1D C(q) UnSmearedvs C0 (q) UnSmeared)STAR preliminarySTAR preliminary
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