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Kaon Freeze-out Dynamics in √s NN =200GeV Au+Au Collisions at RHIC

Michal Šumbera NPI ASCR, Prague (for the Pas: Paul Chung, Petr Chaloupka , Richard Lednický , Robert Vertesi ). Kaon Freeze-out Dynamics in √s NN =200GeV Au+Au Collisions at RHIC . 1. Outline. Why and how to extract the source shape?

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Kaon Freeze-out Dynamics in √s NN =200GeV Au+Au Collisions at RHIC

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  1. M.Š. STAR regional mtg., Warsaw Michal Šumbera NPI ASCR, Prague (for the Pas: Paul Chung, PetrChaloupka, Richard Lednický, Robert Vertesi) Kaon Freeze-out Dynamics in √sNN=200GeV Au+Au Collisions at RHIC 1

  2. Outline Why and how to extract the source shape? 1D source extraction: previous and recent results Kaon data analysis details 3D source function extraction via Cartesian surface – spherical harmonic decomposition technique: correlation moments fitting Comparison to thermal blast wave model mT- dependence of the Gaussain radii in LCMS Conclusions M.Š. STAR regional mtg., Warsaw 2

  3. M.Š. STAR regional mtg., Warsaw Source imaging Technique devised by D. Brown and P. Danielewicz PLB398:252, 1997PRC57:2474, 1998 Inversion of linear integral equation to obtain source function 1DKoonin-Pratt equation Encodes FSI Source function (Distribution of pair separations in pair rest frame) Emitting source Correlation function • Kernel is independent • of freeze-out conditions • Model-independent analysis of emission shape • (goes beyond Gaussian shape assumption) 3

  4. M.Š. STAR regional mtg., Warsaw Inversion procedure Freeze-out occurs after last scattering.  Only Coulomb & quantum statistics effects included the kernel. Expansion into B-spline basis 4

  5. M.Š. STAR regional mtg., Warsaw Particle correlations at low relative momenta: How far we can go and what it means for the source function. (1D example)

  6. M.Š. STAR regional mtg., Warsaw Particle correlations at low relative momenta: How far we can go and what it means for the source function. (1D example)

  7. M.Š. STAR regional mtg., Warsaw Particle correlations at low relative momenta: How far we can go and what it means for the source function. (1D example)

  8. M.Š. STAR regional mtg., Warsaw Particle correlations at low relative momenta: How far we can go and what it means for the source function. (1D example)

  9. M.Š. STAR regional mtg., Warsaw Particle correlations at low relative momenta: How far we can go and what it means for the source function. (1D example)

  10. Previous 1D source imaging results PHENIX, PRL 98:132301,2007 M.Š. STAR regional mtg., Warsaw PHENIX, PRL 103:142301,2009 Observed long non-gaussian tails attributed to non-zero particle emision duration and contribution of long-lived resonances

  11. M.Š. STAR regional mtg., Warsaw Pions: STAR Run 4 vs PHENIX Excellent point by point agreement!!!

  12. Kaon data analysis M.Š. STAR regional mtg., Warsaw 20% most central Au+Au @ √sNN=200 GeV Run 4: 4.6 Mevts, Run 7: 16 Mevts 30% most centralAu+Au @ √sNN=200 GeV Run 4: 6.6 Mevts Particle ID selection via TPC dE/dx: NSigmaKaon<2.0 && NSigmaPion>3.0 && NSigmaElectron>2.0 TPC dE/dx vs rigidity: before after PID cuts |y| < 0.5 & 0.2 < pT < 0.4 GeV/c

  13. M.Š. STAR regional mtg., Warsaw Kaon PID @ 0.2<pT<0.36 GeV/c Au+Au (0-30%) No PID selection -1.5<Number of Sigma<2.0 dE/dx STAR PRELIMINARY STAR PRELIMINARY Rigidity (GeV/c) Rigidity (GeV/c)

  14. M.Š. STAR regional mtg., Warsaw Kaon PID @ 0.36<pT<0.48 GeV/cAu+Au (0-30%) -0.5<Number of Sigma<2.0 No PID selection dE/dx STAR PRELIMINARY STAR PRELIMINARY Rigidity (GeV/c) Rigidity (GeV/c)

  15. M.Š. STAR regional mtg., Warsaw STAR kaon 1D source shape result 34M+83M=117M K+K+ & K-K- pairs STAR data are well described by Gaussian. Contrary to PHENIX no non-gaussian tails are observed. May be due to a different kT-range: STAR bin is 4x narrower. PHENIX, PRL 103:142301,2009

  16. M.Š. STAR regional mtg., Warsaw 3D source shape analysis:Spherical Harmonics basis • The disadvantage of expansion in the spherical harmonics Yℓm: connection between the geometric features of the real source function S(r) and the complex valued projections Sℓm(r) is not transparent. The Yℓm harmonics are convenient for analyzing quantum angular momentum, but are clumsy for expressing anisotropies of real-valued functions.

  17. M.Š. STAR regional mtg., Warsaw Cartesian 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.

  18. M.Š. STAR regional mtg., Warsaw 3D source shape analysis:Cartesin Harmonics basis Danielewicz and Pratt, Phys.Lett. B618:60, 2005 ai = x, y or z x = out-direction y = side-direction z = long-direction 3D Koonin-Pratt:  Plug (1) and (2) into (3)  Invert (1)  Invert (2)

  19. M.Š. STAR regional mtg., Warsaw C0(qinv) vs.C(qinv): comparison K+K+ & K-K-l=0 moment C0(qinv) C(qinv)

  20. M.Š. STAR regional mtg., Warsaw Run4 Kaon CF: l=0 moment l=0 moment in agreement with 1D C(q)

  21. M.Š. STAR regional mtg., Warsaw Extracting 3D source function S(r) • 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.

  22. M.Š. STAR regional mtg., Warsaw Independent correlation moments Rlα1…αl, 0≤l≤4 Extracted 3D Gaussian fit parameters: λ = 0.48 ± 0.01 rx = (4.8 ± 0.1) fm ry = (4.3 ± 0.1) fm rz = (4.7 ± 0.1) fm N.B. Contributions decresewith increasingℓ. For ℓ > 4 are zero.

  23. M.Š. STAR regional mtg., Warsaw Independent correlation moments Rlα1…αl, 0≤l≤4 Withtwo 3D Gaussians fit getsevenworse: λ1 = 0.48 ± 0.01 rx1 = (4.7 ± 0.1) fm ry1 = (4.4 ± 0.1) fm rz1 = (4.6 ± 0.1) fm λ2= 0.16 ± 0.10 rx2 = (38 ± 17) fm ry2 = (0.6 ± 0.6) fm rz2 = (46 ± 31) fm

  24. M.Š. STAR regional mtg., Warsaw Kaon3D Gaussian Fits 0<cent.<30% 0.20<kT<36 GeV/c 0.36<kT<48 GeV/c 3D Gaussian shape provides an adequate representation at both kTbins

  25. M.Š. STAR regional mtg., Warsaw Kaon correlation function profiles C(qx)  C(qx,0,0) C(qy)  C(0,qy,0) C(qz)  C(0,0,qz)

  26. Kaon vs. pion 3D source shape M.Š. STAR regional mtg., Warsaw P. Chung, STAR, arXiv:1012.5674 [nucl-ex] PRL 98:13230 PRL 98:13230 Pion 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 STAR

  27. M.Š. STAR regional mtg., Warsaw Comparison 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 preliminary

  28. M.Š. STAR regional mtg., Warsaw And to the HYDJET++ modelTherminator: Comp.Phys.Com. 174, 669 (2006) HYDJET++: Comp.Phys.Com. 180, 779 (2009) HYDJET++ gives larger source lifetime than Terminator

  29. M.Š. STAR regional mtg., Warsaw mT-dependence of the radii in LCMS Buda-Lund: arXiv:0801.4434v2HKM: PRC81, 054903 (2010) • Rout=Rx/γ,Rside=Ry , Rlong=Rz • Buda-Lund describes mT–dependence of Rout & Rside but fails for Rlongat low mT violation of mT -scaling between pion and kaon Gaussian radii. • HKM is more representative of fireball expansion dynamics than the simpler perfect fluid hydrodynamics.

  30. M.Š. STAR regional mtg., Warsaw Conclusions • First model-independent extraction of kaon 3D source shape. • Source function of mid-rapidity, low-momentum kaons from 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. • 3D source function shapes for kaons and pions are very different. The narrower shape observed for the kaons indicates a much smaller role of resonance decays and/or of the exponential emission duration width ∆τ on kaon emission.

  31. M.Š. STAR regional mtg., Warsaw Conclusions • The Gaussian radii for the kaon source function display monotonic decrease with increasing transverse mass mTover the interval of 0.55≤ mT≤ 1.15 GeV/c2. • In the outward and sideward directions this decrease is adequately described by the mT–scaling. However, in the longitudinal direction the scaling is broken, favoring the HKM model as more representative of the expansion dynamics of the fireball than the simpler perfect fluid hydrodynamics.

  32. M.Š. STAR regional mtg., Warsaw Backup slides

  33. M.Š. STAR regional mtg., Warsaw Momentum resolution correction 1D C(q) Corrected vsC(q) UnSmeared 1D C(q) UnSmearedvs C0 (q) UnSmeared) STAR preliminary STAR preliminary

  34. BulkCorr PWG Two-pion Correlation Function from Run4 Au+Au 200GeV:Run4 Tracker vs ITTF Paul Chung Nuclear Physics Institute ASCR Prague

  35. BulkCorr PWG Run4vsRun4 P10ik: Tracker Effect Tracker ITTF significantly underestimates CF Essentially no effect of centrality definition

  36. BulkCorr PWG Run4 P10ik vs Run7 & Run10 Run4 P10ik agrees with Run7 P10ik Run4 P10ik disagrees with Run10 P10ik

  37. BulkCorr PWG Conclusion Run 4 CF significantly different from Run 4 P10ik => Direct effect of tracker change Run 4 P10ik in reasonable agreement with Run 7 P10ik => Use of same tracker gives same result Run 4 P10ik in sharp disagreement with Run 10 P10ik => very confusing state of affairs => Need to check effect of Run 4 tracker on Run 10 data 37

  38. M.Š. STAR regional mtg., Warsaw Buda-Lund and HKM Comparison Buda-Lund: arXiv:0801.4434v2HKM: PRC81, 054903 (2010) • Rout=Rx/γ,Rside=Ry , Rlong=Rz • Buda-Lund describes mT–dependence of Rout & Rside but fails for Rlongat low mT violation of mT -scaling between pion and kaon Gaussian radii. • HKM is more representative of fireball expansion dynamics than the simpler perfect fluid hydrodynamics.

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