November 6, 2012M.Š. STAR regional mtg., Warsaw11 Kaon Freeze-out Dynamics in √s NN =200GeV Au+Au Collisions at RHIC Michal Šumbera NPI ASCR, Prague (for.

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November 6, 2012M.Š. STAR regional mtg., Warsaw11 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)

22 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 m T - dependence of the Gaussain radii in LCMS Conclusions M.Š. STAR regional mtg., WarsawNovember 6, 2012

33 Technique devised by D. Brown and P. Danielewicz PLB398:252, 1997 PRC57:2474, 1998 Emitting source Kernel is independent of freeze-out conditions  Model-independent analysis of emission shape (goes beyond Gaussian shape assumption) Source imaging Inversion of linear integral equation to obtain source function Source function (Distribution of pair separations in pair rest frame) Encodes FSI Correlation function 1D Koonin-Pratt equation M.Š. STAR regional mtg., WarsawNovember 6, 2012

44 Inversion procedure Freeze-out occurs after last scattering.  Only Coulomb & quantum statistics effects included the kernel. Expansion into B-spline basis M.Š. STAR regional mtg., WarsawNovember 6, 2012

5 Particle correlations at low relative momenta: How far we can go and what it means for the source function. (1D example) M.Š. STAR regional mtg., WarsawNovember 6, 2012

6 Particle correlations at low relative momenta: How far we can go and what it means for the source function. (1D example) M.Š. STAR regional mtg., WarsawNovember 6, 2012

7 Particle correlations at low relative momenta: How far we can go and what it means for the source function. (1D example) M.Š. STAR regional mtg., WarsawNovember 6, 2012

8 Particle correlations at low relative momenta: How far we can go and what it means for the source function. (1D example) M.Š. STAR regional mtg., WarsawNovember 6, 2012

9 Particle correlations at low relative momenta: How far we can go and what it means for the source function. (1D example) M.Š. STAR regional mtg., WarsawNovember 6, 2012

10 Previous 1D source imaging results PHENIX, PRL 98:132301,2007 PHENIX, PRL 103:142301,2009 Observed long non-gaussian tails attributed to non-zero particle emision duration and contribution of long-lived resonances M.Š. STAR regional mtg., WarsawNovember 6, 2012

Pions: STAR Run 4 vs PHENIX 11 Excellent point by point agreement!!! November 6, 2012M.Š. STAR regional mtg., Warsaw

TPC 12 Kaon data analysis 20% most central √s NN =200 GeV Run 4: 4.6 Mevts, Run 7: 16 Mevts 30% most central √s NN =200 GeV Run 4: 6.6 Mevts Particle ID selection via TPC dE/dx: NSigmaKaon 3.0 && NSigmaElectron>2.0 |y| < 0.5 & 0.2 < p T < 0.4 GeV/c dE/dx vs rigidity: before after PID cuts M.Š. STAR regional mtg., WarsawNovember 6, 2012

Kaon 0.2<p T <0.36 GeV/c Au+Au (0-30%) -1.5<Number of Sigma< Rigidity (GeV/c) dE/dx No PID selection STAR PRELIMINARY M.Š. STAR regional mtg., WarsawNovember 6, 2012

Kaon 0.36<p T <0.48 GeV/c Au+Au (0-30%) -0.5<Number of Sigma< Rigidity (GeV/c) dE/dx No PID selection STAR PRELIMINARY M.Š. STAR regional mtg., WarsawNovember 6, 2012

STAR kaon 1D source shape result 15 PHENIX, PRL 103:142301, M+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 k T -range: STAR bin is 4x narrower. M.Š. STAR regional mtg., WarsawNovember 6, 2012

3D source shape analysis: Spherical Harmonics basis The disadvantage of expansion in the spherical harmonics Y ℓm : connection between the geometric features of the real source function S(r) and the complex valued projections S ℓm (r) is not transparent. The Y ℓm harmonics are convenient for analyzing quantum angular momentum, but are clumsy for expressing anisotropies of real-valued functions. 16November 6, 2012 M.Š. STAR regional mtg., Warsaw

Cartesian harmonics basis Based on the products of unit vector components, n α1 n α2,…, n αℓ. Unlike the spherical harmonics they are real. Due to the normalization identity n 2 x + n 2 y + n 2 z = 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. 17 M.Š. STAR regional mtg., WarsawNovember 6, 2012

18 3D Koonin-Pratt: Plug (1) and (2) into (3) Invert (1) Invert (2) Danielewicz and Pratt, Phys.Lett. B618:60, 2005    x = out-direction y = side-direction z = long-direction  i = x, y or z M.Š. STAR regional mtg., WarsawNovember 6, D source shape analysis: Cartesin Harmonics basis

19 C 0 (q inv ) vs. C(q inv ): comparison K + K + & K - K - l =0 moment C 0 (q inv ) C(q inv ) M.Š. STAR regional mtg., WarsawNovember 6, 2012

Run4 Kaon CF: l =0 moment 20 l =0 moment in agreement with 1D C(q) M.Š. STAR regional mtg., WarsawNovember 6, 2012

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. 21 Extracting 3D source function S(r) M.Š. STAR regional mtg., WarsawNovember 6, 2012

Independent correlation moments R l α1…α l, 0≤ l ≤4 22 Extracted 3D Gaussian fit parameters: λ = 0.48 ± 0.01 r x = (4.8 ± 0.1) fm r y = (4.3 ± 0.1) fm r z = (4.7 ± 0.1) fm N.B. Contributions decrese with increasing ℓ. For ℓ > 4 are zero. M.Š. STAR regional mtg., WarsawNovember 6, 2012

Independent correlation moments R l α1…α l, 0≤ l ≤4 23 With two 3D Gaussians fit gets even worse: λ 1 = 0.48 ± 0.01 r x1 = (4.7 ± 0.1) fm r y1 = (4.4 ± 0.1) fm r z1 = (4.6 ± 0.1) fm λ 2 = 0.16 ± 0.10 r x2 = (38 ± 17) fm r y2 = (0.6 ± 0.6) fm r z2 = (46 ± 31) fm M.Š. STAR regional mtg., WarsawNovember 6, 2012

Kaon 3D Gaussian Fits 0<cent.<30% 24 3D Gaussian shape provides an adequate representation at both k T bins M.Š. STAR regional mtg., WarsawNovember 6, <k T <36 GeV/c0.36<k T <48 GeV/c

Kaon correlation function profiles 25 C(q x )  C(q x,0,0) C(q y )  C(0,q y,0) C(q z )  C(0,0,q z ) M.Š. STAR regional mtg., WarsawNovember 6, 2012

P. Chung, STAR, arXiv: [nucl-ex] 26 Kaon vs. pion 3D source shape Pion and kaon 3D source shapes are very different: Is this due to the different dynamics? PRL 98:13230 Very good agreement on 3D pion source shape between PHENIX and STAR PRL 98:13230 M.Š. STAR regional mtg., WarsawNovember 6, 2012

Comparison to thermal BW model 27 Therminator ( A. Kisiel et al., Phys. Rev. C 73: ) basic ingredients: 1.Longitudinal boost invariance. 1.Blast-wave expansion with transverse velocity profile semi-linear in transverse radius ρ: v r (ρ)=(ρ/ρ max )/(ρ/ρ max +v t ). Value of v t =0.445 comes from the BW fits to particle spectra from 200GeV: STAR, PRC 79:034909, Thermal emission takes place at proper time , from a cylinder of infinite longitudinal size and finite transverse dimension ρ max. Freeze-out occurs at  =  0 +aρ. Particles which are emitted at (z, ρ) have LAB emission time t 2 = (  0 +aρ) 2 +z 2. Emission duration is included via Δ  M.Š. STAR regional mtg., WarsawNovember 6, 2012

And to the HYDJET++ model Therminator: Comp.Phys.Com. 174, 669 (2006) HYDJET++: Comp.Phys.Com. 180, 779 (2009) 28 HYDJET++ gives larger source lifetime than Terminator M.Š. STAR regional mtg., WarsawNovember 6, 2012

m T -dependence of the radii in LCMS 29 M.Š. STAR regional mtg., WarsawNovember 6, 2012 Buda-Lund: arXiv: v2 HKM: PRC81, (2010) R out =R x / ,  R side =R y, R long =R z Buda-Lund describes m T – dependence of R out & R side but fails for R long at low m T  violation of m T -scaling between pion and kaon Gaussian radii. HKM is more representative of fireball expansion dynamics than the simpler perfect fluid hydrodynamics.

Conclusions First model-independent extraction of kaon 3D source shape. Source function of mid-rapidity, low-momentum kaons from central Au+Au collisions at √s NN =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-pion interferometry. 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. 30 M.Š. STAR regional mtg., WarsawNovember 6, 2012

Conclusions The Gaussian radii for the kaon source function display monotonic decrease with increasing transverse mass m T over the interval of 0.55≤ m T ≤ 1.15 GeV/c 2. In the outward and sideward directions this decrease is adequately described by the m T –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. 31 M.Š. STAR regional mtg., WarsawNovember 6, 2012

Backup slides 32 M.Š. STAR regional mtg., WarsawNovember 6, 2012

Momentum resolution correction 1D C(q) Corrected vs C(q) UnSmeared 1D C(q) UnSmeared vs C 0 (q) UnSmeared) 33 STAR preliminary M.Š. STAR regional mtg., WarsawNovember 6, 2012

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

Run4 vs Run4 P10ik: Tracker Effect BulkCorr PWG 35 Tracker ITTF significantly underestimates CFEssentially no effect of centrality definition

Run4 P10ik vs Run7 & Run BulkCorr PWG 36 Run4 P10ik agrees with Run7 P10ikRun4 P10ik disagrees with Run10 P10ik

BulkCorr PWG 37 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

Buda-Lund and HKM Comparison 38 M.Š. STAR regional mtg., WarsawNovember 6, 2012 Buda-Lund: arXiv: v2 HKM: PRC81, (2010) R out =R x / ,  R side =R y, R long =R z Buda-Lund describes m T – dependence of R out & R side but fails for R long at low m T  violation of m T -scaling between pion and kaon Gaussian radii. HKM is more representative of fireball expansion dynamics than the simpler perfect fluid hydrodynamics.