kaon freeze-out dynamics in √s nn =200gev au+au collisions at rhic

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

Warsaw 11

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

Michal ŠumberaNPI ASCR, Prague(for the Pas: Paul Chung, Petr Chaloupka, Richard Lednický, Robert Vertesi)

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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

ConclusionsM.Š. STAR regional mtg.,

WarsawNovember 6, 2012

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Technique devised by

D. Brown and P. DanielewiczPLB398:252, 1997 PRC57:2474, 1998 Emitting source

Kernel is independent of freeze-out conditions

ÞModel-independent analysis of emission shape(goes beyond Gaussian shape assumption)

Source imagingInversion of linear integral equation

to obtain source function

Source function(Distribution of pair separations in pair

rest frame)

Encodes FSI

Correlationfunction

1D Koonin-Pratt equation

M.Š. STAR regional mtg., WarsawNovember 6, 2012

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Inversion procedure

Freeze-out occurs after last scattering. Þ Only Coulomb & quantum statistics effects included the kernel.

Expansion into B-spline basis


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Particle correlations at low relative momenta:How far we can go and what it means for the source function.(1D example)


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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


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Pions: STAR Run 4 vs PHENIX

Excellent point by point agreement!!!November 6, 2012

M.Š. STAR regional mtg., Warsaw

TPC

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Kaon data analysis20% most central Au+Au @ √sNN=200 GeV Run 4: 4.6 Mevts, Run 7: 16 Mevts30% most central Au+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

|y| < 0.5 & 0.2 < pT < 0.4 GeV/c

dE/dx vs rigidity: before

after PID cuts


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Kaon PID @ 0.2<pT<0.36 GeV/c Au+Au (0-30%)

-1.5<Number of Sigma<2.0

Rigidity (GeV/c)

Rigidity (GeV/c)

dE/dx

No PID selection

STAR PRELIMINARY STAR PRELIMINARY


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Kaon PID @ 0.36<pT<0.48 GeV/cAu+Au (0-30%)

-0.5<Number of Sigma<2.0

Rigidity (GeV/c)Rigidity (GeV/c)

dE/dx

No PID selection

STAR PRELIMINARYSTAR PRELIMINARY


STAR kaon 1D source shape result

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PHENIX, PRL 103:142301,2009

34M+83M=117M K+K+ & K-K- pairs

STAR data arewell described by Gaussian.Contrary toPHENIX no non-gaussiantails are observed.

May be due to a differentkT-range:STAR bin is4x narrower.


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.

16November 6, 2012M.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 n2

x + n2y + n2

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.

17M.Š. STAR regional mtg.,


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3D Koonin-Pratt:

Plug (1) and (2) into (3)

Invert (1)

Invert (2)

Danielewicz and Pratt, Phys.Lett. B618:60, 2005

Þ

Þ

Þ

x = out-directiony = side-directionz = long-direction

ai = x, y or z


3D source shape analysis:Cartesin Harmonics basis

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C0(qinv) vs. C(qinv): comparison

K+K+ & K-K- l=0 moment

C0(qinv)

C(qinv)


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Run4 Kaon CF: l=0 moment

l=0 moment in agreement with 1D C(q)M.Š. STAR regional mtg.,


• 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.

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Extracting 3D source function S(r)


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Independent correlation moments Rl

α1…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) fm

N.B. Contributionsdecrese with increasing ℓ. For ℓ > 4 are zero.


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Independent correlation moments Rl

α1…αl , 0≤l≤4With two 3D Gaussiansfit gets even worse:λ1 = 0.48 ± 0.01rx1 = (4.7 ± 0.1) fmry1 = (4.4 ± 0.1) fmrz1 = (4.6 ± 0.1) fmλ2 = 0.16 ± 0.10rx2 = (38 ± 17) fmry2 = (0.6 ± 0.6) fmrz2 = (46 ± 31) fm


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Kaon 3D Gaussian Fits 0<cent.<30%

3D Gaussian shape provides an adequate representation at both kT binsM.Š. STAR regional mtg.,


0.20<kT<36 GeV/c 0.36<kT<48 GeV/c

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Kaon correlation function profilesC(qx) C(qx,0,0)

C(qy) C(0,qy,0)

C(qz) C(0,0,qz)


P. Chung, STAR, arXiv:1012.5674 [nucl-ex]

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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


Comparison to thermal BW model

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Therminator (A. Kisiel et al., Phys. Rev. C 73:064902 2006) basic ingredients:

1. Longitudinal boost invariance.

2. 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 comes from the BW fits to particle spectra from Au+Au @ 200GeV: STAR, PRC 79:034909, 2009.

3. 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


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And to the HYDJET++ modelTherminator: Comp.Phys.Com. 174, 669 (2006) HYDJET++: Comp.Phys.Com. 180, 779 (2009)

HYDJET++ gives larger source lifetime than TerminatorM.Š. STAR regional mtg., WarsawNovember 6, 2012

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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 Rlong at low mT Þ 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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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-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.


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Conclusions The Gaussian radii for the kaon source function display

monotonic decrease with increasing transverse mass mT over 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.


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Backup slides


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Momentum resolution correction1D C(q) Corrected vs C(q)

UnSmeared1D C(q) UnSmeared vs C0 (q) UnSmeared)

STAR preliminary

STAR preliminary


Two-pion Correlation Function from Run4 Au+Au 200GeV:Run4 Tracker vs ITTF

Paul ChungNuclear Physics Institute ASCR

Prague

BulkCorr PWG29.06.2011 34

Run4 vs Run4 P10ik: Tracker Effect

29.06.2011 BulkCorr PWG 35

Tracker ITTF significantly underestimates CF Essentially no effect of centrality definition

Run4 P10ik vs Run7 & Run10

29.06.2011 BulkCorr PWG 36

Run4 P10ik agrees with Run7 P10ik Run4 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

29.06.2011 37

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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 Rlong at low mT Þ violation of mT -scaling between pion and kaon Gaussian radii.

HKM is more representative of fireball expansion dynamics than the simpler perfect fluid hydrodynamics.

kaon freeze-out dynamics in √s nn =200gev au+au collisions at rhic

Documents

star regional

d source extraction

d source function extraction

d example

source shape

particle correlations

low relative momenta

central au au