Michal umbera npi ascr prague for the pas paul chung petr chaloupka richard lednick robert vertesi
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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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Michal umbera npi ascr prague for the pas paul chung petr chaloupka richard lednick robert vertesi

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


Outline
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


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


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


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)


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)


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)


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)


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)


Previous 1d s ource imaging results
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


Pions star run 4 vs phenix

M.Š. STAR regional mtg., Warsaw

Pions: STAR Run 4 vs PHENIX

Excellent point by point agreement!!!


Kaon data analysis
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


Kaon pid @ 0 2 p t 0 36 gev c au au 0 30

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)


K aon pid @ 0 36 p t 0 48 gev c au au 0 30

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)


Star kaon 1d source shape result

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


3d source shape analysis spherical harmonics basis

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.


Cartesian harmonics basis

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.


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)


C 0 q inv vs c q inv comparison

M.Š. STAR regional mtg., Warsaw

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

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

C0(qinv)

C(qinv)


Run4 kaon cf l 0 moment

M.Š. STAR regional mtg., Warsaw

Run4 Kaon CF: l=0 moment

l=0 moment in agreement with 1D C(q)


Extracting 3d source function s r

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.


Independent correlation moments r l 1 l 0 l 4

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.


Independent correlation moments r l 1 l 0 l 41

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


Kaon 3d gaussian fits 0 cent 30

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


Kaon correlation function profiles

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)


Kaon vs pion 3d source shape
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


Comparison to thermal bw model

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


And to the hydjet model therminator comp phys com 174 669 2006 hydjet comp phys com 180 779 2009

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


M t dependence of the radii in lcms

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.


Conclusions

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.


Conclusions1

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.



Momentum resolution correction

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


Two pion correlation function from run4 au au 200gev run4 tracker vs ittf

BulkCorr PWG

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

Paul Chung

Nuclear Physics Institute ASCR

Prague


Run4 vs run4 p10ik tracker effect

BulkCorr PWG

Run4vsRun4 P10ik: Tracker Effect

Tracker ITTF significantly underestimates CF

Essentially no effect of centrality definition


Run4 p10ik vs run7 run10

BulkCorr PWG

Run4 P10ik vs Run7 & Run10

Run4 P10ik agrees with Run7 P10ik

Run4 P10ik disagrees with Run10 P10ik


Conclusion

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


Buda lund and hkm comparison

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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