three-dimensional kaon source extraction from star experiment at rhic
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: Three-dimensional Kaon Source Extraction from STAR Experiment at RHIC](https://reader035.vdocuments.us/reader035/viewer/2022081514/5681614f550346895dd0d48d/html5/thumbnails/1.jpg)
July 21, 2011M.Š. EPS-HEP 2011,
Grenoble 11
Three-dimensional Kaon Source Extraction from STAR Experiment at RHIC
Michal ŠumberaNPI ASCR Prague(for the STAR Collaboration)
![Page 2: Three-dimensional Kaon Source Extraction from STAR Experiment at RHIC](https://reader035.vdocuments.us/reader035/viewer/2022081514/5681614f550346895dd0d48d/html5/thumbnails/2.jpg)
July 21, 2011 22
Outline Why and how to extract the source shape?
1D source extraction: previous and recent results
Kaon data analysis details
3D source shape analysis: Cartesian surface – spherical harmonic decomposition technique
3D source function extraction: correlation moments fitting
Comparison to thermal blast wave model
ConclusionsM.Š. EPS-HEP 2011,
Grenoble
![Page 3: Three-dimensional Kaon Source Extraction from STAR Experiment at RHIC](https://reader035.vdocuments.us/reader035/viewer/2022081514/5681614f550346895dd0d48d/html5/thumbnails/3.jpg)
July 21, 2011 33
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 imaging
M.Š. EPS-HEP 2011, Grenoble
Inversion 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
€
C q( ) −1 = 4π drr2∫ K q,r( )S r( )
![Page 4: Three-dimensional Kaon Source Extraction from STAR Experiment at RHIC](https://reader035.vdocuments.us/reader035/viewer/2022081514/5681614f550346895dd0d48d/html5/thumbnails/4.jpg)
€
R q( ) ≡ C q( ) −1 = 4π drr2∫ K q,r( )S r( )
K q,r( ) =12
d cosθ r q ,
r r ∫ φ r q , r r ( )
2−1[ ]
July 21, 2011 44
Inversion procedure
Freeze-out occurs after last scattering. Þ Only Coulomb & quantum statistics effects included the kernel.
M.Š. EPS-HEP 2011, Grenoble
( ) ( )j jj
S r S B r Expansion into B-spline basis
€
χ2 =
CExpt qi( ) − K ij ⋅ S jj
∑ ⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
2
ΔCExpt qi( )( )2
![Page 5: Three-dimensional Kaon Source Extraction from STAR Experiment at RHIC](https://reader035.vdocuments.us/reader035/viewer/2022081514/5681614f550346895dd0d48d/html5/thumbnails/5.jpg)
July 21, 2011M.Š. EPS-HEP 2011,
Grenoble 5
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
![Page 6: Three-dimensional Kaon Source Extraction from STAR Experiment at RHIC](https://reader035.vdocuments.us/reader035/viewer/2022081514/5681614f550346895dd0d48d/html5/thumbnails/6.jpg)
TPC
July 21, 2011M.Š. EPS-HEP 2011,
Grenoble 6
Kaon data analysis20% most central Au+Au @ √sNN=200 GeV Run 4: 4.6 Mevts, Run 7: 16 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
![Page 7: Three-dimensional Kaon Source Extraction from STAR Experiment at RHIC](https://reader035.vdocuments.us/reader035/viewer/2022081514/5681614f550346895dd0d48d/html5/thumbnails/7.jpg)
STAR kaon 1D source shape result
July 21, 2011 7
PHENIX, PRL 103:142301,2009
M.Š. EPS-HEP 2011, Grenoble
STAR preliminary
STAR preliminary
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.
![Page 8: Three-dimensional Kaon Source Extraction from STAR Experiment at RHIC](https://reader035.vdocuments.us/reader035/viewer/2022081514/5681614f550346895dd0d48d/html5/thumbnails/8.jpg)
8
1 11
1 11
.... ........
.... ........
( ) ( ) (1)
( ) ( ) (2)
l ll
l ll
l lq
l
l lr
l
R q R q
S r S r
3D Koonin-Pratt:
Plug (1) and (2) into (3) 1 1
2.... ....
( ) 4 ( , ) ( ) (4)l l
l llR q drr K q r S r
1 1
1 1
.... ....
.... ....
2 1 !!( ) ( ) ( ) (4)
! 42 1 !!
( ) ( ) ( ) (5)! 4
l l
l l
ql lq
l lrr
dlR q R q
ll dS r S rl
Invert (1)
Invert (2)
Expansion of R(q) and S(r) in Cartesian Harmonic basis
Danielewicz and Pratt, Phys.Lett. B618:60, 20053D source shape analysis
Þ
Þ
Þ
July 21, 2011M.Š. EPS-HEP 2011,
Grenoble
x = out-directiony = side-directionz = long-direction
i = x, y or z
3( ) ( ) 1 4 ( , ) ( )R q C q dr K q r S r (3)
![Page 9: Three-dimensional Kaon Source Extraction from STAR Experiment at RHIC](https://reader035.vdocuments.us/reader035/viewer/2022081514/5681614f550346895dd0d48d/html5/thumbnails/9.jpg)
9July 21, 2011
C0(qinv) vs C(qinv): comparison
M.Š. EPS-HEP 2011, Grenoble
STAR preliminary
K+K+ & K-K- l=0 moment
C0(qinv)
C(qinv)
![Page 10: Three-dimensional Kaon Source Extraction from STAR Experiment at RHIC](https://reader035.vdocuments.us/reader035/viewer/2022081514/5681614f550346895dd0d48d/html5/thumbnails/10.jpg)
July 21, 2011 10
Extracting 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, Grenoble
€
SG x, y,z( ) ≡l
2p( )3 rxryrz
exp −x 2
4rx2 +
y 2
4ry2 +
z2
4rz2
⎛
⎝ ⎜ ⎜
⎞
⎠ ⎟ ⎟
⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥
![Page 11: Three-dimensional Kaon Source Extraction from STAR Experiment at RHIC](https://reader035.vdocuments.us/reader035/viewer/2022081514/5681614f550346895dd0d48d/html5/thumbnails/11.jpg)
11
Independent correlation moments Rl
α1…αl , 0≤l≤4
July 21, 2011M.Š. EPS-HEP 2011,
Grenoble
STAR preliminary
Extracted 3D Gaussianfit parameters:λ = 0.48 ± 0.01rx = (4.8 ± 0.1) fmry = (4.3 ± 0.1) fmrz = (4.7 ± 0.1) fm
![Page 12: Three-dimensional Kaon Source Extraction from STAR Experiment at RHIC](https://reader035.vdocuments.us/reader035/viewer/2022081514/5681614f550346895dd0d48d/html5/thumbnails/12.jpg)
12
Kaon correlation function profiles
July 21, 2011M.Š. EPS-HEP 2011,
Grenoble
C(qx) C(qx,0,0)
C(qy) C(0,qy,0)
C(qz) C(0,0,qz)
STAR preliminary
![Page 13: Three-dimensional Kaon Source Extraction from STAR Experiment at RHIC](https://reader035.vdocuments.us/reader035/viewer/2022081514/5681614f550346895dd0d48d/html5/thumbnails/13.jpg)
P. Chung, STAR, arXiv:1012.5674 [nucl-ex]
STAR preliminary
July 21, 2011M.Š. EPS-HEP 2011,
Grenoble 13
Kaon vs. pion 3D source shape
STAR preliminary
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
![Page 14: Three-dimensional Kaon Source Extraction from STAR Experiment at RHIC](https://reader035.vdocuments.us/reader035/viewer/2022081514/5681614f550346895dd0d48d/html5/thumbnails/14.jpg)
Comparison to thermal BW model
July 21, 2011M.Š. EPS-HEP 2011,
Grenoble 14
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
![Page 15: Three-dimensional Kaon Source Extraction from STAR Experiment at RHIC](https://reader035.vdocuments.us/reader035/viewer/2022081514/5681614f550346895dd0d48d/html5/thumbnails/15.jpg)
15
Conclusions 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-pion interferometry.
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.
July 21, 2011M.Š. EPS-HEP 2011,
Grenoble
![Page 16: Three-dimensional Kaon Source Extraction from STAR Experiment at RHIC](https://reader035.vdocuments.us/reader035/viewer/2022081514/5681614f550346895dd0d48d/html5/thumbnails/16.jpg)
16
Backup slides
July 21, 2011M.Š. EPS-HEP 2011,
Grenoble
![Page 17: Three-dimensional Kaon Source Extraction from STAR Experiment at RHIC](https://reader035.vdocuments.us/reader035/viewer/2022081514/5681614f550346895dd0d48d/html5/thumbnails/17.jpg)
P. Chung, STAR, arXiv:1012.5674 [nucl-ex]
STAR preliminary
July 21, 2011M.Š. EPS-HEP 2011,
Grenoble 17
Kaon vs. pion 3D source shape
STAR preliminary
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
![Page 18: Three-dimensional Kaon Source Extraction from STAR Experiment at RHIC](https://reader035.vdocuments.us/reader035/viewer/2022081514/5681614f550346895dd0d48d/html5/thumbnails/18.jpg)
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.
18M.Š. EPS-HEP 2011,
GrenobleJuly 21, 2011
![Page 19: Three-dimensional Kaon Source Extraction from STAR Experiment at RHIC](https://reader035.vdocuments.us/reader035/viewer/2022081514/5681614f550346895dd0d48d/html5/thumbnails/19.jpg)
19
Ellipsoid fit
July 21, 2011M.Š. EPS-HEP 2011,
Grenoble
STAR preliminary
STAR preliminary
![Page 20: Three-dimensional Kaon Source Extraction from STAR Experiment at RHIC](https://reader035.vdocuments.us/reader035/viewer/2022081514/5681614f550346895dd0d48d/html5/thumbnails/20.jpg)
20
Momentum resolution correction1D C(q) Corrected vs C(q)
UnSmeared1D C(q) UnSmeared vs C0 (q) UnSmeared)
July 21, 2011M.Š. EPS-HEP 2011,
Grenoble
STAR preliminary
STAR preliminary