freeze-out information and light nucleus production kaijia sun( 孙开佳 ) 2013 08 09 in...
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![Page 1: Freeze-out information and light nucleus production KAIJIA SUN( 孙开佳 ) 2013 08 09 in relativistic heavy-ion collisions (INPAC and Department of Physics](https://reader035.vdocuments.site/reader035/viewer/2022081519/56649d035503460f949d6490/html5/thumbnails/1.jpg)
Freeze-out information and light nucleus production
KAIJIA SUN(孙开佳 )
2013 08 09
in relativistic heavy-ion collisions
(INPAC and Department of Physics and Astronomy, Shanghai Jiao Tong University. [email protected])
Advisor: Lie-wen Chen (陈列文 )
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1. Retière-Lisa model
Transverse momentum distribution,
Freeze-out information
2. Coalescence model
Wigner function : a semi-classical method to
calculate coalescence probability of multiple particles
3. Yields of Light nucleus, Hypertriton, and di-Lambda
4. Summary and outlook
outli
ne
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Local Thermal EquilibriumLongitudinal boost invariance Freeze-out in momentum space
x
yz
Physical variables:
Temperature T
Radial flow(rapidity)
Size τ0 R02
Number density n
or Fugacity ξ
(Form factor as)
Basic hypothesis
J.D.Bjorken, Phys.Rev.D 27, 140(1983)
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Retière-Lisa Model
Fabrice Retière et.al, PRC70, 044907(2004)
One particle invariant distribution
Covariant distribution function
Parameterization of transverse flow
Fred Cooper and Graham Frye, Phys. Rev D. 10, 186 (1974)
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Parameters :Temperature T =0.1115(GeV)
Radial flow =0.978 Size τ0 R02 ξ=104.2
(Form factor as=0) <>=1.02 GeV
Freeze-out Information
0 0.5 1 1.5 2 2.5 310
-2
10-1
100
101
pT(GeV)
d2 N/2
p Tdp
Tdy
PHENIX
R-L Model
Spectrum of proton , centrality 0~5%The PHENIX Collaboration, Phys. Rev.C. 69, 034909 (2004)
0.09 0.1 0.11 0.12 0.13 0.140
0.5
1
1.5
2
T
2
0.85 0.9 0.95 1 1.050
0.5
1
1.5
2
0
2
0.8 1 1.2 1.4 1.6 1.8 20
0.5
1
1.5
2
ln(ln(0))
2
In preparation Sun and Chen
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3
1 131
1 2
( ; ) ( , , ; , , )(2 )
MWi
C C i i i i i C M Mi i
M C
d pN g p d f x p x x p p
E
Dover/Heinz/Schnedermann/Zimanyi, PRC44, 1636 (1991)
The structure of freeze-out space-time Neglecting binding energy
coalescence probability : Wigner function
Statistical factor
Invariant phase factor
Phase space distribution
Wigner function
Covariant Coalescence model
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Wigner phase-space density for t/3He
3
3
2 2 2 2 2 2 2 2 21 2 1 2t/ He
2 2 22 1 2 3 2 3 1 3 1 32
t/ He1 2 3 1 2 3
1 21 1 3
1 2 1 2
( , ; , ) 8 exp( / / )
( ) ( ) ((t
)1
2 ( )
1 3( ), ( ) (Jaco
: 1.61 fm; He: 1.
bi Transformat22
74 fm)
W k k
m m m m m m m m mr
m m m mm m
m m
m m m m
2 2
ρ λ k k
ρ r r λ r r r
2 1 3 3 1 21 2 1 2 3
2 1 2 11 1 2 2
11
1 21 2 1 2 3
ion)
2 6( ), ( ( ) )
2( )
( ) and ( ) with
1 1 3 1 12 and
2
m m m m m mm m m m m
m m m m m
1 2 1 2 2k k k k k k k
t/3He Wigner phase-space density and root-mean-square radius:
Assume nucleon wave function in t/3He can be described by the harmonic oscillator wave function, i.e.,
RMS radius is the only parameter determining wigner function !
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Light nucleus spectrum
particles dN/dy
proton 15.9
deuteron 0.086
He3 1.3E-4
4.21E-5
He4 1.62E-7
1.21E-8
5.72E-11
(The PHENIX Collaboration), Phys. Rev. C. 69, 034909 (2004)(The STAR Collaboration), Phys. Lett.B. 655, 104(2007)(The STAR Collaboration), Phys. Rev.Lett. 108, 072301(2004)(The STAR Collaboration), arXiv:0909.0566[nucl-ex]
Fugacity ξ = 8.3Size τ0 = 9.9 (fm/c) R0
=18.0 ( fm)
In preparation Sun and Chen
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Yields of light nucleus
H. Agakishiev, et al. (Star Collaboration) Nature473 (2011) 353 .L.Xue and Y.G.Ma, et al. PRC85,064912. 2012
In preparation Sun and Chen
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Ratio
A.Andronic, P.Braun-Munzinger,J.Stchel, Phys. Lett.B. 673, 142-145 (2009)A.Andronic, P.Braun-Munzinger,J.Stchel, H.Stcker, Phys. Lett.B. 697, 203-207 (2011)
In preparation Sun and Chen
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Physics with strangeness
1. Signal for QGP2. Test QCD and Nature of nuclear force3. De-confined Phase transition
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Yields of Hypertriton and Di-Lambda with S=-2
H. Garcilazo et.al, PRL 012503(2013)
1 1.5 2 2.5 3 3.5 4 4.5 52
4
6
8x 10
-5
RMS radius(fm)
dN/d
y
-3 He
0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.02
0.03
0.04
0.05
0.06
RMS radius(fm)
dN/d
y
-
D=0.086
He3=12.9E-5
In preparation Sun and Chen
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Summary and outlook
Parameters:
Temperature T =0.1115 ( GeV)
Radial flow =0.978
Size τ0 = 9.9 (fm/c)
R0 =18.0
( fm)
Fugacity ξ = 8.3
(Form factor as=0)
Coalescence model is a useful tool to describe the light nucleus production at relativistic HIC’s and extract freeze-out informationH-dibaryon yield at RHIC is between that of d and 3HeIt is interesting to see the HBT correlation…..This method is easy to extend to quark level to investigate hardronization
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Thank you!