freeze-out information and light nucleus production kaijia sun( 孙开佳 ) 2013 08 09 in...
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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 )
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
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)
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)
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
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
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 !
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
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
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
Physics with strangeness
1. Signal for QGP2. Test QCD and Nature of nuclear force3. De-confined Phase transition
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
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
Thank you!