Quantum Opacity and Refractivity in HBT Puzzle
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Transcript of Quantum Opacity and Refractivity in HBT Puzzle
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2005. 11. 5 Inha Nuclear Physics Group
Quantum Opacity andQuantum Opacity and
Refractivity in HBT Refractivity in HBT
PuzzlePuzzleJin-Hee Yoon
Dept. of Physics, Inha University, Korea
John G. Cramer, Gerald A. Miller, M. S. WuDept. of Physics, University of Washington, US
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11/05/2005 HIM@Pohang
Inha Nuclear Physics Group
Correlations in Phase-Space
Space-time structure of fireball can be studied by HBT interferometry
Correlation function
)()(
),(),(
2112
21221 pp
pppp
PP
PNC
is typically parametrized as
2121
22222221
ppq )/2p(pK
1pp
]exp[),( llssoo qRqRqRC
l
s
o
K
TKBeam direction
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11/05/2005 HIM@Pohang
Inha Nuclear Physics Group
Correlations in Phase-Space
Hydrodynamic calculation predicts(D. H. Rischke and M. Gyulassy, Nucl. Phys. A608, 479 (1996); P. F. Kolb and U. Heinz, Quark Gluon Plasma 3, World Scientific, Singapore, 2004)
But, experimental results are
(STAR Collaboration, C. Adler et al., Phys. Rev. Lett. 87, 082301 (2001); PHENIX Collaboration, K. Adcox et al., Phys. Rev. Lett. 88, 192302 (2002); PHENIX Collaboration, A. Enokizono, Nucl. Phys. A715, 595 (2003))
HBT Puzzle
2.1~1/ so RR
10~5.1/ so RR
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11/05/2005 HIM@Pohang
Inha Nuclear Physics Group
Correlations in Phase-Space
Experimental Data(Au+Au@200 GeV) shows Dense Medium
OPACITY and Refractive Effects
Our Purpose : Quantum mechanical treatment of Opacity & Refractive effects
which reproduces lso RRR ,,
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11/05/2005 HIM@Pohang
Inha Nuclear Physics Group
Correlations in Phase-Space
Theoretically, the observables are expressed by
)/()/(*)exp()(
),( 2222 3
4
0 yxJyxJyiKyd
KxS
),(),(
|),(|),(),(
204
104
20
4
0210
1Kqpp
pxSxdpxSxd
eKxSxdCC
xiq
Subscript 0 means no final state interaction (FSI).
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11/05/2005 HIM@Pohang
Inha Nuclear Physics Group
Final State Interaction
FSI replaces
)/(*)/( )'exp()(
)',('),( )(p
)(p 21
222 4
4
04 yxΨyxΨyiK
ydKxSKdKxS
),( ),(
|),( |1)K,q()p,p(
24
14
24
21pxSxdpxSxd
KxSxdCC
xipexΨxJxJ )(* )( )( (-)P
: full scattering outgoing wave function*(-)PΨ
Includes two 4-dimensional integration
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11/05/2005 HIM@Pohang
Inha Nuclear Physics Group
Wigner Emission Function
Using the hydrodynamic source parameterization (B. Tomasik and U. W. Heinz, Eur. Phys. J. C4, 327 (1998); U. A. Wiedermann and U. W. Heinz, Phys. Rep. 319, 145 (1999))
With boost-invariant longitudinal dynamics
cos)(sinh)(coshcosh
),(ln2
1
)(1exp),(
)(2)(2
)(exp
)(2
)cosh(),(
)2/(),(),(),(
21
22
1
2
2
2
2
0
20
3
00
bKbMuK
xxzt
ztzt
bT
uKMB
YΖ
BΖKxS
tTtT
T
b
Kb
Kb
T
T
of potential chemical:
,222 mKM TT
),( bKT
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11/05/2005 HIM@Pohang
Inha Nuclear Physics Group
Wigner Emission Function
)(b
: cylindrically symmetric source density
21/)(exp WSWS aRb
)(bt : transverse flow rapidityWS
f R
b
0ln2
1
LK
LK
KE
KEY Since KL=0 for midrapidity data
Parameters : RWS , aWS , 0 , f , T
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11/05/2005 HIM@Pohang
Inha Nuclear Physics Group
Full Scattering Wavefunction
Assumption : Matter is cylindrically symmetric with a long axis in a central collision region
2/2/
)()( 2/0
l
ziqxilp eexΨ
qqKP
bx
T1,2
(-)
P
(-)
P 1,21,2
Reduced 2-dimensional Klein-Gordon Eq.
)(*)(*))(( 22 bb (-)p
(-)p pbU
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11/05/2005 HIM@Pohang
Inha Nuclear Physics Group
Full Scattering Wavefunction
,1
0 cos))(,(2),()(*m
mm mibpfbpf b(-)
p
Optical Potential )()()( 220 bpwwbU p
0w :real
At p=0, no opacity
Parameters : w0 , w2
Using partial wave expansion,
we can solve K-G Eq. exactly.
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11/05/2005 HIM@Pohang
Inha Nuclear Physics Group
Full Scattering Wavefunction
ppf )](Im[4
In Impulse Approximation, central optical potential
00 4 fU
Significant opacity
Using
f : complex forward scattering amplitude
For low energy interaction
0 : central density
-30
-1 1.5fm ,fm 1p mb, 1 2
0 fm 15.0]Im[ U
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11/05/2005 HIM@Pohang
Inha Nuclear Physics Group
Correlation Function
Now our Emission Function is
)2/(*)2/(
)(~
'),()2(
1),(
)()(
202
0
b'bb'b
b'b,
21 pp
BbdeZKxS ziqtiq l
with ]exp[)(')(~ 2 b''K'Kb,b'b, TT iBKdB T
Large Source Approximation : b’~1/T~1 fm << RWS
/2b'Kpppp
T
2121bb
b'b
b'b
ie)(*)(
2*
2)()()()(
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11/05/2005 HIM@Pohang
Inha Nuclear Physics Group
Correlation Function
2
00
220
2
0
320
22
0
120
22
)*()(0
2
2211
21222222
)(
)()(
)(
)()3(
~
)(
)()3(
)(cos)(sinh
exp)(
)()()())((
||~1),(
-
Kb,
Kb,b b
Kq
T
Tpp
T
ji
KF
KF
KF
KF
KF
KFR
bMT
bKB
Bbfbd
qRqC
l
Tn
tTn
nn
nij
oll
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11/05/2005 HIM@Pohang
Inha Nuclear Physics Group
Correlation Function
)(
/)()(2)(
)()()(
/)(4/)(2)(
)(2)(
/1/)(cosh)(
)())(()()(
213
202
2101
10
2
2)(2
i
ntTn
nmnn
m
K
KKf
KKf
KKf
Kf
TbMb
bfBbdKF
b Kb, TKT
Here,
Are Modified Bessel function .
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11/05/2005 HIM@Pohang
Inha Nuclear Physics Group
HBT Radii
40/
),(2)(
,
2,
,2,
Tso
so
TsoTso
Kq
q
KqCKR
Then our transverse radii can be calculated by
with
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11/05/2005 HIM@Pohang
Inha Nuclear Physics Group
Fitting Parameters
(MeV)0(fm/c)w2w0(fm-2)
(fm/c)aWS(fm)RWS(fm)fT(MeV)
6.1
2.173
025.0
314.1
056.0
782.11
015.0
725.0
067.0
852.2
046.0
137.0
002.0014.0
121.0582.0
i
i
10.0
23.8
032.0
063.1
1.1
2.123
2 /N ~ 7.8
AuGeV AusSTAR@ NN 200
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11/05/2005 HIM@Pohang
Inha Nuclear Physics Group
Fitting Parameters Check
Temperature T (173 MeV) ~ Tc (160 MeV)
f=1.31 maximum flow velocity ~ 0.85c
Source Size RWS (11.7 fm) ~ RAu (7.3 fm)+4.4 fm
Expansion time 0 (8.2 fm/c)
average expansion velocity ~ 0.5c
Emission duration (2.9 fm/c) << 0(8.2 fm/c)
Longitudinal length
system’s axial length (17.5 fm)
: large enough for long cilyndrical symmetry
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full calculation
no flow
no refraction
no potentialBoltzmann for BE thermal distribution
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full calculation
no flow
no refraction
no potentialBoltzmann for BE thermal distribution
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Thank you.