Post on 02-Jan-2016
description
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
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
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
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 ,,
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).
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
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
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
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
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.
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
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)()()()(
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
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 .
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
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
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
full calculation
no flow
no refraction
no potentialBoltzmann for BE thermal distribution
full calculation
no flow
no refraction
no potentialBoltzmann for BE thermal distribution
Thank you.