su houng lee with kie sang jeong 1. few words on nuclear symmetry energy
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Nuclear Symmetry Energy from QCD sum rules. Su Houng Lee with Kie Sang Jeong 1. Few words on Nuclear Symmetry Energy 2. A QCD sum rule method 3. Preliminary results . Korea Rare Isotope Accelerator ( KoRIA ) Talk by B. Hong. Nuclear Symmetry Energy . - PowerPoint PPT PresentationTRANSCRIPT
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Su Houng Lee with Kie Sang Jeong 1. Few words on Nuclear Symmetry Energy 2. A QCD sum rule method 3. Preliminary results
Nuclear Symmetry Energy from QCD sum rules
2
Korea Rare Isotope Accelerator (KoRIA) Talk by B. Hong
3
Nuclear Symmetry Energy Shetty, Yennello,
arXiv:1002.0313
/3 0 symEL
.., 423 IOIEsym
npnp I
,
4
Nuclear Symmetry Energy
Li, Chen, Ko, Phys. Rep. 464, 113 (08)
5
1. Few words on symmetry energy
6
mDiF
gDiFFT 2
4
QCD Energy Momentum Tensor
np
T
003,
Energy Density in asymmetric nuclear matter
dduuqq
InqqnpqqpmmNTN
nTnpTp
du
np
21 where
||||41||
||||,
1
1100
00003
• Linear density approximation
IEEEE npnp 21
21
7
0
21....., 3
du mm
np IEE
• Linear density approximation
n p
n p
EE
EI
IEE
sym
mm
np
du
41
21
21.....,
2
3
• Nucleons in a background potential
nucleons in the vacuum
Ep
Ep
Ep
Ep
EI
nucleons in the asymmet-ric matter
8
Medium modification
Nucleon in Relativistic mean fields: (Di Toro et al)
Hadrons in nuclear medium from QCD
kkmm pnpn
*,
*, ,
pnspsn jjff ,
*
*0
*
22*
*
2
61
21
61
FF
fB
FF
fsym E
mEk
Emff
Ek
E
1. Nucleons in symmetric nuclear matter: Cohen, Griegel, Furnstahl (91) consistent with a strong scalar attraction and vector repulsion
2. Vector meson in medium: Hatsuda and Lee (92) : 4 quark condensate are important
Symmetry Energy
Average potential
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QCD sum rules for Nucleon
ssV
Pole
mk
1
22 /exp)( MssdsMBT
• Small M2
n
nnnOPE O
MCM 2
2
• Large M2
m
M2
ukikx ukxdxik 10e
)(s
0sm
10
QCD sum rules for Nucleon in symmetric nuclear matter
ssV
Pole
mk
1
qqM
qqM
V
s
2
2
2
2
364
8
22 /exp)( MssdsMBT
ukikx ukxdxik 10e
• Cohen, Griegel, Furnstahl 92
sss mm /)(
sV m/
.....)log(12
8
......)log()(64
1
......)log(41
222
2224
221
qkk
kk
qqkk
u
k
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QCD sum rules for Nucleon asymmetric nuclear matter
ssV
Pole
mk1
dduuM
dduuM
2
2
2
2
348
8 termsLeading
22 /exp)( MssdsMBT
ukikx ukxdxik 10e
• K.S. Jeong, Lee 11
.....68)log(12
1
......)log()(64
1
......)log(41
10
222
2224
1022
1
qqqqkk
kk
qqqqkk
u
k
dduuqq
dduuqq
21
21 where
0
1
12
some detail
.....68)(12
1
......)(32
1
......4
1
10
222
/2
324
/2
104
2/*2
22
22
22
qqqqMe
Me
qqqqMem
MEvN
MEN
MENN
N
N
N
112
2
002
2
, 28388 qqqq
Mqqqq
ME np
112
2
28 qqqqM
IEsym
pqqppqqpM
Esym ||2||8112
2
Expectation values
saturation Vacuum DIS
tensor momentumenergy : 45 ||/ ||
densities : 12||/ ||
pddppuup
pddppuup
13
Results – Symmetry Energy
symE
Id
dudu
du
IddIuuEE
I
III
I
Ipn
200
0
0
0
)()()(
)()(
)()(
)()()()(
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Results – Uncertainty
contMO
En
nn
sym 2
m
)(s
0s
15
Results
Important operator
dduu
222 1
qqfqqfqqvac
16
NN
NN
N
mxdxxGmG
mGm
0.9 ),(2
MeV 750 N|(Chiral)T|N ,N|Op|N2
Op Op
22
000
• Linear density approximation
• Condensate at finite density
n.m.0
000 0.061-1
98
GmGG N
167.0 2.0
167.0 2.0
2
2
s
s
B
E
9.02
sG
Operators in at finite density
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1. An attempt to get some insight of Symmetry energy from QCD
2. Vector densities are important
3. Higher dimensional operators are important at higher density
Summary