su houng lee with kie sang jeong 1. few words on nuclear symmetry energy
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1
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
9
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
11
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
)()()(
)()(
)()(
)()()()(
14
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
17
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
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