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

2

1 where

||||4

1||

||||,

1

1100

00003

• Linear density approximation

IEEEE npnp 2

1

2

1

7

0

2

1....., 3

du mm

np IEE

• Linear density approximation

n p

n p

EE

EI

IEE

sym

mm

np

du

4

1

2

1

2

1.....,

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

6

1

2

1

6

1

FF

fB

FF

fsym E

m

E

k

E

mff

E

kE

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

M

CM

22

• 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

3

64

8

22 /exp)( MssdsMBT

ukikx ukxdxik 10e

• Cohen, Griegel, Furnstahl 92

sss mm /)(

sV m/

.....)log(12

8

......)log()(64

1

......)log(4

1

222

2224

221

qkk

kk

qqkk

u

k

11

QCD sum rules for Nucleon asymmetric nuclear matter

ssV

Pole

mk

1

dduuM

dduuM

2

2

2

2

3

48

8 termsLeading

22 /exp)( MssdsMBT

ukikx ukxdxik 10e

• K.S. Jeong, Lee 11

.....68)log(12

1

......)log()(64

1

......)log(4

1

10

222

2224

10

221

qqqqkk

kk

qqqqkk

u

k

dduuqq

dduuqq

2

1

2

1 where

0

1

12

some detail

.....68)(12

1

......)(32

1

......4

1

10

222

/2

324

/2

10

42

/*2

22

22

22

qqqqMe

Me

qqqqMem

MEvN

MEN

MENN

N

N

N

112

2

002

2

, 28

3

88qqqq

Mqqqq

ME np

112

2

28

qqqqM

IEsym

pqqppqqp

MEsym ||2||

8112

2

Expectation values

saturation Vacuum DIS

tensor momentumenergy : 4

5 ||/ ||

densities : 1

2||/ ||

pddppuup

pddppuup

13

Results – Symmetry Energy

symE

Id

du

d

u

d

u

Idd

IuuEE

I

III

I

Ipn

200

0

0

0

)(

)()(

)(

)(

)(

)(

)()(

)()(

14

Results – Uncertainty

contM

OE

nn

nsym 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

9

8

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