1

Su Houng Lee

1. Quark condensate and the h’ mass

2. Gluon condensate and the Heavy quark system

3. Summary

Medium dependence; are all hadrons alike?

2

1. Quark condensate and the h’ meson

1. Some introduction

2. Casher Banks formula

3. Lee-Hatsuda formula

4. Witten – Veneziano formula

5. At finite temperature and den-

sity

3

• Kapusta, Kharzeev, McLerran PRD 96 : Effective U(1)A restoration in medium in SPS data

Some introduction

• Rapp, Wambach, van Hees: SPS dilepton data

• RHIC dilepton puzzle

• Csorgo, Vertesi, Sziklai : Additional contribution from h’ mass reduction

• Experimental and theoretical works on h‘ in nuclear medium

• QCD symmetry: SU(N)Lx SU(N)R SU(N)V and U(1)A is always broken by Anomaly

QCD confinement

4

Finite temperature

qq

T/Tc

/r rn

0/ TT qqqq

18.0/ 0 TT qqss

Tmmss ssT /exp

Quark condensate – Chiral order parameter

Finite density

Lattice gauge theory

Linear density approximation

2

12

1G

mcc

c

5

• Quark condensate

Casher Banks formula - Chiral symmetry breaking (m0)

0

10Tr)0,(Trlim00

0 mDdAexSqq QCDS

x

0 0001

0Tr00 022

m

m

md

mDqq

Phenomenologically need constituent quark mass

Casher Banks formula in the chiral limit

6

• Other order parameters: - s p correlator (mass difference)

),0( )0,( Tr xSxS

00, 00, 1 554 qiqxqixqqqxqxqxdV

aa

0 c 2

1 1

a5 a5

)0,0(Tr),(Tr SxxS

),0( )0,(Tr 55 xSixSi aa

Phenomenologically constituent quark mass terms survives

Generalized Casher Banks formula in the chiral limit

1 1

7

Correlation function for h ‘ (Lee, Hatsuda 96)

• h ‘- p correlator (mass difference)

00,00,1 55554 qiqxqixqqiqxqixqxedV

aaikx

),0()0,(Tr 55 xSixSi

3q

x SU(2)for const qqmq

nspermutatio 0 01

000

40000

4

ysmysydxuddxuxdV s

n=1

)0,0(Tr),(Tr 55 SixxSi

GG~

),0()0,(Tr 55 xSixSi aa

5i 5i

U(1) A symmetry will effectively be restored up to quark mass terms in SU(3)

20

T. Cohen (96)

Lee, Hatsuda (96)

8

• Contributions from glue only from low energy theorem

• When massless quarks are added

• Correlation function

h’ mass? Witten-Veneziano formula - I

0~

,~

e GGxGGdxikP ikx

000 kP

• Large Nc argument

mesons nglueballs n mk

mesonGG

mk

glueballGGkP

22

2

22

2|

~|0

|

~|0

00,e 055 kikx PkkjxjdxikP

GG~

GG~

GG~

GG~

cNOm

mk

GG 1 with

'|~

|02

'2'

2

2

2cN cN

• Need h‘ meson

2

'

2

0

'|~

|00)0(

m

GGPkP c

9

Witten-Veneziano formula – II

• h‘ meson 0

'|~

|002

'

2

Pm

GG

22

2'

2

'2

'

2

11

8

3

424

Gm

fmNNN

FF

MeV 432 11

8

3

2'

22

2'

2'

mG

NNfm F

MeV 411)547()958(' mm

Lee, Zahed (01)

10

• Large Nc counting

Witten-Veneziano formula in medium (Kwon, Morita, Wolf, Lee in prep )

m

ikx GGxGGdxikP 0~

,~

e

2cN

• LET (Novikov, Shifman, Vainshtein, Zhakarov) at finite temperature for S(k): Ellis, Kapusta, Tang (98)

2cN cN

0,e4/1

202

0

GGgxOpdxiOpgd

d ikx

d

T

d

d

TTcOpTc

bgMconstOp ''

8exp

020

2

0

0

22

20

3232

4/1 TTTOp

TTd

bOp

TTd

bOp

gd

d

11

• LET at finite temperature for P(k) : Lee, Zahed (01)

•

22

11

2

3

40 G

TTdkP

'|~

|0 GG

00,00,

2 55

2

4 qiqxqixqqiqxqixqN

Nxedkk

F

ikx

0 phase restored sym chiral

...0|

~|0

0~

,~

2'

2

24

4

mk

GGkGGxGGxedkP ikx

Therefore, 0'|~

|0 GG

12

• W-V formula at finite temperature:

22

11

2

3

4G

TTd

0

2442 GTagG

0'|

~|0

02'

2

Pm

GG

2'

2

m

qq

0

22

22

11

2

3

4

11

2

3

4GdG

TTd

Smoothes out temperature change because if

Therefore , : Observable consequences ?qqm '

13

3. Heavy quark system

1. Charmonium system

2. Panda

14

rr

rrV s )(

3

4)(

)(GeV 2

small

r

b decdec /)0()( TTTT

dec/TT

T/Tc

sString Tension: QCD order pa-rameter

Early work on J/y at finite T (Hashimoto, Miyamura, Hirose, Kanki)

15

J/y suppression in RHIC

• Matsui and Satz: J/y will dissolve at Tc due to color screening

• Lattice MEM : Asakawa, Hatsuda, Karsch, Petreczky , Bielefield, Nonaka….

J/y will survive Tc and dissolve at 2 Tc .. Still not settled at QM2011

• Potential models (Wong …) : .

• Refined Potential models with lattice (Mocsy, Petreczky…)

: J/y will dissolve slightly above Tc

• Lattice after zero mode subtraction (WHOT-QCD)

: J/y wave function hardly changes at 2.3 Tc

• AdS/QCD (Kim, Lee, Fukushima, Stephanov…. ..) • NRQCD: UK group+ S.Y. Kim

• QCD sum rule (Morita, Lee) , QCD sum rule+ MEM (Gluber, Oka, Morita)

• Perturbative approaches: Blaizot et al… Imaginary potential• pNRQCD: N. Brambial et al.

Recent works on J/y in QGP

16

AdS/QCD (Y.Kim, J.P.Lee, SHLee 07)

J/y

y’

Deconfinement

Thermal effect?

Mass (GeV)

17

mqqS

1)( where,...........)()()()( qSGqSqSqSG

Perturbative treatment are possible

because

0for even qqm QCD

q

Heavy quark propagator

18

..)12(4

),(...)(

2222

21

0

n

n Gqxqm

xqFdxq

Perturbative treatment are possible when

222 4 QCDqm

2q

Two Heavy quark propagator

19

q2 process expansion parameter

example

0 Photo-production of open charm

m2J/ y

> 0 Bound state properties

Formalism by Peskin (79)

J/y dissociation: NLOJ/y mass shift: LO

-Q2 < 0 QCD sum rules for heavy quarks

Predicted mhc <mJ/y before experiment

Perturbative treatment are possible when 222 4 QCDqm

2

2

4mQCD

22

2

4 QmQCD

2/

2

2

4 J

QCD

mm

0/

2

2

J

QCD

mm

20

• At finite temperature: from

02 GG

• Two independent operators

Twist-2 Gluon

Gluon condensate

24

1GguuGGs

or

2E

2Bs

<a/p B2

>T

<a/p E2 >T

G0

G2

pGpG 20 ,3

9

8

400 MeV 18984

9B

GTG c

Lowest dimensional - Gluon operators

21

W(ST)=exp(-s ST)

Time

Space

Space

SW(S-T) = 1- <a/p E2> (ST)2 +

…

W(S-S) = 1- <a/p B2> (SS)2 +…

OPE for Wilson lines: Shifman NPB73 (80)

<E2>, <B2> vs confinement potential

• Local vs non local behavior

W(SS)= exp(-s SS)

T

• Behavior at T>Tc

W(SS)= exp(-s SS)

W(ST)= exp(- g(1/S) S)

<a/p B2

>T

<a/p E2 >T

22

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

Tc

2

0

2

5

2 0.7 ..

GGGmn

• At r = 5 x r n.m.

167.0 2.0

167.0 2.0

2

2

s

s

B

E

9.02

sG

Operators in at finite density and hadronic phase

23

• Hatsuda, Adami, Brown.. (90)

....440

2 TagTGG

• Lattice calculation (Lee 89)

Non zero above Tc

Non-perturbative Gluon condensate ;

06.0 00 TGTG

<a/p B2

>T

<a/p E2 >T

Gluon condensate – Non perturbative

• Morita, Lee (08)

24

• In terms of density of eigenvalues

Gluon condensate – Non perturbative

dmm

md

mDhh m 1

0001

0Tr0022

2

12

1G

mm

25

• Morita and Lee (08 present)

In Vacuum

In medium

Heavy quark system – QCD sum rule constraints

,,,/ ccJ

4430,3872 ZX

26

qc

c

OPE for bound state: m infinity

)( || ),( 16/ 24220 mgOkmgOgNm c

Mass shift: QCD 2nd order Stark Effect : Peskin 79 e > L qcd

Medium

220

6

2/3

0

20

2

2

/

1

)1(9

128E

maxx

xdx

a

EE

nzEim

n niJ

Attractive for ground state

)1( ))()((

)(2244

3242 O

mgmgmg

mgmgg

c

c

c

c

=

<a/p B2

>T<a/p E2 >T

27

Summary of analysis • Due to the sudden change of condensate near Tc

<a/p B2

>T

<a/p E2 >T

G0

G2

• Abrupt changes for mass and width near Tc

(GeV)/Jm

28

0 50 100 150 200 250 300 350 4000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

No. of participants

RAANuclear absorption &Thermal decay in QGP & HG

Recombination

Total

With g=1.85

Melting of y’ cc

Slope: GJ/yMelting T

of J/y

Height: mass of J/y

RAA from RHIC (√s=200 GeV y=0 , 2-comp model (Rapp) Song, Park, Lee 10)

29

Quantum numbers

QCD 2nd Stark eff.

Potential model

QCD sum rules

Effects of DD loop

hc0-+ –8 MeV –5 MeV

(Klingl, SHL ,Weise,

Morita)

No effect

J/y 1-- –8 MeV(Peskin, Luke)

-10 MeV(Brodsky et al).

–7 MeV(Klingl,

SHL ,Weise, Morita)

<2 MeV(SHL, Ko)

cc0,1,2++ -20 MeV -15 MeV

(Morita, Lee)

No effect on cc1

y(3686)

1-- -100 MeV(SHL, Ko)

< 30 MeV

y(3770)

1-- -140 MeV(SHL, Ko)

< 30 MeV

Other approaches for mass shift in nuclear matter

30

Anti pro-ton

4 to 6 GeV/ck

Heavy nuclei

3 2

11.2

0.17 5fm

fm fm

e

e

Observation of Dm through p-A reaction

Expected luminosity at GSI 2x 1032cm-2s-1

Can be done at J-PARC

31

1. h’ mass is related to quark condensate and thus should reduce in medium

a) Could serve as signature of chiral symmetry restoration

b) Dilepton in Heavy Ion collision

c) Measurements from nuclear targets

2. Heavy quark system - related to confinement phenomena

a) Refined measurements in Heavy Ion collisions

b) Measurements from nuclear target

Summary

32

• Other order parameters: - s p correlator (mass difference)

xmDmD

x1

001

Tr

00, 00, 1 554 qiqxqixqqqxqxqxdV

aa

0 c 2

a a

a5 a5

01

0Tr1

Tr mD

xmD

x

1

001

Tr 55

xmD

imD

xi aa