Introduction on sQGP and Bag model Gluon condensates in sQGP and in vacuum

Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee

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1. Introduction on sQGP and Bag model

2. Gluon condensates in sQGP and in vacuum

3. J/ suppression in RHIC

4. Pertubative QCD approach for heavy quarkonium

Perturbative QCD apporach to Heavy quarkonium

at finite temperature and density

Su Houng LeeYonsei Univ., Korea

Thanks to : Recent Collegues: C.M. Ko, W. Weise, B. Friman, T. Barnes, H. Kim, Y. Oh, .. Students: Y. Sarac, Taesoo Song, Y. Park, Y. Kwon, Y. Heo,..


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At high T and/or Density

Quark Gluon Plasma

Proton

Proton

Proton

Nucleons in vacuum

Quark Gluon Plasma (T.D. Lee and E. Shuryak)


3

QCD Phase Diagram at finite T and

~ 170 MeV

0.17 / fm3

Quark Gluon Plasma (s

QGP) Different

• Particle spectrum (mass)

• Vacuum

• Deconfinement

• Theoretical approach

Lattice result:

sudden change in p and E above Tc


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Signal of QGP

Relativistic Heavy Ion collision


5

Some highlights from RHIC

Data from STAR coll. At RHIC

Jet quenching: strongly interacting matter

V2: very low viscosity


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Vacuum property of sQGP

MIT Bag model and Quark Gluon Plasma (QGP)

sQGP strongly interacting and very small viscosity


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Bag model and sQGP

MIT Bag model : inside the Bag vac=0, perturbative vacuume

outside the Bag vac = non zero , non perturbative vacuum

R

B }{4 BDixdSinside

4

4

3

3

MeV) 206( ,8.0

MeV) 120( ,1

43

44

3

404.2

BfmR

BfmR

BVRB

RBR

NE qnucleon

Original bag model

Later models Outside pressure is balanced by confined quark pressure


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Bag model and sQGP

Phase transition in MIT Bag model

B

B CTT

BTgPQGP ..90

42

BTgEQGP ..90

3 42

B4

Outside pressure is balanced by thermal quark gluon pressure

BPE

PE

QGPQGP

QGPQGP

43

but scorrection large need ,

Asakawa, Hatsuda PRD 97


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QCD vacuum vs. sQGP

MIT Bag

B

Vacuum with negative pressure

Nonperturbative QCD vacuum

sQGP

1. What is B in terms of QCD variables (operators)

2. Can understand soft modes associated with phase transition


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Gluon condsenates in QGP and Vacuum


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Gluon condensate

1. , dominated by non-perturbative contribution3222 MeV/fm 1500)(2 EBG

2. RG invariant, gauge invariant, characteristic vacuum property, couples to spin 0 field

3. Can be calculated on the lattice (DiGiacomo et al. )

pGpmpTp p20

8

9||

5. Nucleon expectation value is

22

8

9

4GGhhmqqmTD hl

4. Related to trace of energy momentum tensor through trace anomaly (Hatsuda 87)

ussddup

dssduup

ssdduupp

BmBmBmmm

BmBmBmmm

BmBmBmmm

0

0

0

MeV 45)(|| duqq BBmpdduupm

MeV 6500 pm

6. From we find


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Gluon condensate in MIT Bag model

4332

0

22

MeV) 200(for MeV/fm 711MeV/fm 1500

49

83

8

9

BG

BpGG

QGP

QGP

Inside QGP

MeV 650for /MeV 578MeV/fm 1500

49

8)/(

9

8/

032

0222

pInside

poutsideInside

mVG

BVmVpGpGG

Inside nucleon

TG

9

82 Using

Explicit lattice calculation of non-pertur

bative gluon condensate?

89) (SHLee

84) (Digiacomo

2

0

2

QGPG

G


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Gluon condensate in QGP from lattice calculation

.....)(signal latticevalue 424

222

dgcga

GGGonperturbatilatticelatticeveperturbatinon


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Lattice data show

1. Gluon condensate at T=0 is consistent with QCD sum rule value

2. Gluon condensate at T>Tc is 50 to 70 % of its vacuum value

consistent with estimates of gluon condensate inside the Bag (nucleon)

3. The change occurs at the phase transition point

T D Lee’s spin 0 field seems dominantly gluon condensate

and their expectation value indeed changes similarly in Bag and QGP


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QCD vacuum vs. sQGP

MIT Bag

B

Vacuum with negative pressure

Nonperturbative QCD vacuum

sQGP

If phase transition occurs, there will be enhancement of massless glueball excitation

2

%70

2 7.0 GGVac

02

%30

2

%70

2 GGGVac


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Summary ISummary I

1. Vacuum expectation value of Gluon condensate inside the Bag and QGP seems similar. sQGP is a large Bag

What will the viscosity be ?? What is the property of sQGP?

Physical consequence of phase transition?

2. Future GSI (FAIR) will be able to prove vacuum change through charmonium spectrum in nuclear matter


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J/ in QGP


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Karsch et al. (2000)

c c

r

r

( )V r0T

Higher T

c c

Heavy quark potential on the lattice

J/ in Quark Gluon Plasma

J/ melt above Tc


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1986: Matsui and Satz claimed J/ suppression is a signature of formation of Quark Gluon Plasma in Heavy Ion collision

J/ suppression in Heavy Ion collision

/J

e

e

New RHIC data


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2003: Asakawa and Hatsuda claimed J/ will survive up to 1.6 Tc

Quenched lattice calculation by Asakawa and Hatsuda using MEM

T< 1.6 Tc

T> 1.6 Tc

J/ peak at 3.1 GeV

J/ in Quark Gluon Plasma


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Theoretical interpretations

1. C. H. Lee, G. Brown, M. Rho… : Deeply bound states

2. C. Y. Wong… : Deby screened potential

1. Strong s at Tc < T < ~2 Tc

2. J/ form Coulomb bound states at Tc < T < ~2 Tc


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Became a question of quntative analysis

a) What are the effects of Dynamical quarks ?

b) What is the survial probability of J/ in QGP

Relevant questions in J/ suppression

need to know J/ – gluon dissociation

need to know J/ – quark dissociation


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Progress in QCD calculations

LO and NLO


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Basics in Heavy Quark system

1. Heavy quark propagation

mqqS

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

Perturbative treatment are possible

because 0for even qqm QCD

q


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2. System with two heavy quarks

..)2/1(4

),(...)(

2222

21

0

n

n Gqxqm

xqFdxq

Perturbative treatment are possible when

222 4 QCDqm

2q


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q2 processexpansion para

meter

0Photo production of open ch

arm

-Q2 < 0QCD sum rules for heavy q

uarks

m2J/

> 0 Dissociation cross section of bound states

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


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Historical perspective on Quarkonium Haron interaction in QCD

1. Peskin (79), Bhanot and Peskin (79)

a) From OPE

b) Binding energy= 0 >>

2. Kharzeev and Satz (94,96) , Arleo et.al.(02,04)

a) Rederive, target mass correction

b) Application to J/ physics in HIC

gluon

/J


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Rederivation of Peskin formula using Bethe-Salpeter equation (Lee,Oh 02)

Resum Bound state by Bethe-Salpeter Equation

)( )( ),( )( )2(

), 221214

42

21 pKVKiKppKppKiKd

Cigpp F


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NR Power counting in Heavy bound state

)( ||

)( 16/2

4220

mgOk

mgOgNm c

)1(

))()((

)(2244

3242

O

mgmgmg

mgmgg

1. Perturbative part

2. External interaction: OPE

)( ||

2

||

2

||2

41

01

22

210

1/

mgOkk

m

p

m

pmkmJ


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LO Amplitude

cN

1by suppressed

220

222

)(3

4p

N

kMmgM

c


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1

2

3

However, near threshold, LO result is expected to have large correctionHowever, near threshold, LO result is expected to have large correction

)()( )( xgxdx ghad

mb

s1/2 (GeV)

Exp data

/J

N

DD

C

/J

N

D

C

/J

N

C

C

C


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NLO Amplitude

)(, ),(,,

)()()()()2(

)()()()()2( : NLO

)(, ),(,

)()()()2( : LO

221

4210

22110

22110

221

40

210

mgOppmgOkk

kgpcpckgm

kqpcpckqm

mgOppmgOk

pcpckgm


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NLO Amplitude : qccq

1

Collinear divergence when 1=0.

Cured by mass factroization


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Mass factorization

1 Gluons whose kcos1 < Q scale,

should be included in parton distribution function

Integration of transverse momentum from zero to scale Q

11

21

02

2

11

2

11

2 ˆ'ˆ

4ln

4

2 )(

2

ˆ

dudt

ds

Q

DxP

x

dx

dudt

ds

dudt

ds iLO

EjisiNLOiNLO

1


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NLO Amplitude : gccg

Higher order in g counting


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NLO Amplitude : - cont gccg

Previous diagrams can be reproduced with effective four point vertex


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Cancellation of infrared divergence

Remaining Infrared Divergence cancells after adding one loop corrections


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Application to Upsilon dissociation cross section

Fit quark mass and coupling from fitting

to coulomb bound state gives)2()1( , SS mm

0.5

GeV 1.5

GeV 1 0

bm

qQQq gQQg


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Total cross section for Upsilon by nucleon: NLO vs LO

Large higher order corrections

Even larger correction for charmonium

NLO/LO


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1. Large NLO correction near threshold, due to log terms1. Large NLO correction near threshold, due to log terms

J/for MeV 700 e wher2

log 00

0,2

k

2. Dissociation by quarks are less than 10% of that by gluons2. Dissociation by quarks are less than 10% of that by gluons

qQQq gQQg

Thermal quark and gluon masses of 300 MeV will Reduce the large correction

Quenched lattice results at finite temperature are reliable

What do we learn from NLO calculation ?


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Total cross section: gluon vs quark effects

With thermal mq = mg = 200 MeV


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Effective Thermal cross section: gluon vs quark effects

1

1)(

/

2

/

2

Tp

Tp

edppe

dppp


43

Effective Thermal width: gluon vs quark effects

1)(deg

/

2

Tpg e

dpppn


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Summary IISummary II

1.1. We reported on the QCD NLO Quarkonium-hadron dissociatioWe reported on the QCD NLO Quarkonium-hadron dissociation cross section. n cross section.

Large correction even for upsilon system, especially near threshold

2. The corrections becomes smaller with thermal quark and gluon mass of larger than 200 MeV

Obtained realistic J/ dissociation cross section by thermal quark and gluons

3. The dissociation cross section due to quarks are less than 10 % of that due to the gluons.

The quenched lattice calculation of the mass and width of J/ at finite temperature should be reliable.


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Reference for part IReference for part I

Gluon condensates

• A. Di Giacomo and G. C. Rossi, PLB 100(1981) 481; PLB 1008 (1982) 327.

• Su Houng Lee, PRD 40 (1989) 2484.

Charmonium in nuclear matter

3. F. Klingl, S. Kim, S.H.Lee, P. Morath, W. Weise, PRL 82 (1999) 3396.

4. S.Kim and S.H.Lee, NPA 679 (2001) 517.

5. S.H.Lee and C.M. Ko, PRC 67 (2003) 038202.

6. S.J.Brodsky et al. PRL 64 (1990) 1011

Quarkonium hadron interaction

7. M.E. Peskin, NPB 156 (1979) 365; G.Bhanot and M. E. Peskin, NPB156 (1979) 391

8. Y.Oh, S.Kim and S.H.Lee, PRC 65 (2002) 067901.

Additional

9. T.D. Lee, hep-ph/06 05017

Documents

Introduction on sQGP and Bag model Gluon condensates in sQGP and in vacuum