Heavy quark system in medium

Su Houng Lee1. Introduction on phase transition2. Perturbative methods3. QCD sum rule methods4. Experiments

1S H Lee

2

T

Color superconductivity

Early universe

FAIR

RHIC

, LH

C

ΛC /D

ρ, ω

J/ψ, χC Quark-gluon plasma

Nuclear matter

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mB

g

QCD Phase Diagram

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Confinement: L=e-F

Chiral sym: <qq>

EOS: e , pHeavy quark V(r)

Susceptibility cmq cLQuark number cq

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Lattice results for QCD phase transition (from Karsch’s review)

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Order Parameter r

Order parameter in QCD?

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Order parameter in Superconductivity

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rrrrV s )(

34)(

)(GeV 2

small

r

b decdec /)0()( TTTT

dec/TT

T/Tc

String Tension: QCD order parameter

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

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J/y suppression in RHIC

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

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• Lattice MEM : Asakawa, Hatsuda, Karsch, Petreczky …. J/y will survive Tc and dissolve at 2 Tc

• 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, Hohler, Stephanov…. ..) : J/y mass change by Y. Kim, J. Lee, SHLee (PRD 07)

• Wiki page …https://wiki.bnl.gov/qpg/index.php/Quarkonia.

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

Recent works on J/y in QGP

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• Lattice result on singlet potential F(T,r) =V(T,r) -TS(T,r)

J/y from potential models

Kaczmarek , Zantow hep-lat/0510094

V(T,r) at 1.3 Tc

F(T,r) at 1.3 Tc

V(r) at T=0

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• Quarkonium dissociation temperature for different potentials

Using F(T,r)

Using V(T,r) Wong 04

Another model independent approach ?

2/1

/

2

yJr

2/12

c

rc

r [fm]

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1-- States from ISR

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• Tc region is important in HIC Statistical production may oc-

cur at or slightly below Tc

• Large non-perturbative change at Tc

• Resumed perturbation fails near Tc

Karsch hep-lat/0106019

T (G

eV)

Au+Au 200 Agev, b=0

t (fm/c)

(e-3

p)/

T4

T/Tc

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Few things to note about Tc region

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Approaches to Heavy quark system in medium

Mass: Real partWidth: Imaginary part

1. Introduction2. Perturbation for bound states3. QCD sum rule approach

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mqqS

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

Perturbative treatment are possible because

0for even qqm QCD

q

Basics in Heavy quark system

Heavy quark propagator

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..)12(4

),(...)(2222

21

0

n

n Gqxqm

xqFdxq

Perturbative treatment are possible when

222 4 QCDqm

2q

System with two heavy quarks

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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 yJ

QCD

mm

0/

2

2 y

J

QCD

mm

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n

nQCDn

nnn

FGqxqm

xqFdxq

..)12(4

),(...)(2222

21

0

2/

2yJmq

Subtlety for bound states Applequist, Dine, Muzinich (78), Peskin (79), pNRQCD.......

)1( ))()((

)(2244

3242 O

mgmgmgmgmgg

c

c

c

c

42 1 ,1 , mgt

mga

pm

Separation scale

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Approaches to Heavy quark system in medium

Mass: Real partWidth: Imaginary part

1. Introduction2. Perturbation for bound states3. QCD sum rule approach

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1. Peskin (79), Bhanot and Peskin (79) 2. Kharzeev and Satz (94,96) , Arleo et.al.(02,04) 3. Y.Oh, SHL (02) Rederived using Bethe-Salpeter amplitude

)( || 41

01 mgOkk

1k

)( ||

)( 16/2

4220

mgOk

mgOgNm c

Quarkonium Hadron interaction in QCD Imaginary part

LO calculation

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gluon

y/J

k p

0 ),()(|)()( mm

mm y MkpdpdkpcckM

LO Amplitude

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Not so large, however, LO QCD result is known to underestimate nucleon absorption cross section

)()( )( xgxdx ghad

s1/2 (GeV)

Exp data from pA

Oh, Kim ,SHL 02

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)(, ),(,,

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

)(, ),(,

)()()()2( : LO

221

4210

22110

22110

221

40

210

mgOppmgOkk

kgpcpckgmkqpcpckqm

mgOppmgOk

pcpckgm

NLO Amplitude (Song, SHL, PRD 05)

Quasi-free approximation: R. Rapp et al. (02)

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q1

Collinear divergence when q1=0. Cured by mass factroization

NLO Amplitude : y+ q c + c + q

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q1 Gluons whose kcos q1 < 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

42 )(

2

ˆdudt

dsQD

xPxdx

dudtds

dudtds iLO

EjisiNLOiNLO

mg

q1

Mass factorization

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NLO Amplitude : y+ g c + c + g

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Large higher order correctionsEven larger correction for charmonium

NLO/LO

T. Song and SHL, PRD 72, 034002 (2006)

Total cross section for Upsilon by nucleon: NLO vs LO

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

y

J/for MeV 700 e wher2

log 00

0,2

k

2. But at finite temperature, thermal masses will regulate the large correction

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

Lessons from NLO calculation

3. But should be used for T<

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n

nQCDn

nnn aTFG

qxqmxqFdxq

..)12(4

),(...)(2222

21

0

2/

2yJmq

Thermal dissociation cross section

42 1 ,1 , mgt

mga

pm

Separation scale

For large T modify Wilson Coefficient

For small T modify matrix element

Ways to asses convergence 1. T< 2. D (Matrix) < (Matrix element in Vacuum)

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Summary

LO NLO

• Thermal width: J/y x thermal gluon (Park, Song, Lee, Wong 08,09)

y

/3

3

2 Jrelpeff vpnpdd

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No further regularization (mass factorization) needed if thermal mass is in-troduced.

Need lattice EOM.

Thermal width with model EOS near Tc

y /J

s

y /J

s

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)()()(2

)(

)()()(6

)(

22

4

2

TBEkEfTCdkT

TBEkEfTCdkTp

kkBg

kkB

g

• E,B Condensate

Confinement model: Schneider, Weise

TTTGTm

TTCTC

Cg

Cc

c

1)(

1)(

0

0

•

•

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SummaryThermal width of J/y near Tc (Morita, Lee 08, Park, etal.07, M, L & Song 09)

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qc

c

OPE for bound state: m infinity

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

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

DMedium

220

6

2/3

0

20

2/1

)1(9128 E

maxxxdxamJ

y

Attractive for ground state

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Separation scale

For small T modify matrix element

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LO Singlet potential from pNRQCD : Brambilla et al.

S O Derivation

1/r > Binding > QCD,

• Take expectation value

• Large Nc limit

• Static condensate

• Energy

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Derivation of 2nd order Stark effect from pNRQCD

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Lattice result for purge gauge (Boyd et al 96)

p/T4

/T4

Rescaled pressure (Karsch 01) Karsch hep-lat/0106019

Sudden increase in Slow increase in p

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Lattice data on ( e ,p) near Tc

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• At finite temperature: from

Gluon Operators near Tc

02 GG

• Two independent operators

Twist-2 Gluon

Gluon condensate

241 GguuGGs

mm

or 2E

2Bs

< B2

>T

< E2 >T

G0

G2

pGpG 20 ,3

98

400 MeV 18984

9B

GTG c

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W(ST)=exp(- ST)

Time

Space

Space

SW(S-T) = 1- </ E2> (ST)2 +…

W(S-S) = 1- </ B2> (SS)2 +…

OPE for Wilson lines: Shifman NPB73 (80)

<E2>, <B2> vs confinement potential

• Local vs non local behavior

W(SS)= exp(- SS)

T

• Behavior at T>Tc

W(SS)= exp(- SS)

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

< B2

>T

< E2 >T

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NN

NN

N

mxdxxGmG

mGm

0.9 ),(2

MeV 750 N|(Chiral)T|N ,N|Op|N2

Op Op

22

000

D

m

r mmr

• Linear density approximation

• Condensate at finite density

n.m.0

000 0.061-1

98

rrrr GmGG N

Tc

2

0

2

5

2 0.7 ..

GGGmn

r

• At r = 5 x r n.m.

167.0 2.0

167.0 2.0

2

2

r

r

r

r

D

D

s

s

B

E

rr 9.02

sG

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Operators in at finite density and hadronic phase

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Result using Stark effect

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J/y mass shift near Tc (Morita, Lee 08)

J/y mass shift in nuclear matter : Luke, Manohar, Savage (92)

similar to other approaches, potential model (glue ball exchange) (Brodsky (97) , Teramond.. (98)

D

..// 08.01

mnJJ mm

rr

yy

(GeV)/yJmD

Dm from QCD Stark Effect

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Approaches to Heavy quark system in medium

Mass: Real partWidth: Imaginary part

1. Introduction2. Perturbation for bound states3. QCD sum rule approach

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..)2/1(4

),(...)(2222

21

0

n

n Gqxqm

xqFdxq

2q

Including Temperature effects

For High T > 2 Tc

For small and T close to Tc

224 Qm Separation scale

38

n

n

n QssdsJQJ

dQdM

)()()0(),( 22

r

n

J

J

JJ

n

n

mm

fmm

mMM

2'

2/

/

2/

2'2

/1

y

y

y

yyy

Constraints from QCD sum rules for Heavy quark system

OPE

..

4!)!4(1 22

2

c

nnm

G

nnaM

Phenomenological side

..1

2'

2/

/2/

n

JJn

J

n mm

cfm

My

yy

y

s

rJ/y

Y’

n

n

MM 1

2with G

02 G

sum rule at T=0 : can take any Q2 >=0, 2vacuum

22 G 4 QCDQm

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QCD sum rule constraint (Morita, Lee PRL08)

MeV

]

MeV

]Dm MeV]

Dm MeV]

)( !

112

22

n

n

QssdsQ

dQd

nr

2/exp)( MssdsMB rCan also use Borel sum rule

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OPE breaks down

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Summary

GeV/yJMD Dm from QCD Stark Effect

Mass and width of J/y near Tc (Morita, Lee 08, M, L & Song 09)

QCD sum rule limit with D =0

=constraint-Dm (Stark effect)

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Constraints from Borel sum rule

NLO QCD + confine-model

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

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< B2

>T

< E2 >T

G0

G2

• Abrupt changes for mass and width near Tc

(GeV)/yJmD

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Karsch et al.

0.75Tc

0.9 Tc

K.Morita, Y. Song, SHL

1.1Tc

400 MeV

1.1Tc

1 GeV

0.9Tc

0.9 Tc

1.5Tc

400 MeV

1.5Tc

400 MeV

Karsch et al.

K.Morita, Y. Song, SHL

Comparison to other approach

T=0

1.1Tc

Mocsy, Petreczkycc state from lattice

cb state from lattice

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At higher temperature

• Within our approach, need additional information

1. For mass, need lattice information for temperature dependence of higher dimensional operators

2. For width, Need information of higher twist contribution

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• Other possible approach

1. NLO or resumed perturbation, ………………. ? 2. AdS/QCD Y. Kim, J.P.Lee, SHLee (07) sudden drop followed by steady increase.

Jy

Y’

deconfinementThermal effect?

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Can such effect be observed ?

RAA from RHIC and

Charmonium production ratio in RHICand

Mass shift at Nuclear matter

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0 50 100 150 200 250 300 350 4000

0.10.20.30.40.50.60.70.80.9

1

No. of participants

RAA Nuclear absorption &Thermal decay in QGP & HG

Recombination

Total

With g=1.85

Melting of y’ cc

Slope: J/yMelting T

of J/y

Height: mass of J/y

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

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• Effects of width and mass

• At LHC

Mass shift by -100 MeVAssumed recombination effect to be the same

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Charmonium production ratio in HIC (K. Morita, SHL in preparation)

• Chemical freeze-out at near phase boundary (Andronic et al NPA772)

CERN-SPS

BNL-RHIC

QCD sum rules

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• Matrix element

• Hadron gas model with excluded volume

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Calculation in hadron gas

0hm

)( xdxxG

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Results using QCD sum rules

• Only 17 GeV Pb+Pb data is available with large error bars

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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 < 30 MeV

y(3770)

1-- -140 MeV < 30 MeV

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Application to nuclear matter

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Anti proton

4 to 6 GeV/ck

Heavy nuclei

3 2

1 1.20.17 5

fmfm fm

y

e

e

Observation of Dm through p-A reaction

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

Can be done at J-PARC

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1. Deconfinement Disappearance of mass gap Quarkonium masses

2. Abrupt changes for quarkonium masses and widths

3. Looking forward to charmonium production ratio and finer mass resolution from RHIC and LHC

4. production inside a nuclear at FAIR and hopefully Jparc

Summary

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1. Perturbative approach at Finite temperature: T. Song, Y. Park, SHLee, C.Y. Wong, PLB 659 (2008) 621; PRC 76, 044907 (2007). SHLee, K. Morita, PRD79, 011501 (2009).

2. Sum rule method at finite: K.Morita, SHLee, PRL 100, 022301 (2008). K. Morita, SHLee, PRC 77, 064904 (2008). T: Y. Song, SHLee, K. Morita, PRC 79,014907 (2009). https://wiki.bnl.gov/qpg/index.php/Sum_rule_approach

3. AdS/QCD: Y. Kim, JP Lee, SHLee, PRD 75, 114008 (2007). 4. J/Psi Phenomenology: T.Song, W. Park, SHLee, PRC 81, 034914 (2010)5. LO,NLO: Y Oh, S. Kim, SHLee, PRC 65, 067901 (2002). T. Song,

SHLee, PRD 72, 034002 (2005)6. Nuclear medium: S. Kim, SHLee, NPA 679 (2001) 517. SHLee, C.M.Ko,

PRC 67, 038202 (2003).

My reference

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