Heavy quark system in medium
Su Houng Lee1. Introduction on phase transition2. Perturbative methods3. QCD sum rule methods4. Experiments
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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
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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
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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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