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1
Su Houng Lee
1. Mesons with one heavy quark
2. Baryons with one heavy quark
3. Quarkonium
Arguments based on two point function
can be generalized to higher point function
Heavy quark system and OPE
2
QCD
Chiral sym-metry break-
ing
Confinement
Phenomenol-ogy
One heavy quark
Two heavy quark
Heavy quark
3
1. Mesons with one heavy quark
4
Heavy quark propagator
mqqS
1)( where,...........)()()()( qSGqSqSqSG
Perturbative treatment are possible
because
0for even qqm QCD
q
•
hh 2
12
1G
m
5
..),(
............
......Tr0,)(
2
1
0
222
kmn
k
mn
GmqLp
dxdp
Gpmqp
dplhqhlq
Perturbative treatment are possible when
222 1),( QCDxmqxxmqL
q
p
qp
which breaks down at x=0 due to light quark propaga-tor
One Heavy quark and one Light antiquark
6
n
Gh
mq
mqmqGG
qShqhq
22..
........
0,)(
Contribution from light quark condensate
222 QCDqm
q
qp
q
converges for large
7
.... 0,0,22
55
h
hiqx
mq
mhxhihxhidxe
Chiral order parameters
D(1870) D(2400)
qqm
qicxciqxdqcxcqxdc
mc2
)0(),()0(),( 5544
),(),(
0
s
msmsds DD
),( 0Dms ),( Dms
8
0 0||0d
V
1
00||0Tr
11
2
10||0Tr
0|1
|00|1
|0Tr2
1 0|
1|0Tr0
4
0
55
xxx
mimi
imD
imDmD
m
Chasher-Banks formula
hh
h
iqxm
h
iqx
h
iqx
iqx
mm
xmD
xdxe
mimix
mDxdxe
mDxi
mDxi
mDxdxe
hxhihxhidxe
2 00||0
2
020||0|1
|Tr
110||0|
1|Tr
0|1
|0|1
|0|1
|Tr
0,0,
0
55
55
9
Chasher-Banks formula –correlator with h-quark
h
hh
h
iqxm
h
iqx
h
iqx
iqx
m
mm
xmD
xdxe
mimix
mDxdxe
mDxi
mDxi
mDxdxe
hxhihxhidxe
8
0|00|08
02|00|4
020||0|1
|Tr
110||0|
1|Tr
0|1
|0|1
|0|1
|Tr
0,0,
0
55
55
10
hh
h
iqxm
h
iqx
h
iqx
h
iqx
iqx
mm
xmD
xdxe
mimix
mDxdxe
mDx
mDx
mDxdxe
mDxi
mDxi
mDxdxe
hxhihxhidxe
2 00||0
1
00||0|1
|Tr
110||0|
1|Tr
0|1
|0|1
|0|1
|Tr
0|1
|0|1
|0|1
|Tr
0,0,
0
55
55
Chasher-Banks formula – with heavy quark
qqm
qicxciqxdqcxcqxdc
mc2
)0(),()0(),( 5544
11
• Direct observation of chiral symmetry restoration in medium
D(1870) 0-
D(2400) Belle
G > 200 MeV
0+
D p0qq
..0
)3.0 to2.0(1mn
qqqq
Hayashigaki (00)
Weise, Morath, Lee (99)
Generalization to other channels: Kampfer et a. (10), Mishra et.al., Z. Wang
• QCD sum rule approach: Hayashigaki, Weise, Morath, Lee
12
..1
2
1........
0,)(
0
0
22..
kmq
mqmqGG
qShqhq
n
Gh
but no convergence model approach
Heavy quark symmetry
ii
ki
ki
0
05
0
05 1
2
11
2
1
ii ik
ik
5
0
05
0
0 1
2
11
1
2
11
D D*
D0 D1
near mass shell kmvq
13
Qq quark system in vacuum and medium: Chiral symme-try
D(1870)
0-
D(2400)
2318 ?
0+
D*(2007)
1-
D1(2420)
1+
Ds(1968)
Ds(2317)
D*(2112)
Ds1(2460)
530
448 ?
413 349348
0- 0+ 1- 1+
137144
xxx? 396xxx 345
B(5279)
B(57xx)?
B*(5325)
B1(5721)
Bs(5366)
Bs(58xx)?
Bs*(5415)
Bs1(5830)
4646
14
2. Baryons with one heavy quark
15
Chasher-Banks formula - < - * * LL L L >
2
'
0
'
55
55
2
1
0|00|00|00|02
1
00||0'0|''|2
1Tr0|
1|
110||
'
1
'
10|''|
2
1Tr0|
1|
0|1
|0|1
|0|1
|Tr0|1
|
0,0,
h
h
h
iqxm
h
iqx
h
iqx
TTTTiqx
m
m
xxmD
xdxe
mimix
mimix
mDxdxe
mDxi
mDxi
mDx
mDxdxe
hdCuxhCduhdCiuxhCdiudxe
),(),(
*
s
msmsds
16
3. Quarkonium
17
..),(
............
......Tr0,)(
2
1
0
222
kmn
kmn
GmqLp
dxdp
Gqpmp
dplhqhlq
Perturbative treatment are possible when
2222 412),( QCDqmqxmqL
2q
System with heavy quark anti-quark
p
qp
222 4 QCDqm
18
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
19
n
nQCDn
nnn
FG
qxqm
xqFdxq
..
)12(4
),(...)(
2222
21
0
2/
2Jmq
Subtlety for bound states Applequist, Dine, Muzinich (78), Peskin (79), Basis for pNRQCD ........
)1( ))()((
)(2244
3242 O
mgmgmg
mgmgg
c
c
c
c
=
42 1 ,
1 , mg
tmg
apm
Separation scale
20
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/
1
)1(9
128E
maxx
xdx
amJ
Attractive for ground state
Separation scale
For small T modify matrix el-ement
21
Summary of analysis of Stark effect+ QCD sum rule (Morita-Lee)
• 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
22
• QCD sum rule for Quarkonia at nuclear matter:
Klingl, Kim, SHL,Weise (99), Hayashigai (99)
• Contribution from complete dim 6 operators: Kim SHL (01)
mass shift at nuclear matter: -7 MeV (dim 4)
-4 MeV (dim4+ dim6)
• QCD sum rule + MEM at finite temperature: Gubler, Oka, Morita
QCD sum rule for Quarkonia in medium
• looking forward to further work
23
W(S-T)=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(S-S)= exp(-s SS)
T
• Behavior at T>Tc
W(SS)= exp(-s SS)
W(ST)= exp(- g(1/S)T)
<a/p B2
>T
<a/p E2 >T
24
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)
25
Chiral sym-metry break-
ing
Confinement
JPARCOne heavy
quark
Two heavy quark
Heavy quark
Analytic approaches
Lattice calculation
26
2. Correlators with one Heavy quark: lead to sum rules relating well known chiral operators to spectral density
+ others that will be worked out.
b) Obtain Weinberg type sum rule
c) Nuclear target ? Heavy ion at JPAR
1. All Chiral symmetry order parameters zero eigenvalue solutions in QCD
Summary
3. Correlators with heavy quarks only :
Quarkonium in medium will give new insights into confinement problem
qqm
qicxciqxdqcxcqxdc
mc2
)0(),()0(),( 5544
..... )( ,)0()( , AAxVVxqq
