Upload
sheba
View
33
Download
1
Embed Size (px)
DESCRIPTION
Perturbative QCD apporach to Heavy quarkonium at finite temperature and density. Su Houng Lee Yonsei Univ., Korea. Introduction on sQGP and Bag model Gluon condensates in sQGP and in vacuum J/ y suppression in RHIC Pertubative QCD approach for heavy quarkonium. - PowerPoint PPT Presentation
Citation preview
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
1
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,..
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
2
At high T and/or Density
Quark Gluon Plasma
Proton
Proton
Proton
Nucleons in vacuum
Quark Gluon Plasma (T.D. Lee and E. Shuryak)
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
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
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
4
Signal of QGP
Relativistic Heavy Ion collision
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
5
Some highlights from RHIC
Data from STAR coll. At RHIC
Jet quenching: strongly interacting matter
V2: very low viscosity
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
6
Vacuum property of sQGP
MIT Bag model and Quark Gluon Plasma (QGP)
sQGP strongly interacting and very small viscosity
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
7
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
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
8
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
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
9
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
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
10
Gluon condsenates in QGP and Vacuum
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
11
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
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
12
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
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
13
Gluon condensate in QGP from lattice calculation
.....)(signal latticevalue 424
222
dgcga
GGGonperturbatilatticelatticeveperturbatinon
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
14
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
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
15
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
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
16
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
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
17
J/ in QGP
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
18
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
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
19
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
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
20
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
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
21
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
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
22
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
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
23
Progress in QCD calculations
LO and NLO
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
24
Basics in Heavy Quark system
1. Heavy quark propagation
mqqS
1)( where,...........)()()()( qSGqSqSqSG
Perturbative treatment are possible
because 0for even qqm QCD
q
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
25
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
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
26
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
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
27
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
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
28
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
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
29
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
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
30
LO Amplitude
cN
1by suppressed
220
222
)(3
4p
N
kMmgM
c
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
31
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
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
32
NLO Amplitude
)(, ),(,,
)()()()()2(
)()()()()2( : NLO
)(, ),(,
)()()()2( : LO
221
4210
22110
22110
221
40
210
mgOppmgOkk
kgpcpckgm
kqpcpckqm
mgOppmgOk
pcpckgm
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
33
NLO Amplitude : qccq
1
Collinear divergence when 1=0.
Cured by mass factroization
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
34
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
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
35
NLO Amplitude : gccg
Higher order in g counting
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
36
NLO Amplitude : - cont gccg
Previous diagrams can be reproduced with effective four point vertex
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
37
Cancellation of infrared divergence
Remaining Infrared Divergence cancells after adding one loop corrections
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
38
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
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
39
Total cross section for Upsilon by nucleon: NLO vs LO
Large higher order corrections
Even larger correction for charmonium
NLO/LO
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
40
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 ?
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
41
Total cross section: gluon vs quark effects
With thermal mq = mg = 200 MeV
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
42
Effective Thermal cross section: gluon vs quark effects
1
1)(
/
2
/
2
Tp
Tp
edppe
dppp
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
43
Effective Thermal width: gluon vs quark effects
1)(deg
/
2
Tpg e
dpppn
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
44
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.
Istanbul 06 S.H.LeeIstanbul 06 S.H.Lee
45
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