Transcript effects of thermal partons on J/psi

Perturbative QCD apporach to
Heavy quarkonium
at finite temperature and density
Su Houng Lee
Yonsei Univ., Korea
1. Introduction on sQGP and Bag model
2. Gluon condensates in sQGP and in vacuum
3. J/y suppression in RHIC
4. Pertubative QCD approach for heavy quarkonium
Thanks to :
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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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Quark Gluon Plasma (T.D. Lee and E. Shuryak)
Proton
At high T
Proton
and/or
Density
Proton
Nucleons in vacuum
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Quark Gluon Plasma
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QCD Phase Diagram at finite T and r
Lattice result:
sudden change in p and E
above Tc
Quark Gluon Plasma
(sQGP)
~ 170 MeV
Different
•
Particle spectrum
(mass)
•
Vacuum
•
Deconfinement
•
Theoretical
approach
0.17 / fm3
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Relativistic Heavy Ion collision
Signal of QGP
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Some highlights from RHIC
Data from STAR coll. At RHIC
Jet quenching: strongly interacting matter
V2: very low viscosity
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sQGP  strongly interacting and very small viscosity
Vacuum property of sQGP
MIT Bag model and Quark
Gluon Plasma (QGP)
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Bag model and sQGP
MIT Bag model : inside the Bag fvac=0, perturbative vacuume
outside the Bag fvac = non zero , non perturbative vacuum
Sinside   d 4 x{y iD
 y  B}
B
2.04
4 3
B
R
R
3
4 3
 4B
R  4 BV
3
Enucleon  N q
R  1 fm,
B  (120 MeV)4
R  0.8 fm, B  (206 MeV)4
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R
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
EQGP  3g
2
90
Outside pressure is
balanced by thermal
quark gluon pressure
B
T 4 ..  B
PQGP  g
2
90
T 4 ..  B
4B
B
TC
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T
EQGP , PQGP need large corrections but
EQGP  3PQGP  4 B
Asakawa, Hatsuda PRD 97
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QCD vacuum vs. sQGP
Nonperturbative QCD vacuum
B
sQGP
MIT Bag
Vacuum with negative pressure
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.
 2

G  2 ( B 2  E 2 )  1500MeV/fm3 , dominated by non-perturbative contribution


2.
RG invariant, gauge invariant, characteristic vacuum property, couples to spin 0 field
3.
Can be calculated on the lattice (DiGiacomo et al. )
4.
Related to trace of energy momentum tensor through trace anomaly (Hatsuda 87)
 2
9 2
  D  T  ml q q  mh h h 
G 
G
4
8



5.
Nucleon expectation value is
6.
From
p | T | p  m 0p  
9

p G2 p
8

mq p | u u  d d | p  mq ( Bu  Bd )  45 MeV
m p  m0p  mu Bu  md Bd  ms Bs
we find
m0p  650MeV
m  m0p  mu Bu  md Bs  ms Bd
m  m0p  mu Bd  md Bs  ms Bu
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Gluon condensate in MIT Bag model
Using
 2
8
G   T

9
Inside nucleon
 2
G

 2
G

Inside
Inside

 2
G

outside
 p
 2
8
8
G p / V   (m 0p / V )   4 B

9
9
 1500MeV/fm3  578 MeV / V
for
m 0p  650 MeV
Inside QGP
 2
G

 2
G

QGP
QGP

 2
G

0

9
  3 p   8 4 B
8
9
 1500MeV/fm3  711MeV/fm3
Explicit lattice calculation of nonperturbative gluon condensate?
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 2
G

 2
G

for B  (200 MeV)4
0
QGP
(Digiacomo84)
(SHLee 89)
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Gluon condensate in QGP from lattice calculation
 2
G


non  perturbati ve
 2
G


lattice
 2
G

lattice perturbati on
value a 4  lattice signal  (cg 2  dg 4  .....)
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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
Nonperturbative QCD vacuum
fVac 
 2
G


70%
 2
G


30%
 2
G 0

B
sQGP
MIT Bag
Vacuum with negative pressure
fVac 
 2
G

 0.7
70%
 2
G

If phase transition occurs, there will be enhancement of massless
glueball excitation
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Summary 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/y in QGP
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J/y in Quark Gluon Plasma
Heavy quark potential on the lattice
T 0
V (r )
r
Karsch et al. (2000)
c
Higher T
c
c
c
J/y melt above Tc
r
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J/y suppression in Heavy Ion collision
1986: Matsui and Satz claimed J/y suppression is a signature of
formation of Quark Gluon Plasma in Heavy Ion collision
e
e
J /y
New RHIC data
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J/y in Quark Gluon Plasma
2003: Asakawa and Hatsuda claimed J/y 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/y peak at 3.1 GeV
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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/y form Coulomb bound states at Tc < T < ~2 Tc
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Relevant questions in J/y suppression
Became a question of quntative analysis
a) What are the effects of Dynamical quarks ?
b) What is the survial probability of J/y in QGP
 need to know J/y – gluon dissociation
 need to know J/y – 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
q
SG (q)  S (q)  S (q)G
 S (q)  ........... where,
S (q) 
1
q  m
Perturbative treatment are possible
because
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m  q   QCD even for q  0
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2. System with two heavy quarks
q
2
1
(q)  ...   dx
0
4m
F (q 2 , x)
2
 q 2  ( x  1 / 2) 2 q 2
n


G
 ..
n

Perturbative treatment are possible when
4m  q  
2
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2
2
QCD
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Perturbative treatment are possible when
q2
0
-Q2
<0
m2J/ y > 0
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4m2  q2  2QCD
expansion
parameter
process
2QCD
Photo production of open
charm
4m

2
QCD
2
QCD sum rules for heavy
quarks
Dissociation cross section
of bound states
2
4m  Q 2
2

2QCD
QCD
2
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mm2mJ m
/y J /y 0


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Historical perspective on
Quarkonium Haron interaction in QCD
1. Peskin (79), Bhanot and Peskin (79)
a) From OPE
gluon
J /y
b) Binding energy= 0 >> 
2. Kharzeev and Satz (94,96) , Arleo et.al.(02,04)
a) Rederive, target mass correction
b) Application to J/y physics in HIC
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Rederivation of Peskin formula
using Bethe-Salpeter equation (Lee,Oh 02)
Resum Bound state by
Bethe-Salpeter Equation
d 4K 
  p1 , p2 )   ig CF 
 i( K  p1  p2 )  ( K  p1  p2 , K ) i( K )   V ( K  p2 )
4
(2 )
2
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NR Power counting in Heavy bound state
1. Perturbative part
 0  mN c g 2 / 16   O(m g4 )
2

|k | 
O(m g2 )
4
2 3
m
g
(
m
g
)
2
g
(m g4 )(m g4 )(m g2 ) 2
 O(1)
2. External interaction: OPE
 2
 2
|p | |p |
0
mJ /y  k1  2m  1  2
2m
2m

0
k1  | k1 |  O(m g4 )
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LO Amplitude
suppressedby
M 
2
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4 g 2 m2 M f k02
3N c
y ( p)
1
Nc
2
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 had ( )   dx  g ( x ) g ( x)
However, near threshold, LO result is expected to have large correction
J /y
D
N
J /y
N
J /y
D
C
2
D
C
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Exp data
1
3
C
C
N
mb
s1/2 (GeV)
C
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NLO Amplitude
LO
:
(2m   0 )  g (k )  c ( p1 )  c( p2 )
 0 , k  O(m g4 ),
NLO :
p1 , p2  O(m g2 )
(2m   0 )  q(k1 )  c ( p1 )  c( p2 )  q(k 2 )
(2m   0 )  g (k1 )  c ( p1 )  c( p2 )  g (k 2 )
 0 , k1 , k 2  O(m g4 ),
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p1 , p2  O(m g2 )
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NLO Amplitude :   q  c  c  q
q1
Collinear divergence when q1=0.
Cured by mass factroization
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Mass factorization
q1
Gluons whose kcos q1 < Q scale,
should be included in parton
distribution function
q1
1
 2
ˆ
d

d


dx
Q 2  2 dˆ LO i
2
2
NLO i
NLO i
s
 sˆ'
s
 s

Pji ( x) 
  E  ln
2 

dt1du1
dt1du1 2 0 x
4 
dt1du1
 D4
Integration of transverse momentum from zero to scale Q
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NLO Amplitude :   g  c  c  g
Higher order
in g counting
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NLO Amplitude :   g  c  c  g - cont
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
m (1S ) , m ( 2S )
Fit quark mass and coupling from fitting
to coulomb bound state gives
0  1
GeV
mb  5.1 GeV
  0.5
 q QQ q
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  g QQ  g
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Total cross section for Upsilon by nucleon: NLO vs LO
NLO/LO
Large higher order corrections
Even larger correction for charmonium
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What do we learn from NLO calculation ?
1.
Large NLO correction near threshold, due to log terms
 2k 2 , 0 
log


 0 
where
 0  700 MeV for J/y
Thermal quark and gluon masses of 300 MeV will
Reduce the large correction
2.
Dissociation by quarks are less than 10% of that by gluons
 q QQ q

  g QQ  g
Quenched lattice results at finite temperature are reliable
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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
p 2 dp
  ( p) e p / T  1
  
p 2 dp
 e p /T 1
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Effective Thermal width: gluon vs quark effects
p 2 dp
 ng  deg   ( p) p / T
e 1
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Summary II
1.
We reported on the QCD NLO Quarkonium-hadron
dissociation 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/y 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/y
at finite temperature should be reliable.
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Reference 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
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