lee

Effects of thermal partons on

Charmonium states at finite Temperature



Su Houng Lee

Yonsei Univ., Korea



1. Introduction on J/y suppression in heavy ion

collision

2. Progress in QCD calculations: LO and NLO

3. Dissociation due to thermal gluons and quarks







References: Y. Oh, S. Kim, S.H.Lee, (LO) : PRC 65 (2002) 067901

Taesoo Song, S.H.Lee, (NLO) : PRD 72 (2005) 034002

K. Han, K. Kim, Y. Park, S.H.Lee: in preparation



CMT05 S.H.Lee 1

Quark Gluon Plasma





Proton

At high T Proton

and/or

Density







Proton









Nucleons in vacuum Quark Gluon Plasma





CMT05 S.H.Lee 2

J/y in Quark Gluon Plasma



Heavy quark potential on the lattice

c c

T 0

V (r ) Karsch et al. (2000) r

c c







Higher T J/y melt above Tc







r

CMT05 S.H.Lee 3

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

CMT05 S.H.Lee 4

J/y in Quark Gluon Plasma



2003: Asakawa and Hatsuda claimed J/y will survive up to 1.6 Tc







Quenched lattice calculation by Askawa and Hatsuda using MEM









T 1.6 Tc









J/y peak at 3.1 GeV

CMT05 S.H.Lee 5

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









CMT05 S.H.Lee 6

Progress in QCD calculations



LO and NLO









CMT05 S.H.Lee 7

Basics in Heavy Quark system





1. Heavy quark propagation



q







SG (q)  S (q)  S (q)GS (q)  .......... where,

. S (q) 

1

qm





Perturbative treatment are possible

because m  q  QCD even for q  0











CMT05 S.H.Lee 8

2. System with two heavy quarks







2

q





1 F (q 2 , x)

 (q)  ...   dx   G n  ..

0

4m 2

 q 2  ( x  1 / 2) 2 q 2 

n









Perturbative treatment are possible when



4m 2  q 2  2QCD



CMT05 S.H.Lee 9

Perturbative treatment are possible when 4m 2  q 2  2QCD





expansion

q2 process

parameter



Photo production of open 2QCD

0 charm 2

4m



QCD sum rules for heavy 2QCD

-Q2 0 of bound states  

24m 2mJmJ /y 0

m   /y 2



CMT05 S.H.Lee 10

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





CMT05 S.H.Lee 11

Rederivation of Peskin formula

using Bethe-Salpeter equation (Lee,Oh 02)



Resum Bound state by

Bethe-Salpeter Equation









d 4K 

  p1 , p2 )   ig 2CF   i( K  p1  p2 )  ( K  p1  p2 , K ) i( K )   V ( K  p2 )

(2 ) 4









CMT05 S.H.Lee 12

NR Power counting in Heavy bound state



 0  mN c g 2 / 16   O(mg 4 )

2

1. Perturbative part



|k |  O(mg 2 )





mg 4 (mg 2 ) 3

g2

(mg 4 )(mg 4 )(mg 2 ) 2

 O (1)





2. External interaction: OPE  2  2

|p | |p |

mJ /y  k1  2m  1  2

0



2m 2m



k1  | k1 |  O(mg 4 )

0









CMT05 S.H.Lee 13

LO Amplitude









1

suppressed by

Nc







4 g 2 m 2 M  k02

M  y ( p)

2 2



3N c





CMT05 S.H.Lee 14

 had ( )   dx  g ( x ) g ( x)

However, near threshold, LO result is expected to have large correction





J /y D mb

D

N C





2

J /y D

Exp data

1 3

N C



C

J /y

C

s1/2 (GeV)

N C







CMT05 S.H.Lee 15

NLO Amplitude





LO :  (2m   0 )  g (k )  c ( p1 )  c( p2 )





 0 , k  O(mg 4 ), p1 , p2  O(mg 2 )





NLO :  (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(mg 4 ), p1 , p2  O(mg 2 )









CMT05 S.H.Lee 16

NLO Amplitude :   q  c  c  q









q1









Collinear divergence when q1=0.

Cured by mass factroization









CMT05 S.H.Lee 17

Mass factorization







q1 Gluons whose kcos q1 < Q scale,

should be included in parton

distribution function









q1



d NLO i

ˆ d NLO i  s  2 Q 2  2 d LO i

ˆ

1

dx

s 2

dt1du1

 s 2 

dt1du1 2 x

0

Pji ( x) 

 D4



  E  ln  s'

4 2 



ˆ

dt1du1



Integration of transverse momentum from zero to scale Q





CMT05 S.H.Lee 18

NLO Amplitude :   g  c  c  g









Higher order

in g counting









CMT05 S.H.Lee 19

NLO Amplitude :   g  c  c  g - cont



Previous diagrams can be reproduced with effective four point vertex









CMT05 S.H.Lee 20

Cancellation of infrared divergence



Remaining Infrared Divergence cancells after adding one loop corrections









CMT05 S.H.Lee 21

Application to Upsilon dissociation cross section



Fit quark mass and coupling from fitting m (1S ) , m ( 2 S )

to coulomb bound state gives

0  1 GeV

mb  5.1 GeV

  0.5









 q QQ q   g QQ  g





CMT05 S.H.Lee 22

Total cross section for Upsilon by nucleon: NLO vs LO





NLO

NLO/LO







LO









Large higher order corrections

Even larger correction for charmonium







CMT05 S.H.Lee 23

What do we learn from NLO calculation ?



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

 2k 2 , 0 

log   0  700 MeV for J/y

0 

where

 





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









CMT05 S.H.Lee 24

Total cross section: gluon vs quark effects





With thermal mq = mg = 200 MeV









CMT05 S.H.Lee 25

Effective Thermal cross section: gluon vs quark effects



p 2 dp

  ( p) e p / T  1

  

p 2 dp

 e p /T 1









CMT05 S.H.Lee 26

Effective Thermal width: gluon vs quark effects





p 2 dp

 ng  deg   ( p) p / T

e 1









CMT05 S.H.Lee 27

Summary



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.



CMT05 S.H.Lee 28