Comments on J/ y dissociation by partons Progress in QCD calculations: LO and NLO

QM06 - S.H.LeeQM06 - S.H.Lee

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1. Comments on J/ dissociation by partons

2. Progress in QCD calculations: LO and NLO

3. Dissociation due to thermal gluons and quarks

J/ hadron interaction in vacuum and in QGP

Su Houng LeeYonsei Univ., Korea

References: Y. Oh, S. Kim, S.H.Lee, (LO) : PRC 65 (2002) 067901 Taesoo Song, S.H.Lee, (NLO) : PRD 72 (2005) 034002 Y. Park, K. Kim, T. Song, K. Ohnishi, K. Morita S.H.Lee …


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1. 1986: Matsui and Satz J/ suppression

2. Nuclear and comover suppression

3. SPS data

J/ suppression in Heavy Ion collision

4. Thermal enhancement

5. Lattice shows J/ survives up to 1.6 Tc (Asakawa, Hatsuda .. )

6. Preliminary RHIC data

SPS data

RHIC data


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Relevant questions and steps in J/ suppression

c

c

J/

cc

1. c c are produced by hard collision2. Tinitial > 300 MeV in RHIC3. As systems cools, J/is formed at 1.6 Tc4. Dissociation effects until Tc ? 5. Suppression in hadronic phase …

Calculate J/ dissociation cross section by partons


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Progress in QCD calculations

LO and NLO


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Basics in Heavy Quark system

1. Heavy quark propagation

mqqS

1)( where,...........)()()()( qSGqSqSqSG

Perturbative treatment are possible

because 0for even qqm QCD

q


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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


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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


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Quarkonium Hadron interaction in QCD - LO

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 (02)

)( || 41

01 mgOkk

1k

NR Power counting in Heavy bound state

)( ||

)( 16/2

4220

mgOk

mgOgNm c

)1(

))()((

)(2244

3242

O

mgmgmg

mgmgg


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LO Amplitude

gluon

/J

k p

0 ),()(|)()(

Mkpdp

dkpcckM


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Not so large, however, LO QCD result is known to underestimate nucleoNot so large, however, LO QCD result is known to underestimate nucleon absorption cross sectionn absorption cross section

)()( )( xgxdx ghad

s1/2 (GeV)

Exp data from pA

Oh, Kim ,SHL 02


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NLO Amplitude (Song, SHL 05)

)(, ),(,,

)()()()()2(

)()()()()2( : NLO

)(, ),(,

)()()()2( : LO

221

4210

22110

22110

221

40

210

mgOppmgOkk

kgpcpckgm

kqpcpckqm

mgOppmgOk

pcpckgm


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NLO Amplitude : qccq

1

Collinear divergence when 1=0.

Cured by mass factroization


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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


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NLO Amplitude : gccg


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Total cross section for Upsilon by nucleon: NLO vs LO

Large higher order corrections

Even larger correction for charmonium

NLO/LO

T. Song and SHL, PRD 72, 034002 (2006)


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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. But at finite temperature, thermal masses will regulate the large correction2. 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


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Thermal width of J/

LO and NLO


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Assume cc bound state above Tc

2. C. Y. Wong… : Deby screened potential

(Ge V)

0

-0.8

Tc 1.6xTc

J/ Binding energy as a function T J/ wave functions at finite T

These will be used throughout this workBut result is the same when <r2> is fixed


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LO +g c+c

kp

pkg

2

2

and 0.5

)(...)(

)( )( )( 2 knkkvdkcvT ggg

k

Increasing T

0en smaller wh becoms gm


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NLO +q c+c+q

kpm

pmkk

g

qg

2

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and 0.5, MeV, 300

)(]./)log[(..)(

)( )( )( 2 knkkvdkcvT qqNLOqNLO

k

)(kgLO

)(kgNLO

Low T

Hight T


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NLO +g c+c+g

kp

pmkgk gg

2

22

and

)(]./)log[(..)(

)( )( )( 2 knkkvdkcvT ggNLOgNLO

kNLO

)(kqNLO

)(kgNLO

4 body decay ?


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Result and SummaryResult and Summary

2. We showed that the process q(g)+J/2. We showed that the process q(g)+J/ c+ c+cc+q(g) gives large ther+q(g) gives large thermal width (200 MeV) for J/mal width (200 MeV) for J/ from 1.3 to 1.6 T from 1.3 to 1.6 Tcc

this corresponds to about <>= 2-3 mb

3. In heavy ion collision, as the initial QGP cools down, J/will start forming at 1.6 Tc. However, the dissociation from 3 body decay is very large.

J/ dissociation will become smaller only near Tc

1.1. Reported on the quarkonium parton dissociation cross section Reported on the quarkonium parton dissociation cross section at NLO in QCD at NLO in QCD

Result depends of wave function or size <r2>

Documents

Comments on J/ y dissociation by partons Progress in QCD calculations: LO and NLO