Comments on J/ y dissociation by partons Progress in QCD calculations: LO and NLO
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Transcript of Comments on J/ y dissociation by partons Progress in QCD calculations: LO and NLO
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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
22
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>