A NLO Analysis on Fragility of Dihadron Tomography in High Energy AA Collisions
I. IntroductionII. Numerical analysis on single
hadron and dihadron productionIII. Conclusions
Han-Zhong ZhangInstitute of Particle Physics, Huazhong Normal University, China
Co-authors: J. Owens E. Wang X.-N. Wang
Quark Matter 2006 Nov. 18 , 2006
I. Introduction
Hard Probe Signal of QGP in RHIC and LHC
Jet quenching:
Induced by multiple scattering in QGP medium, a parton
jet will radiate gluon and lose its energy.
Han-Zhong Zhang IOPPQM 2006 Shanghai 2
hadrons
q
q
hadrons
leadingparticle
leading particle
N-N collision
hadrons
q
q
hadrons
Leading particle suppressed
leading particle suppressed
A-A collision
3
)(),,(|)|,,(),,(
2
1|)(|)(
2
1
2/
2/
2/
22
)(
cdabEQzDbrQxfrQxf
sxxbrtrtdzdxrdxbdddK
d
d
ccchbAbaAa
baBAcba
eabcd
hAA
Jet quenching in 2→2 processes
LO analysis of jet quenching in AA:
2→2 processes (tree level)
A factor K=1.5-2 was put by hand to account for higher order corrections
Han-Zhong Zhang IOPPQM 2006 Shanghai
4
Jet quenching in 2→3 processes
Motivation : 1) contribution for higher order correction?
2) find a robust probe of dense matter
2→3 processes (tree level)
NLO (Next to Leading Order ) corrections:
One-loop corrections
(Jeff. Owens , PRD65(2002)034011; B.W. Harris and J. Owens , PRD65(2002)094032)
qg EE 4
9
K is absent
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Jet Quenching effects lead to the modification of FF
Modified Fragmentation Function (FF)
),(
)],(/),()[1(),,(
2'0/
/
2'0/
'2'0
/
'/2
/
cchL
gghc
gcch
c
cLccch
zDe
zDz
zLzD
z
zeEzD
0000
/1),,,(0
0
nrb
dLg
L
5
KKP
(X. -N. Wang , PRC70(2004)031901)
,//),/( ''cTgcTcTc EpLzEppz
and the averaged scattering number,
where
It determines the thickness of the outer corona where a parton jet survives in the overlapped region.
Han-Zhong Zhang IOPPQM 2006 Shanghai
),,(0
000
0
1
nrbd
dL
dEE g
L
d
)/5.7/()6.1/( 02.1
001
EEdL
dE
d
In 1-demension expanding medium, the total energy loss:
The energy loss with detailed balance:(Enke Wang and Xin-Nian Wang, PRL87(2001)142301)
6
An energy loss parameter proportional to the initial gluon density
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II. Numerical analysis on single hadron and dihadron production
7
1) fix scales and energy loss parameter
2) the centrality dependent of the
suppression factor
3) hadron contour plot
4) fragility of single and dihadron tomography
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p-p data at 200GeV are used to fix scales,
The invariant p_T spectra of single hadron
Th p2.1
8Han-Zhong Zhang IOPPQM 2006 Shanghai
0-10% AuAu data at 200GeV are used to fix the energy
loss parameter (proportional to the initial gluon density):
fmGevGeVAuAu /68.1)200(0
9Han-Zhong Zhang IOPPQM 2006 Shanghai
fmy 0
11
y
xSingle hadron
Color strength = single hadron yield from partons in the square
parton jet
emission surface
completely suppressed
Single hadron is dominated by surface emission
fmGev /68.10
coronathickness
Han-Zhong Zhang IOPPQM 2006 Shanghai
12
1.68
Similar to the study by K. J. Eskola , H. Honkanen, C. A. Salgado, U. A. Wiedemann, NPA747 (2005) 511-529
is a fragile probe of dense matter.AAR
loses its effectiveness as a good probe of dense matter
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Fit dAu data by pp result to fix scales,
Mhh 2.1
Invariant mass2
212 )( ppM
TtrigTassoTT
hhAA
trigAA
TAA ppzdz
dN
NzD /,
1)( No jet quenching in d+Au,
)()( TppTdAu zDzD
13
of dihadron in Au+Au collisions)( TAA zD
0.3
ppD
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The ratio between the yield/trigger in AA and in pp:
trigpp
hhpp
trigAA
hhAA
trigpp
hhpp
trigAA
hhAA
yieldpp
partyieldAA
partAA
bb
NN
bNbN
D
NDNI
/
)(/)(
/
)(/)()()(
If no jet quen-ching,
1AAI
15
PRL95(2005)152301
0.3
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partonic di-jet
N
Stangential
fmx 0
16
y
xtriggered hadron
associated hadron
Color strength = dihadron yield from partons in the square
Dihadron is from surface emission + punch-through jets
fmGev /68.10
punch-through jets25% left
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LOAA
NLOAA
LOAA
NLOAA IIRR ,
17
3.0AAI
1.68
is a robust probe of dense matter.AAI at 200GeV
Trigger:8GeVat RHIC
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18
is a robust probe of dense matter.AAI at 5.5TeV
LOAA
NLOAA
LOAA
NLOAA IIRR ,
Trigger:20GeVat LHC
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LHC
III. Conclusions
19
Because of the additional 2→3 processes, NLO contributions
behave with stronger quenching effect than LO contributions: LOAA
NLOAA RR LO
AANLOAA II
Because of the stronger quenching effects, the single hadron is dominated by surface emission;the dihadron is from surface emission + punch-through jets.
The dihadron is more sensitive to the initial gluon densitythan the single hadron . When becomes fragile in higher energy AA, is a robust probe of dense matter.
AAIAAR
AAIAAR
Without inputing K factor by hand, NLO results fit data well.
1)
2)
3)
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))((),,(|)|,,(),,(
2
1|)(|)(
2
1
2/
2/
2/
22
)(
ecdabEQzDbrQxfrQxf
sxxbrtrtdzdxrdxbddd
d
d
ccchbAbaAa
baBAcba
eabcd
hAA
))((),,(),,(|)|,,(),,(
2
1|)(|)(
2
1
2/
2/
2/
2/
22
)(
ecdabEQzDEQzDbrQxfrQxf
sxxbrtrtdzdzdxrdxbddd
d
d
dddhccchbAbaAa
baBAdcba
eabcd
hhAA
is the differential 2-body or 3-body phase space elementd
The inclusive cross sections for single hadron production:
The inclusive cross sections for dihadron production:
32~))(( ssecdab is the squared matrix elements
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Hard sphere model
|)(|)()( 2 brtrrtdbT BAAB
222
/12
3)( Rr
R
ArtA
R bT
b bT
ABNNin
ABNNin
ebd
ebdcentrality 2
0
)(2
0
)(2
]1[
]1[
r
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nuclear modification factor
dydpdN
dydpdpR
TNN
binary
TAA
TAA 2
2
/
/)(
|)(|)(),(max
min
22maxmin brtrrtbddbbN
b
b AAbinary
)(
2222
/13
)(br
partpart RrrdR
AbNN
dydp
bbd
bbdydp
dN
T
hAA
AAinT
hAA
2maxmin
maxmin2
),(
),(
1
the formula of spectra in AATp
dydpddpbT
dydpdbddpNR
TNN
TAA
TAA
T
partAA
22
222
/)(
/)(
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(Shi-Yuan Li and Xin-Nian Wang , PLB527(2002)85)
(Enke Wang and Xin-Nian Wang, PRL87(2001)142301)
(B. B. Back et al. [PHOBOS collaboration], PRC70(2004)021902)
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Nuclear shadowing
effects only
in small pT region
So in large pT,
medium effects
only come from
Jet Quenching !!!
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Invariant mass: 221
2 )( ppM
How to fix scales: M
trigTtrighAAtrigTtrig
assotrigTassoTtrighhAATtrigassotrigTtrig
T
hhAA
trigAA
TAA
TtrigTassoT
dydpddydp
ddydydpdpdpddydydp
dz
dN
NzD
ppz
/
/
1)(
,/
If no medium effects, )()()( TppTdAuTAuAu zDzDzD
(X. –N. Wang , PLB 595(2004)165
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The dihadron azimuthal distributions
trigTtrighAAtrigTtrig
assotrigTassoTtrighhAAassotrigTassoTtrig
hhAA
trigAA dydpddydp
ddydydpdpddydydpdp
d
dN
N /
/1
ddydydpdppp
bbd
bbddydydpdppp
dN
TTTT
hhAA
AAinTTTT
hhAA
212121
maxmin
maxmin212121 2
),(
),(
1
2
212
221
maxmin
maxmin212
221
),(
),(
1
dydydpdp
bbd
bbdydydpdp
dN
TT
hhAA
AAinTT
hhAA
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There are much more punch-through jets in higher energy AAcollisions, increases while decreases with collision energy.
AARAAI
RHIC LHC
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