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Dihadron Tomography of High Energy AA Collisions in NLO pQCD
Hanzhong Zhang
Department of Physics, Shandong UniversityInstitute of Particle Physics, Central China Normal University
Jinan, Jan. 9, 2008
Collaborators: Enke Wang Joseph F. Owens Xin-Nian Wang
1) Phys. Rev. Lett. 98(2007)212301 2) J. Phys. G. 34(2007)S8013) To be submitted.
2
Outline
I. Introduction
II. Modified fragmentation function model
III. Numerical analysis on single hadron and dihadron production
IV. Conclusions
3
I. Introduction
1. What is “Dihadron tomography” ?
1) Medical x-ray tomography:
see inside a “bone” by x-ray.
2) Jet tomography:
see inside “QGP” by a parton jet,
not only by single jet, but also by dijet.
3) Hadron/Dihadron tomography:
we can’t “catch” a parton jet/dijet,
but can “catch” a hadron/dihadron.
4
2. How to know a tomography of QGP ?---- Jet Quenching !
Jet quenching:
Induced by multiple scattering in QGP medium, a parton
jet will radiate gluon and lose its energy.
hadrons
q
q
hadrons
leadingparticle
leading particle
N-N collision
hadrons
q
q
hadrons
Leading particle suppressed
leading particle suppressed
A-A collision
5
),,()(|)|,,(),,(
2
1|)(|)(
2
1
2/
2/
2/
22
)(
ccchbAbaAa
baBAcba
eabcd
hAA
EQzDcdabbrQxfrQxf
sxxbrtrtdzdxrdxbdddK
d
d
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
3. Why NLO study?
pQCD
Parton
Model
6
Jet quenching in 2→3 processes2→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
NLO:More stronger quenching;More clearer QGP picture.
7
4. Why dihadron tomography study?
• Single hadron suppression factor is found to be
fragile to probe the dense matter. K. J. Eskola , et al, NPA747 (2005) 511-529
• One of the motives of this work:
How about dihadron? fragile or robust?
8
Jet Quenching effect in AA is incorporated via a model of modified fragmentation functions:
II. Modified fragmentation functions model
),(
)],(/),()[1(),,(
2'0/
/
2'0/
'2'0
/
'/2
/
cchL
gghc
gcch
c
cLccch
zDe
zDz
zLzD
z
zeEzD
(X. -N. Wang , PRC70(2004)031901)
,//),/( ''cTgcTcTc EpLzEppz where
Two contributions from jets in vacuum and medium!
Jet energy loss
9
),(
)],(/),()[1(),,(
2'0/
/
2'0/
'2'0
/
'/2
/
cchL
gghc
gcch
c
cLccch
zDe
zDz
zLzD
z
zeEzD
),,,(0
000
nrb
dLg
L
the averaged scattering number,
It determines the thickness of the outer corona where a parton jet survives in the overlapped region.
|)],(|)([2
),,(2
00 rbtrtA
Rrb AA
Ag
the gluon density distribution,
10
gg
L
d
Lnrbd
dL
dEE
),,(
0
000
0
1
)/5.7/()6.1/( 02.1
001
EEdL
dE
d
In 1-demension expanding medium, the total energy loss is written as a path integration:
The energy loss per unit lenth with detailed balance:(Enke Wang and Xin-Nian Wang, PRL87(2001)142301)
An energy loss parameter proportional to the initial gluon density 00
11
010
0
2ˆ
dCs dL
dE
Nq
In BDMPS calculation for the radiative parton energy loss,
is equivalent to 0q̂0
2 ˆ 4
LqN
E CS Baier, Dokshitzer, Mueller,
Peigne, Schiff, NPB484(1997)265
where is a jet transport or energy loss parameter,q̂
reflects the ability of the medium to “quench” jets.
By Wang2 and BDMPS formulas, estimate the average jet transport parameter by
J. C. Solana and X. -N. Wang,hep-ph/0705.1352
0
12
III. Numerical analysis on single hadron and dihadron production
1. Single hadron tomography
2. Dihadron tomography
3. Estimate jet transport parameter
4. Comparison between different shadowing
5. LHC predictions
0q̂
14
The invariant p_T spectra of single hadron
With ,p_T spectra in AA is not also sensitive to the choice of
Set ,since p_T spectra in pp is not at all sensitive to the choice of
Th p2.1
h
Th p2.1
0
fmGevGeVAuAu /68.1)200(0
15
Nuclear modification factordydpdN
dydpdpR
TNN
binary
TAA
TAA 2
2
/
/)(
NLOAAR
is 10% larger than
LOAAR
is not sensitive to the initial gluon density
)( TAA pR 00
16
Centrality dependence
dydpddpbT
dydpdbddpNR
TNN
TAA
TAA
T
partAA 22
222
/)(
/)(
AAR is not sensitive to ,and
partN
gpartN ~
17
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
1.68
loses its effectiveness as a good probe of dense matter
Why the single hadron tomographyis fragile to probe the dense matter?
The bigger is,the flatter is.
AAR
0
18
y
xSingle hadron
Color strength = single hadron yield from partons in the square
parton jet
emission surface
completely suppressed
Single hadron is dominated by vertical surface emission
fmGev /68.10
coronathickness
AAR
19
Is there a robust probe of the dense matter produced in AA collisions?
Let’s see dihadron production!
Trigger one hadron of a dihadron, check the other hadron --- the associated hadron
2. Dihadron tomography
20
Fit dAu data by pp result to fix scales,
Mhh 2.1
Invariant mass
221
2 )( ppM
trigT
assocTT
T
hhAA
trigAA
TAA ppzdz
dN
NzD /,
1)( No jet quenching in d+Au,
)()( TppTdAu zDzD
The dihadron spectra in Au+Au collisions
68.10
23
Comparison between single hadron and dihadron tomography in Au+Au collisions
dihad
ron
single
had
ron
24
3.0AAI
1.68
Dihadron is a robust probe of dense matter.
The curve is steeper than when AARAAI 0.20.10
25
2 comparison between single hadron and dihadron suppression factor
AAR
N
j TjEx
TjThAATj
ExAA
pN
pRpR
12
20
02
)()1(
)],()([)(
for
95.045.0
158
T
trigT
z
GeVp
GeVpT 204 for single
for dihadron
fmGeV /1.25.10
26
Why does the dihadron behave more robust than single hadron to probe the dense matter?
Single hadron is dominated by vertical surface emission
dihadron ?
27
partonic di-jet
N
Stangential
y
xtriggered hadron
associated hadron
Color strength = dihadron yield from partons in the square
Dihadron is from tangential surface emission + punch-through jets
fmGev /68.10
punch-through jets25% left
30
Au+Au@RHIC 200GeV
Single hadron and dihadron are all not sensitive to different shadowing at RHIC
dihad
ron
single
had
ron
31
Trigger:20GeVat LHC
LHC
5. LHC predictions
0 is estimated as 4.5-5. 5 GeV/fm at LHC
Single hadron fragileDihadron robust
32
There are much more punch-through jets in higher energy AAcollisions, increases while decreases with collision energy.
AARAAI
RHIC LHC
34
Different shadowing in Pb+Pb@LHC 5500GeV
Single hadron not sensitive to different shadowing.
Dihadron sensitive to different shadowing because of much more punch-through jets.
dihad
ron
single
had
ron
36
Why is only Dihadron Iaa at LHC sensitive to different shadowing parameterizations, HIJ, EKS, nDS, nPDF?
1) Punch-through jets are created from central system region;
2) Initial partons participating in strong interaction in central region should be associated with stronger shadowing effects than those initial partons in the outer layer of the system;
3) So punch-through jets manifest a strong shadowing effect. There are much more punch-through jet contributing to dihadron spectra at LHC than at RHIC. So does dihadron than single hadron.
H. Zhang, J.F. Owens, E. Wang and
X.-N. Wang , hep-ph/0000008
37
Because of the stronger quenching effects, the single hadron is dominated by vertical surface emission;the dihadron is from tangential surface emission + punch-through jets.
The dihadron is more sensitive to the initial gluon densitythan the single hadron . When becomes insensitive in higher energy A+A collision, is a sensitive probe of dense matter.
AAI
2
AARAAI
AAR
-fit to both single and dihadron spectra can be achieved with a narrow range of the energy loss parameter
at RHIC energy, it provide convincing evidence for the jet quenching description.
1)
2)
3)
IV. Conclusions
fmGeV /1.25.10
4) Dihadron Iaa at LHC is found to be able to distinguish different shadowing parameterizations.
39
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
40
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
/)(
/)(
41
(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)
42
Nuclear shadowing
effects only
in small pT region
So in large pT,
medium effects
only come from
Jet Quenching !!!
44
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
45
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
46
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
PRL95(2005)152301
0.3
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