Transcript Dihadron Tomography - Shandong University

Dihadron Tomography of High Energy
AA Collisions in NLO pQCD
Hanzhong Zhang
Department of Physics, Shandong University
Institute of Particle Physics, Central China Normal University
1) Phys. Rev. Lett. 98(2007)212301
2) J. Phys. G. 34(2007)S801
3) To be submitted.
Collaborators: Enke Wang
Joseph F. Owens
Xin-Nian Wang
Jinan, Jan. 9, 2008
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Outline
I.
Introduction
II. Modified fragmentation function model
III. Numerical analysis on single hadron
and dihadron production
IV. Conclusions
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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.
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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.
leading
particle
hadrons
Leading
particle
suppressed
hadrons
q
q
q
q
hadrons
leading particle
N-N collision
hadrons
leading
particle
suppressed
A-A collision
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3. Why NLO study?
LO analysis of jet quenching in AA :
A factor K=1.5-2 was put by hand to
account for higher order corrections
h
d AA
1
1

 
pQCD
2
2
K 
d

d
bd
rdx
dx
dz
t
(
r
)
t
(|
r

b
|)
a
b
c A
B

d
2

2 xa xb s
abcd ( e )
Parton



 f a / A ( xa , Q 2 , r ) f b / A ( xb , Q 2 , | r  b |) (ab  cd ) Dh / c ( zc , Q 2 , Ec ) Model
2→2 processes (tree level)
Jet quenching in 2→2 processes
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NLO (Next to Leading Order ) corrections:
K is absent
One-loop corrections
2→3 processes (tree level)
Jeff. Owens ,
PRD65(2002)034011;
B.W. Harris and J. Owens,
PRD65(2002)094032.
E g 
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Eq
4
Jet quenching in 2→3 processes
NLO:
More stronger quenching;
More clearer QGP picture.
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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?
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II. Modified fragmentation functions model
Jet Quenching effect in AA is incorporated
via a model of modified fragmentation functions:
Dh / c ( zc ,  2 , Ec )  (1  e
e
 L/
Dh0/ c ( zc' ,  2 )
 L/
)[
'
c
z g'
z 0 ' 2
Dh / c ( zc ,  )  L / 
Dh0/ g ( z g' ,  2 )]
zc
zc
(X. -N. Wang , PRC70(2004)031901)
where zc'  pT /( pTc  Ec ), zg'  L /  pT / Ec ,
Jet energy loss
Two contributions from jets in vacuum and medium!
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Dh / c ( zc ,  2 , Ec )  (1  e
e
 L/
 L/
z g' 0
zc' 0 ' 2
)[ Dh / c ( zc ,  )  L / 
Dh / g ( z g' ,  2 )]
zc
zc
Dh0/ c ( zc' ,  2 )
the averaged scattering number,
L

0 L

0
d
00
  
 g ( , b , r  n ),
It determines the thickness of the outer corona where
a parton jet survives in the overlapped region.
the gluon density distribution,
   0  0 RA2
 

 g ( , b , r ) 
[t A (r )  t A (| b  r |)],
 2A
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In 1-demension expanding medium,
the total energy loss is written as a path integration:
dE
E 
dL
0 L
1d

0
  
  0
d
 g ( , b , r  n )
 0 0
L

 g
The energy loss per unit lenth with detailed balance:
(Enke Wang and Xin-Nian Wang, PRL87(2001)142301)
dE
dL
  0 ( E / 0  1.6)1.2 /(7.5  E / 0 )
1d
An energy loss parameter
proportional to the initial gluon density
 0  0
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 0 is equivalent to qˆ0
In BDMPS calculation for the radiative parton energy loss,
E 
where
 S NC
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qˆ
Baier, Dokshitzer, Mueller,
Peigne, Schiff, NPB484(1997)265
qˆ L2
is a jet transport or energy loss parameter,
reflects the ability of the medium to “quench” jets.
By Wang2 and BDMPS formulas,
estimate the average jet transport parameter by
qˆ0 
2
dE
 0 s NC dL
 0
0
J. C. Solana and X. -N. Wang,
hep-ph/0705.1352
1d
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III. Numerical analysis on single hadron
and dihadron production
1.
2.
3.
4.
5.
Single hadron tomography
Dihadron tomography
Estimate jet transport parameter qˆ0
Comparison between different shadowing
LHC predictions
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1. Single hadron tomography
single inclusive

0
or


(h  h ) / 2
production
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The invariant p_T spectra of single hadron
h

 1.2 pT ,
Set
since p_T spectra
in pp is not at all
sensitive to the
choice of  h
With   1.2 pT ,
p_T spectra in
AA is not also
sensitive to the
choice of  0
h
 0 ( AuAu200GeV )  1.68Gev / fm
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Nuclear modification factor
is not sensitive to  0  0
the initial gluon density
RAA ( pT )
d AA / dpT2 dy
RAA ( pT ) 
N binary d NN / dpT2 dy
LO
RAA
is 10%
NLO
larger than RAA
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Centrality dependence RAA ( N part ) 
2
AA
2
2
dp
d

/
db
dp
dy
T
T

TAA (b)  dpT2 d NN / dpT2 dy
R AA is not
sensitive
to N part ,
and
N part ~  g
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R AA is a fragile probe of dense matter.
loses its effectiveness as a
good probe of dense matter
Similar to the study
by K. J. Eskola ,
H. Honkanen,
C. A. Salgado,
U. A. Wiedemann,
NPA747 (2005)
511-529
The bigger  0 is,
the flatter R AA is.
1.68
Why the single hadron tomography
is fragile to probe the dense matter?
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Single hadron is dominated by
vertical surface emission
emission surface
y
Single hadron
x
parton jet
Color strength = single hadron
yield from partons in the square
 0  1.68Gev/ fm
completely
suppressed
corona
thickness
R AA18
2. Dihadron tomography
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
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The dihadron spectra in Au+Au collisions
hh
1 dNAA
DAA ( zT )  trig
, zT  pTassoc / pTtrig
N AA dzT
No jet quenching in d+Au,
DdAu ( zT )  Dpp ( zT )
Fit dAu data by pp
result to fix scales,
 hh  1.2M
Invariant mass
M 2  ( p1  p2 ) 2
 0  1.68
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The dihadron suppression factor
in Au+Au collisions I AA ( zT )  DAA ( zT ) / Dpp ( zT )
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If no jet quenching,
yield
DAA
( N part )
 const.
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Comparison between single hadron and
dihadron tomography in Au+Au collisions
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Dihadron is a robust probe of dense matter.
I AA  0.3
1.68
The I AA curve is steeper than R when  0  1.0  2.0
AA
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 2 comparison between single hadron
and dihadron suppression factor
pTtrig  8  15GeV
zT  0.45  0.95
for dihadron
pT  4  20GeV
for single
 0  1.5  2.1GeV / fm
N
Ex
Th
[ RAA
( pTj )  RAA
( 0 , pTj )]2
j 1
( N  1) ( pTj )
 2 ( 0 )  
Ex
2
for R AA
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Why does the dihadron behave more robust
than single hadron to probe the dense matter?

  
Single hadron is dominated by
vertical surface emission

dihadron ?
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Dihadron is from tangential surface
emission + punch-through jets
N
y
triggered hadron
x
associated hadron
 0  1.68Gev/ fm
partonic di-jet
S
tangential
punch-through jets
25% left
Color strength = dihadron yield
from partons in the square
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3. Estimate jet transport parameter qˆ0
qˆ0 0  1.6  2.2GeV 2
 0  1 fm
qˆ0  1.6  2.2GeV 2 / fm
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4. Comparison between different shadowing
p+Au@RHIC 200GeV
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Au+Au@RHIC 200GeV
Single hadron and dihadron are all not
sensitive to different shadowing at RHIC
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5. LHC predictions
 0 is estimated as 4.5-5. 5 GeV/fm at LHC
LHC
Trigger:
20GeV
at LHC
Dihadron robust
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Single hadron fragile
There are much more punch-through jets in higher energy AA
collisions, I AA increases while R AA decreases with collision energy.
RHIC
LHC
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Different shadowing in p+Pb@LHC 5500GeV
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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. 34
2) Punch-through jets contributing to hadron spectra at LHC
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Why is only Dihadron Iaa at LHC sensitive to different
shadowing parameterizations, HIJ, EKS, nDS, nPDF?
H. Zhang, J.F. Owens, E. Wang and
X.-N. Wang , hep-ph/0000008
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.
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IV. Conclusions
1) Because of the stronger quenching effects,
the single hadron is dominated by vertical surface emission;
the dihadron is from tangential surface emission + punchthrough jets.
2) The dihadron I AA is more sensitive to the initial gluon density
than the single hadron R AA . When R AA becomes insensitive in
higher energy A+A collision, I AA is a sensitive probe of dense
matter.
3)
 2-fit to both single and dihadron spectra can be achieved with
a narrow range of the energy loss parameter  0  1.5  2.1GeV / fm
at RHIC energy, it provide convincing evidence for the jet
quenching description.
4) Dihadron Iaa at LHC is found to be able to distinguish
different shadowing parameterizations.
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Thank for your attention!
谢谢！
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Hard sphere model

r


  
3A

2
2
t A (r ) 
1

r
/
R
2R 2

 
2
TAB (b)   d rt A (r )t B (| r  b |)

centrality 

b
d b[1  e
0
2R
0
2
 inNN TAB ( b )
d b[1  e
2
]
 inNN TAB ( b )
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]
the formula of pT spectra in AA
h
h
d AA
(bmin , bmax )
dNAA
1
 AA
2
dpT dy  in (bmin , bmax )
dpT2 dy
nuclear modification factor
d AA / dpT2 dy
RAA ( pT ) 
N binary d NN / dpT2 dy
Nbinary (bmin , bmax )  
R AA ( N part ) 
bmax
bmin
N part
3A
 N part (b)  2
R
2
AA
2
2
dp
d

/
db
dp
T dy
 T
TAA (b)  dpT2 d NN / dpT2 dy

 
d bd rt A (r )t A (| r  b |)
2
2
2
2
2
d
r
1

r
/
R

r (b)
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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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The invariant p_T spectra of single hadron
p-p data at 200GeV are used to fix scales,
 h  1.2 pT
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Invariant mass: M 2  ( p1  p2 ) 2
How to fix scales:   M
zT  pTasso / pTtrig ,
hh
1 dN AA
DAA ( zT )  trig
N AA dzT


  

(X. –N. Wang , PLB 595(2004)165
hh
dp
dy
dy
d



p
d

Ttrig
AA / dpTtrig dpTasso dytrig dyasso d
 Ttrig trig asso
h
dp
dy

d

 Ttrig trig AA / dpTtrig dytrig
If no medium effects,
DAuAu ( zT )  DdAu ( zT )  Dpp ( zT )
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The dihadron azimuthal distributions
hh
hh
d AA
(bmin , bmax )
dNAA
1
 AA
2
2
dpT 1dpT 2 dy1dy2  in (bmin , bmax ) dpT21dpT2 2 dy1dy2
hh
hh
d AA
(bmin , bmax )
dNAA
1
 AA
2pT 1 pT 2 dpT 1dpT 2 dy1dy2 d  in (bmin , bmax ) 2pT 1 pT 2 dpT 1dpT 2 dy1dy2 d
hh
AA
1 dN

trig
N AA d
hh
dp
dp
dy
dy

d

 Ttrig Tasso trig asso AA / dpTtrig dpTasso dytrig dyasso d
h
dp
dy

d

 Ttrig trig AA / dpTtrig dytrig
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The ratio between the yield/trigger in AA and in pp:
I AA ( N part ) 
yield
DAA
( N part )
yield
D pp
hh
trig
hh
trig
N AA
(b) / N AA
(b)  AA
(b) /  AA
(b)


hh
trig
hh
N pp / N pp
 pp
/  trig
pp
If no jet quenching,
I AA  1
0.3
PRL95(2005)152301
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