Download - Xin-Nian Wang LBNL
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Xin-Nian WangLBNL
First Workshop on Quark-Hadron Duality and the Transition to pQCDFrascati, June 6-9, 2005
Quark-hadron Duality of Hadronization in Nuclei
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QCD
hadronsfrom Mars
quarksfrom Venus
Quark-hadron Duality
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Quark scattering or hadron absorption?
e-
Quark propagation and scattering,
Hadronization outside the nuclei
Hadronization inside nuclei
Hadron absorption
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Conclusions
• Never promise any great ideas!
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Quark Fragmentation Function
Sqhhq
zyiphhhq ySpSpTre
dyzzD hh 0)(,,)0(0
222)( /
)()(0 zDzDdz
dhqhq
q S
e+e- annihilation
)(),(42
14
4
qWqpLq
e
shee
tot
4 4
4
( ) 0 (0) (0) 0 (2 ) ( )
Im 0 ( ), (0) 0
XX
iq y
W q J J q p
i d ye T J y J
X X
Collinear factorization
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DGLAP Evolution
z
zDzP
z
zDzP
z
dzdzD h
hqqgqh
hqqgq
z
Shhq
h
)1()(2
)(1
2
22
)1(2
3
)1(
1)(
2
zz
zCzP Fqgq Splitting function
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DIS off Nuclei
e-
, )) (( ,( )qh
q h hHdW
d f x p q Dxd
zz
x
pypedy
xf yixpBq )()0(
2
1
2)(
/( ) 0 (0) , , ( ) 02 2 2
h hip y zhq h h q h h q
S
z dyD z e Tr p S p S y
Frag. Func.
22 )(2)(2
1),,( xpqxpqpTreqpxH q
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Multiple Parton Scattering
_2 1( )
41 1L Lix p y ix p y yS
T
e e
2
1 2 (1 )f
L T
q z z
x p
Formation time
h h
Erm
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Multiple Parton Scattering
1 2( )21 2( , , ) ( ) ( )ik y yD D
T TW d k e H p q k A A y A y A
Generalized factorization:
(LQS’94)
22 )0,,(
)0,,()0,,(),,(
TTD
k
TTD
kTD
TD
kkqpH
kkqpHkqpHkqpH
T
T
Collinear expansion:
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Collinear approximation
AFFAkqpHW TD
kD
T
)0,,(2
Double scattering
22 )0,,(
)0,,()0,,(),,(
TTD
k
TTD
kTD
TD
kkqpH
kkqpHkqpHkqpH
T
T
First term Eikonal
AzAdzigA
AAAzddzgAdzigA
)(exp)0(
2
1 2( )21 2( , , ) ( ) ( )ik y yD D
T TW d k e H p q k A A y A y A
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Modified Fragmentation
2 122
40
( , ) ( , )2
h
Q
S hq h h L q h
z
zd dzD z Q z x D
z z
2 ( , ) 21( , ) (virtual)
(1 ) ( )
Aqg L A S
L Aq c
T x x Czz x
z f x N
Modified splitting functions
Guo & XNW’00
_2 1(
1 2 1 2
2)
1
( , ) (0) ( ) ( ) ( )2 2
( ) ( )1 1
B
L Lix p y ix
ix p yA
y
g
y
q L
pe
dyT x x dy dy e A F y F y y A
y y ye
Two-parton correlation:
LPM
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Twist Expansion
)(~)(2
)0(2
~222 BqsypixsS xAfAyAe
dy
d
dB
AyyFyFAedydydy
d
d yypixypixsD TB )()()(2
)0(222
~ 21)(21
4221
)()(~ 3/44 TTsBqs xGxxfA
])(1)[(~ 3/12222
TTS
BqsDS xGxAcxAf
d
d
d
d
3/1
22 LPM
A
Q 2
3/2
1Q
Ac
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HERMES data
2 20.00065 GeVsC 0.5 GeV/fmdE
dx
in Au nuclei
E. Wang & XNWPRL 2000
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Energy Dependence
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Conclusions
• Never promise any great ideas!
• Leading hadrons suppressed in DIS eA, agrees well with multiple parton scattering
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Di-hadron fragmentation function
1 2 1 2 1 2 1 2( , ) 0 (0) , , ( ) 02q h h q h h h h q
S
D z z Tr p p S p p S y
h1 h2
jet
Majumder & XNW’04
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DGLAP for Dihadron Fragmentation
2
1
1
1
2
2
2 11 2
1 222
21
2
( , , )( ) ( )
ln( , , )q
qh h
q q hg
z z
h
D z z Q dyP
z zD Q
y yy g h h
Q y
h1h2
h1h2
h1
h2
1
1 2
2
22
121ˆ ( ) (( , )
1)
(,
)( )
1q
z
q
z
hg hqgz
Dz
D Qy
dyP y q g
yQ
y y
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Medium Modified Dihadron
D(z1,z2)/D(z1)Triggering h1
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Higher orders or hadron absorption?
f h
Erm
Hadron formation time:
fm for E=10 GeV 70 pionf
protons fm for E=10 V0 Ge1 f
h
h
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Conclusions
• Never promise any great ideas!
• Leading hadrons suppressed in DIS eA, agrees well with multiple parton scattering
• Higher twists might be important
• Hadron absorption likely at lower energies
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Angular distribution of radiative gluons
2
2 2
1 (1 ) 1
2g S
FT T
dN zC
dzdk z k
1gdN
d
max
(1 / )
2g
g
E
R
Radiation in vacuum
2
2 (1 )f
T
Ez z
k
2 2
2 2 2 2
2
1 (1 ) 1
( )1 fg A S
T c T
R
T
dN C zcmR
dzdk N ke
z k
Induced Bremsstrahlung:
Dihadron correlation in relative transverse momentum
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Jet Quenching in Heavy-ion Collisions
Azimuthal asymmetry
jet1
jet2
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Abnormal angular distribution
PHENIX STAR
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Parton Energy Loss
2 1 22
2
2 2 20 0
( ,(1 )
(
1 )
)
Q Aqg L
AA s
gq
TcT T T
Czz
Td dz
N
x x
f xk
0
320( )(
2ln)a
R
A s
EE C C d
2( , )~ 1 cos
( )( )
Aqg L
gAq f
g
ydy
T xy
x
f x
Quark energy loss = energy carried by radiated gluon
0
13.8 3.9 GeV/fmdE
dx
cold matter
0.5 GeV/fmdE
dx
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Conclusions
• Never promise any great ideas!
• Leading hadrons suppressed in DIS eA, agrees well with multiple parton scattering
• Higher twists might be important
• Hadron absorption likely at lower energies
• Initial gluon density in Au+Au is about 30 times higher than cold nuclei
• Multiple hadron correlations critical measurements
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Flavor of Jet Quenching
Parton recombination
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A Perfect Fluid ?
0T
Hydrodynamicmodel with
zero viscosity
1
4
String theoryAdS5/CFTPolicastro,Son,Starinets
Weakly coloredBound states
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Bulk Elliptic Flow
)2cos2cos1( 210
vvNd
dNch
Hydro-dynamics calc.
2cos2 v
Pressure gradient anisotropy
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High density at RHIC
5.5 1.6E GeV for E=10 GeV
0
13.8 3.9 GeV/fmdE
dx
cold matter
0.5 GeV/fmdE
dx
0 0.2 fm/c
From RHIC high pT data: single & di-hadron, v2
Initial (energy) density 30 (100) times of that in a Cold Au Nucleus
Consistent with estimate of initial condition 20
1TdE
dy R t
also consistent with hydrodynamic analysis of radial flow from
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Parton Energy Loss
Same-side jet profile
Same-side jet cone remains the same as in pp collision
Hadron rescattering will change the correlation Between leading and sub-leading hadrons
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Geometry of Heavy Ion Collisions
x
z
y
EZDC
ET
Centrality of the collisions
Impact Parameter (b)
EZDC
ET
NNAB
ABAB
NR
binary
)(2 bbTdN ABbin
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No jet quenching in d+Au
Initial state effect: Shadowing & pt broadening: XNW, PRC61(00)064910
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20-60%
STAR preliminary
20-60%
Azimuthal Anisotropy II
Azimuthal Mapping of jet quenching
out-plane
In-plane
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High pT spectra in A+A collisions
0
0
0
1 0 0
( , , ) ( , , )L
d
dEE b r d b r n
dx
Modified fragmentation f( ) ( ) un cD z D z
2 2 2 2 21 2 1 22
( ) ( )ABA B a a b b
abcdT
dK d b d rd r t r t r dx d k dx d k
dyd p
/ 1 // 2( , , )1
( )( , , ) ab cda A a a b B b b h c c
c
df x k r f x k r
dD z
zt
pQCD Parton Model
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Single hadron suppression
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Comparison with Monte Carlo
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Energy Loss of A Heavy Quark
2
1
1/ (1 ) / 2Hf
f z M zq
02 2 2 2
1
(1 )
dN
d z M
Dead cone effect
B. Zhang & XNW’03
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Jet Quenching at RHIC
XNW’03
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Mono-jet production
0
13.8 3.9 GeV/fmdE
dx
cold matter
0.5 GeV/fmdE
dx 0 0.2 fm/c
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Suppression of away-side jet
20-60%
STAR preliminary
20-60%
Di-hadron invariant mass spectra