modification of fragmentation function in strong interacting medium
DESCRIPTION
Modification of Fragmentation Function in Strong Interacting Medium. Enke Wang (Institute of Particle Physics, Huazhong Normal University) Introduction Modification of Frag. Func. in Cold Nucleus Modification of Frag. Func. in QGP Medium Summary - PowerPoint PPT PresentationTRANSCRIPT
1
Enke Wang (Institute of Particle Physics, Huazhong Normal University)
I. Introduction
II. Modification of Frag. Func. in Cold Nucleus
III. Modification of Frag. Func. in QGP Medium
IV. Summary
Collaborators: X.-N. Wang, B.-W. Zhang
Modification of Fragmentation Function in Strong Interacting Medium
2
I. IntroductionRutherford experiment atom discovery of nucleus
SLAC DIS experiment e proton discovery of quarks
A-A collisions: Naturally provides jet and the QGP
Jet (hard probe) created by parton scattering before QGP is formed
– high transverse momentum
– calculable in pQCD
penetrating beam (jet) absorption or scattering pattern
QGP
Hard Probes of Quark Matter:
3
Jet quenching and Observation
hadrons
q
q
hadrons
Leading particle suppressed
leading particle suppressed
A-A collision
Jet Quenching:
EEE '
E
Modification of Fragmentation Function:
),( 20 QzD hhq
hh zzz ')1(
),(),(),(~ 2202 QzDQzDQzD hhhqhhq
hqABT
AA
Dtd
dPDFsT
dydp
d ~
ˆ2
Particle Production:
hp
S~
'pp
)'
',(
p
pz
p
pz h
hh
h
4
Light Quark Energy Loss
PHENIX,
Nucl. Phys. A757 (2005) 184
Theoretical results from the light quark energy loss is consistent with the experimental data
5
Heavy quark energy loss: Early Expectations
k
E
M
dP
k
dkkdCdP Fs
,
)/1()(
0
2220
022
022
22
B. Zhang, E. Wang, X.-N. Wang, PRL93 (2004) 072301 Y. Dokshitzer & D. Kharzeev PLB 519(2001)199
Heavy quark has less dE/dx due to suppression of small angle gluon radiation
“Dead Cone” effect
J. Adams et. al, PRL 91(2003)072304M. Djordjevic, et. al.
PRL 94(2005)112301
6
STARSTAR
No Significant Difference BetweenHeavy Quark Jet and Light Quark Jet
Non-photonic electrons from heavy quark decays
Charged hadrons fromLight quark fragmentation
7
Question: Heavy Quark Energy Loss?
Theoretical Calculation
How Reasonable?
)1
(1
1),(
~ 0
z
zD
zEzD ahah
Energy loss fraction
8
II. Modification of Frag. Func. in Cold Nucleus
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
e-A DIS:
9
Modified Fragmentation Function
Fragmentation function in vacuum
X.-N. Wang, X. Guo, NPA696 (2001); PRL85 (2000) 3591
),(),(),(~ 2202 QzDQzDQzD hhqhhqh
pQCDhq
Modification term
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Modified Frag. Function in Cold Nuclear Medium
2 122
40
( , ) ( , )2
h
QS h
q 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
_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
11
Rescaling of Modified Fragmentation Function
),1
(1
1),(
~ 202 Qz
zD
zQzD
effhq
eff
rescalinghq
zzeff 6.0
zSolid curve:
Dashed curve:
),(
),(~
20
2
QzD
QzD
hq
pQCDhq
),(
),(~
20
2
QzD
QzD
hq
rescalinghq
12
Comparison with HERMES Data
22 0060.0)(~
GeVQC 33.0)( 2 Qs 22 3GeVQ , ,
E. Wang, X.-N. Wang, Phys. Rev. Lett. 89 (2002) 162301
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Heavy Quark Energy Loss in Cold Nucleus B. Zhang, E. Wang, X.-N. Wang, PRL93 (2004) 072301; NPA757 (2005) 493
Mass effects:
1) Formation time of gluon radiation become shorter
222 )1(
)1(2
Mzl
qzz
T
f
LPM effect is significantly reduced for heavy quark
2) Induced gluon spectra from heavy quark is suppressed by
“dead cone” effect
4
2
2
04
222
2
/]1[][
Mzl
lf
T
T
zq
l
q
M
T
0
Dead cone Suppresses gluon radiation amplitude at 0
14
Heavy Quark Energy Loss in Nuclear Medium
The dependence of the ratio between charm quark and light quark energy loss in a large nucleus
2Q
The dependence of the ratio between charm quark and light quark energy loss in a large nucleus
Bx
15
III. Modification of Frag. Func. in QGP Medium
Cold Nucleus Medium QGP Medium
A| Akykfk
kd||),(
2)2( 23
3
k k
16
Same Framework for Light and Heavy Quark
),(),(),(~ 2202 QzDQzDQzD hhh
pQCD
Light quark:
0M),(),( 2020 QzDQzD hhqh
Heavy quark:
0M)()( 0
,0
hhQnph zDzD
Peterson form
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Generalized Jet Transport Parameter
Unintegrated gluon distribution function:
Average tranverse momentum broading:
averaged transverse momentum transfer squared per unit distanceRq̂
),,(),0,(ˆ nrbyEq gR
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Jet Energy Loss
),0,(ˆ])1([
)1(64222
422 yEq
Mzl
lzdzdldy
E
ER
T
TT
s
])1(4
))1(([sin),,(
22222
1 zEz
MzlyMlza T
T
LPM effect
19
Modified Frag. Function in QGP Medium
Modified splitting functions
])([)2(2
),( 01
0 2
2
2
22
2
z
zD
l
dl
z
dzqdQzD h
qgqz
Q
T
TTsh
h
)(])1([
2
)(
),,,(
)1(
14222
622
virtualMzlN
lC
xf
qMxxT
z
z
Tc
TAsA
q
TLA
qgqgq
Parameters:
fm
MeVT
fmGeVq
1.0
600
/0.1ˆ
0
0
20
20
Modification of Frag. Func. for light quark in QGP
z
)(
)(~
0 zD
zD
Solid Curve:
can be
approached by
)(~
zD pQCDhq
)1
(1
1
)(~
0
effhq
eff
rescalinghq
z
zD
z
zD
Dashed curve:),(
),(~
20
2
QzD
QzD
hq
pQCDhq
),(
),(~
20
2
QzD
QzD
hq
rescalinghq
zzeff 65.0
21
Modified Frag. Func. for heavy quark in QGP
c quark:
can be approached by)(~
zD pQCDHQ
)1
(1
1)(
~ 0
effHQ
eff
rescalingHQ z
zD
zzD
zzeff 9.0
vacuum
medium
rescaling
medium/vacuum
rescaling/vacuum
E=10GeV E=50GeV
vacuum
medium
rescaling
medium/vacuum
rescaling/vacuum
z z
22
b quark:
can be approached by)(~
zD pQCDHQ
)1
(1
1)(
~ 0
effHQ
eff
rescalingHQ z
zD
zzD
zzeff 9.0
vacuum
medium
rescaling
medium/vacuum
rescaling/vacuum
E=10GeV
vacuum
medium
rescaling
medium/vacuum
rescaling/vacuum
E=50GeV
zz
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Ratio of energy loss between heavy and light quark in QGP
q
Q
z
z
Solid Curve:
Dashed curve:
qeff
Qeff
z
z
qpQCD
QpQCD
z
z
E1) In the intermediate jet energy region the ratio increase
rapidly with increasing energy.
2) In the very high jet energy region the effective energy loss of heavy quark is larger than one of light quark
c
b
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IV. Summary
1) The modified fragmentation function in strong interacting medium (cold nucleus and QGP) has been calculated in pQCD.
2) The modified fragmentation function in QGP medium can be approached by rescaling fragmentation function with effective energy loss fraction . For light quark , for heavy quark .
3)The different effective energy fraction shift of the fragmentation function for light and heavy quark will help us to understand the different behavior of the light and heavy quark jet.
effz zzeff 65.0zzeff 9.0