enke wang (institute of particle physics, huazhong normal university) i.jet quenching...
TRANSCRIPT
Enke Wang (Institute of Particle Physics, Huazhong Normal University)
I. Jet Quenching
II. Modification of Hadron Fragmentation Function
III. Jet Tomography of Strong Interaction Matter
IV. An explanation of heavy quark energy loss puzzle
V. Summary and Discussion
Jet Quenching and Its effects in Strong Interaction Matter
I. Jet QuenchingRutherford 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:
27 YEARS AGO
Brief History of Theoretical Research about Jet Quenching
1982: J. D. Bjoken: Fermilab-pub-82/59-THY Energy loss in elastic scattering
1992/1995: X.-N. Wang, M. Gyulassy: PRL68(92) 148, PRD45 (92)844, NPB420(94)583, PRD51(95)3436 Energy loss is dominated by gluon radiation
1995/1997: BDMPS (R. Baier, Yu. L. Dokshitzer, A. Mueller, S. Peigue, D.Schiff) :PLB345(95) 277, NPB478(96)577,NPB483(97)291,NPB484(97)265 Gluon multiple scattering and gluon radiation
2000: GLV(M. Gyulassy, P. Levai, I. Vitev): PRL85(00)5535, NPB594(01)371
U. Wiedemann: NPB588(2000)303 Opacity expansion
2001/2002: E. Wang, X.-N. Wang: PRL87(01)142301, PRL89(02)162301 Detailed Balance; Jet Tomography
Basic Idea for Jet Quenching
hadrons
q
q
hadrons
leadingparticle
leading particle
hadrons
q
q
hadrons
Leading particle suppressed
leading particle suppressed
p-p collision A-A collision
At RHIC: • Hard/Semihard processes is important• High- Pt parton (jet)• Jet quenching• Jet production dominates particle yields
at high Pt
Suppression of high Pt hadron spectra
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
Jet Quenching in QCD-based Model
G-W (M. Gyulassy, X. –N. Wang) Model:
Static Color-Screened Yukawa Potential
First Order in opacity Correction
First Order in opacity Correction
Medium-induced radiation intensity distribution:
Induced radiative energy loss:
Induced gluon number distribution:
)cos(1)2)(( 111122
22
)1(
zBCqvqdLC
kdxd
dNx
g
sR
Non-Abelian LPM Effect
2)1( LE LE )1(
QCD:
QED:
Higher order in Opacity
Reaction Operator Approach: (GLV)
Induced gluon number distribution:Non-Abelian LPM Effect
Radiated Energy Loss vs. Opacity
First order in opacity correction is dominant!
Jet Quenching with Detailed Balance
x0 p
Gluon radiation: E loss radEGluon absorption E absorption absE
Net energy loss of jet:
absrad EEE －)1(
Detailed Balance
Temperature and Density QGP SystemE. Wang, X.-N. Wang, Phys. Rev. Lett. 87 (2001) 142301
Final-state Radiation
k
x0 p
k
x0 p
Energy loss induced by thermal medium:
0
)0()0(
)0(
T
abs d
dp
d
dpdE
22
2 )2('62
4ln
3
E
FsET
E
TC=
Net contribution: Energy gain
Stimulated emission increase E loss Thermal absorption decrease E loss
Energy Loss in First Order of Opacity
Energy loss induced by rescattering in thermal medium: )1()1()1(
absradEEE
Take limit:
1EL E LT 2
Zero Temperature Part:
0
)0(
)1(
T
rad d
dpdE
048.0
2ln
4 2
2
L
EC
g
Fs
L2
GLV ResultTemperature-dependent Part:
0
)1()1(
)1(
T
abs d
dp
d
dpdE
2
22 )2('61ln
3
E
g
Fs
T
L
E
LTC
Energy gain
Numerical Result for Energy Loss
3.0S
)1()1()0(
radabsabsEEEE
• Intemediate large E, absorption is important
•Energy dependence becomes strong
•Very high energy E, net energy gain can be neglected
Parameterization of Jet Quenching with Detailed Balance Effect
)/5.7/()6.1/( 02.1
001
EEdL
dE
d
Average parton energy loss in medium at formation time:
Energy loss parameter proportional to the initial gluon density 2
00
1
ARd
dN
Modified Fragmentation Function (FF)
),(
)],(/),()[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
Light Quark Energy Loss
PHENIX,
Nucl. Phys. A757 (2005) 184
Theoretical results from the light quark energy loss is consistent with the experimental data
II. Modification of Hadron Fragmentation Function
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
Modified Fragmentation Function
2 2 2( , ) ( , ) ( , )h h hD z Q D z Q D z Q
Cold nuclear matter or hot QGP medium lead to the modification of fragmentation function
Twist-four calculationX.-N. Wang, X. Guo, NPA696 (2001); PRL85 (2000) 3591
e-
Modified Frag. Function in Cold Nuclear Matter
2 2 2( , ) ( , ) ( , )h h hD z Q D z Q D z Q 2 12
24
0
( , ) ( , )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
_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
Modified Frag. Function in Cold Nuclear Matter
hadrons
ph
parton
E
),,()(0 EzDzD ahah
)(0 zDah
are measured, and its QCD evolutiontested in e+e-, ep and pp collisions
Suppression of leading particles
Fragmentation function without medium effect:
Fragmentation function with medium effect:
),1
(1
1),( 0
z
zD
zEzD ahah
Heavy Quark Energy Loss in Nuclear MediumB. Zhang, E. Wang, X.-N. Wang, PRL93 (2004) 072301; NPA757 (2005) 493
Mass effects:
1) Formation time of gluon radiation time 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
Heavy Quark Energy Loss in Nuclear Medium
)]},,(),,()[1(),,(2
1{
~)~~(~
)1(
1~
),(
22
2
22
1
/~22
3
4
2~
~
1
0
2
2
2
2
22
MlzcMlzceMlzc
x
xxxd
zz
zdz
xQN
xCCQxz
TT
xx
T
L
ML
x
xL
Ac
BsA
B
Q
g
AL
M
LPM Effect
,~~
2
2
Qx
Mx
x
x
A
B
A
L
AN
A Rmx
1
1) Larg or small :
Bx
2Q
A
A
B
c
SAQ
gR
Qx
x
N
CCz
2
2~~
2) Larg or small :2Q
2
22
2~~
A
A
B
c
SAQ
gR
Qx
x
N
CCz
Bx
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
III. Jet Tomography of Strong Interaction Matter
E. Wang, X.-N. Wang, Phys. Rev. Lett. 89 (2002) 162301
2 21 1 22 2
22 2 2 2
0 0 0 0
1 (1 )( ,
()
, )
( )2
Q Qs A sT
g L T
Aqg
T cT T T
L
Aq
Cd zz dz z z x d dz
Nk
T x x
f x
Jet Tomography in Cold Nuclear Matter:Quark energy loss = energy carried by radiated gluon
2 2 13ln
2A
s N Ac B
CE C m R
N x
Energy loss
3/2AE
Comparison with HERMES Data
HERMES Data: Eur. Phys. J. C20 (2001) 479
22 0060.0)(~
GeVQC 33.0)( 2 Qs22 3GeVQ , ,
Expanding Hot Quark Gluon Medium
_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
2( , )~ ( ) 1 cos
( )
Aqg L
gAq f
T x x ydy y
f x
0
32
( )2
lnR
s dE
E
R. Baier et al
Initial Parton Density and Energy Loss
jet1
jet2
0
32
2( ) ln
R
s
EE d
00( ) ( )R r
01 0
2d
A
E ER
Initial energy loss in a static medium with density 0
:0E
0 0.1 fm 015
2AR
1
0.5 GeV/fmd
dE
dx
6.140
dx
dEGeV/fm
Initial parton density (Energy loss ) is 15~30 times that in cold Au nuclei !
Comparison with STAR data
STAR, Phys. Rev. Lett. 91 (2003) 172302
Tomography of Jet quenching in QGP Medium in NLO
1) Single jet Single hadron spectra
2) Dijet Hadron-triggered away-side hadron spectra
3) Gamma-jet Photon-triggered away-side hadron spectra
Single jet Dijet Gamma-jet
fmy 0
y
x
Single hadron
parton jet
emission surface
completely suppressed
Surface Emission of Single Hadron Production
fmGeV /68.10
coronathickness
H. Zhang, J. F. Owens, E. Wang and X.-N. Wang , Phys. Rev. Lett. 98 (2007) 212301
partonic di-jet
tangential
fmx 0
y
x
triggered hadron
associated hadron
Color strength = dihadron yield from partons in the square
fmGeV /68.10
punch-through jets25% left
Surface Emission + Punch-through jet in Dihadron Production
punch-jets
Surface emission bias
fmGeVFixed /0.50
dihadron
single hadron
At LHC
Prediction at LHC
Gamma-jet by NLO pQCD parton model
LO (tree level): NLO corrections: (e.g. 23)
FFsdPDFsTd ABAA
T
JetT pp
Tp
TJetT
TJetT
pp
pp
,
1JetTp
2JetTp
),( 21 JetT
JetT
JetT ppofOnep
hadrons with transverse momentum may be larger than that of the photon
T
JetT pp
Tp
JetTp
Fix triger: Tp
T
hT
T p
pz
Gamma-Hadron Suppressions Factor
1) NLO radiative corrections lead to hadrons with z_T>1, surface emission,
2) z_T<0.6, volume emission, more sensitive to \eps_0
3) 0.6<z_T<1.4, competition of two mechanisms of hadron emssions.
4) Similarity in value between I_AA for dihadron and Gam-hadron.
)(/)()( TppTAATAA zDzDzI
H.Z. Zhang, J.F. Owens, E. Wang and X.-N. Wang , PRL 103 (2009) 032302
Tomography of surface and volume emissions
1) The spatial transverse distribution of the initial Gama-jet production vertexes that contribute to the Gama-hadron pairs with given values of z_T.
2) The color strength : Gama-hadron yield
3) Projections of the contour plots onto y-axes .
9.0Tz
3.0Tz
At large z_T, jet emissions in the outer corona, no energy loss.At small z_T, jets emisions near the center of the medium, energy loss.
QGP system is not static, it is a expanding system
Reactionplane
Y
XFlow
Flo
w
QED:
Static Charge: Coulomb electric field
Moving Charge: electric and magnetic field
QCD:
Static Target: static color-electric field
Moving Target: color-electric and color-magnetic field
IV. An explanation of heavy quark energy loss puzzle
Puzzle for Heavy Quark Energy Loss
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
STARSTAR
No Significant Difference BetweenHeavy Quark Jet and Light Quark Jet
Non-photonic electrons from heavy quark decays
Charged hadrons fromLight quark fragmentation
Interaction Potential with Flow
system fixed at target parton:
Static potential
'
system for observer:
Lorentz boost from system
'
vqvqvv
qvqq
nnnn
nnn
02
00
)(1
'
)('
vVvAvv
AA
AvVV
nnnn
nnn
')'(1
'
)''(
2
21
1
v
)()()'()'(2' 0 nTRTqvqVnn aannn
0' nA
22'
4)'(
n
sn q
qv
New Model Potential with Flow
)()()(~)(2),(
)()()(~)(2),(
0
0
nTRTveqvqvqxqA
nTRTeqvqvqxqV
nn
nn
nn
nn
aaxqi
nnnnnn
aaxqi
nnnnnn
222 )(
4)(~
nn
sn qvq
qv
The features of the new potential:
1) Collective flow produces a color-magnetic field
2) non-zero energy transfor:
Four-vector potential : )),(),,(( nnnnnnflow xqAxqVA
vxqA nnn
),(
nn qvq0
Dead Cone Reduce Significantly with Flow
Dead Cone:
Reason: Collective flow changes the poles of the propagator
Energy Loss vs. Flow Velocity
Average Flow Velocity and Effective Average Energy Loss
3D ideal Hydrodynamic simulation for 0-10% central events of Au-Au collisions at RHIC energy:
Average Flow Velocity:
Effective Average Energy Loss:
Numerical Results of Effective Average Energy Loss
3D ideal Hydrodynamic simulation for 0-10% central events of Au-Au collisions at RHIC energy
V. Summary and Discussion
1) Jet can be used as a hard probe to explore the QGP.
2) Jet quenching lead to modification of hadron fragmentation function, which result in the suppression of high transverse momentum spectra observed in experiment.
3) Different tomography picture of the QGP for single jet, dijet and gamma-jet: surface vs. volume emission.
4) New potential for the interaction of a hard jet with the parton target has been derived. Collective flow reduce significantly the dead cone from mass effect for heavy quark jet. Heavy quark energy loss increase obviously in the presence of collective flow. An explanation of heavy quark loss puzzle is given in the framework of jet quenching theory.
Discussion
1) Dihadron azimuthal correlations in head-on collisions in AMPT :
Talk this afternoon by Qingjun Liu
2) Multiple parton scattering and modified fragmentation function in medium : Talk this afternoon by Weitian Deng
3) Gamma-jet tomography of high-energy nuclear collisions in NLO pQCD :
Talk this afternoon by Hangzhong Zhang
Thank YouThank You
